Unit Author: Professor Nick J Fox
Having successfully completed this chapter, you will be able to:
- differentiate between variables, values and cases;
- identify the correct measurement scale of your data;
- code your data for entry into a database;
- select an appropriate statistic to analyse your data.
Social scientists frequently report results in a form that quantifies their findings. Quantitative data analysis provides ways of representing study findings numerically, ranging from simple counts of events through to complex statistical interpretations of results. This unit looks at how to prepare data for analysis, and how to report it.
This course does not cover statistical analysis, but the principles of quantitative data analysis are central to the research process, and all those embarking on research should be familiar with these principles. Statistics and statistical computing are useful only within the context of the sound methodological approach to data analysis that this chapter will provide.
1. Why use quantitative data analysis methods?
Quantitative data analysis is about the use of numerical symbols (including graphical representations of numbers). The reasons chosen for reporting data in ways that provide such numerical summaries are worth thinking about briefly.
Firstly, there is always a trade-off in quantitative analysis between detail of data and its manageability. Numbers provide a means of reducing data (the range of ages of subjects in a study is simply reported as a mean value and a range), or of comparing things that are dissimilar from each other (rates of marriage against rates of co-habitation), or reporting proportions (percentages of vegetarians and meat-eaters in a population). We have lost some detail by this reduction, but what we have gained is a way of summarising the data that is easily comprehended or absorbed. These simple counts are examples of descriptive analysis, and provide a summary of study findings without any attempt to interpret or analyse.
Secondly, numbers can be submitted to logical operations (addition, multiplication, squares etc.), so they can be manipulated to draw conclusions. At the simplest level, one figure can be said to be larger than another. More complicated manipulations in the form of statistical analysis can be used analytically to discern trends or to test hypotheses. Such quantitative data analyses make claims about a study’s findings and seek to draw conclusions about their relevance to the natural or social world. Thus an analysis of food consumption might conclude that eating 5-a-day of fruit and vegetables is associated with educational background.
So the objective of any quantitative data analysis is to turn observations into some kind of numbers, which can then be summarised and perhaps analysed statistically. And a study which wishes to use such kinds of analysis must have a clear idea – before any data is actually collected – precisely how such numerical summaries or statistical tests are to be undertaken. As far as quantitative analysis goes, data that cannot be turned into meaningful numbers (and so cannot be analysed) is worthless. Of course, some data cannot be quantified, or quantification would result in the loss of crucial elements of what is to be studied. In such cases, a qualitative approach may be appropriate.
We will now consider the basics of how we turn our findings into numbers that can be analysed quantitatively.
2. Turning data into numbers: cases, variables and values
Before considering how to start quantitative analysis, three definitions are useful: cases, variables and values. The easiest way to understand these three aspects of data is by looking at a typical data array (or ‘dataset’), as would be produced by a statistics programme such as SPSS (Statistical Package for the Social Sciences). Look at Table 7.1, which shows data from a study of meat consumption among adults.
Table 7.1: Raw data on meat consumption
In Table 7.1, the cases are numbered 1–10, down the left-hand column of the array.
In this dataset, the cases are the subjects whose data has been collected and that we wish to analyse, and in this study the first ten cases are shown (more would be visible if we looked further down the array). In this example, the cases are individuals, but they could be anything that is our unit of analysis (for instance, a person, a family or even an entire town or city).
In Table 7.1, we can see that there are five data columns, with codes at the top: these are the variables: the characteristics of the subjects that we wish to measure. Another name for the variables would be indicators: any measurement (for example, a question on a questionnaire) will need to have a variable (and label) in the array.
Each variable has a code at its top and we need to know what this code means. Some of these variables have been given labels, for example:
meat = grams of meat eaten per week
gend = gender of subject (1 = male; 2 = female)
age = age of subject in years
educ = years of education post 16
smoke = cigarette smoking (1 = yes; 2 = no)
The values in the table refer to the actual measurements we have made for each case on the five variables. In Table 7.1, these are the figures in the boxes. Each box represents the value of a measurement of one variable for one case.
In this dataset, the value of an individual measurement of the meat eaten per week for subject #5 can be read off by looking down the meat column to row 5. In this case the value is 453.
Note that values are numbers, but refer to specific units of measurement. Thus meat eaten will be measured in grams per week, while education post-16 will be in years. The data array does not show the units in which the measurements are made, but these are essential if the data is to have any meaning.
Also note that this array is a simple form of descriptive report. It would be very unlikely that a large array would be reported in a paper, as it would be totally useless as a manageable summary. However we can see the first step in data reduction in this representation of findings as an array of numbers, which can be subjected to manipulation.
SAQ 7.1 Tables
Are the following underlined terms cases, variables or values?
3. Coding data for analysis
An array (or database) based on cross-referencing cases and variables in terms of values, such as that shown in Table 7.1, is a pre-requisite for quantitative analysis, and all the techniques covered in this chapter require such an array.
But we have glossed over one essential step before this array or database was constructed. Before it can be summarised, all data must be coded so that it can be represented numerically. This may seem obvious, but it is worth reflecting upon in some detail.
The simplest coding of data is based upon readings from an instrument: for example a thermometer. Readings may be taken from the instrument, and entered directly because they are pre-coded numerically, for instance from zero to 100 degrees Celsius. Few social research variables provide such an opportunity, though in the study reported in Table 7.1, the amount of meat eaten will have been weighed on a scale prior to consumption. Age is also a measure with a numeric value already attached to it.
In Table 7.1, gender has been coded according to an arbitrary basis so that male = 1 and female = 2. In each case, the transformation of the observation into a numerical value is an example of coding.
Other data must be submitted to a more complex coding procedure to turn observation into numerical value. Look at the following questionnaire (Figure 7.1), which might be used to investigate meat eating.
Figure 7.1: Meat consumption questionnaire
|1. How old are you?|
|2. Are you male or female?|
|3. What is your occupation?|
|4. What is your annual income?|
|5000 to 20,000|
|20,001 to 40,000|
|5. Which of the following describes your highest educational achievement?|
|No qualification post-16|
|PhD or higher|
|6. Are you a smoker?|
|7. Mark below your enjoyment of eating meat.|
|Equal to other food|
These questions need to be coded so that values can be entered into the data array. The following fig 7.2 shows the same questionnaire with a coding frame. The relevant code can be circled by the interviewer.
Figure 7.2: Meat consumption questionnaire with coding frame
Question 1 remains open-ended, with the proviso that we can convert into bands later if we wish.
Questions 2, 4 and 6 have been allocated numerical codes.
Question 3 is currently open-ended but once the data has been collected it will need to be coded using the SES scale, to transform it into socio-economic groupings.
Question 5 has been coded to calculate from the answer the numbers of years of education undertaken post-16.
Question 7 could be coded in a number of ways. You could visually assess the position of the respondent’s mark on the line but this could be difficult and would be subjective. It would be preferable to measure the line accurately.
3.1 Recoding data
Sometimes having coded data initially, we may wish to re-code it later on in data analysis. For instance, in our questionnaire Question 1 asks people to state their age and provides a box to write their actual age in. It is useful to have data at this level of detail, because the type of statistical analysis that can be undertaken is more sophisticated. On the other hand, it can be more difficult to analyse the data when it is at this level of detail. So, in this case, we might wish to set up a new variable (called something like ‘ageband’), that re-codes the age variable data into age bands, according to the following.
|under 20 years||1|
|20- 29 years||2|
|30 – 49 years||3|
|50 – 59 years||4|
Software such as SPSS can automatically do this kind of re-coding very easily. Note that such banding makes data less detailed, but may make it easier to manipulate. However, we need to retain information about what the new codes mean: clearly, in the coding of age bands, a code of 2 does not have an obvious meaning unless one is aware of what the original data were!
4. Nominal, ordinal and interval scales of measurement
Although it is possible to code all data so that it can be represented numerically, the meanings of these numbers differ. There are three different kinds of numerical data that we encounter in quantitative research, each of which permits differing kinds of analysis. We can see this if we refer back to the example of the meat consumption questionnaire used earlier.
4.1 Nominal data
Nominal data is composed of a set of unordered categories. The allocation of numbers to a nominal scale is on an arbitrary basis, since the nominal codes have no numerical meaning. One example is the coding of the sex of respondents in a study (Male = 1, Female = 2). Another example might be the occupation of respondents in the study above, in which a coding frame is constructed so that various occupations are coded 1, 2, 3 and so on.
In all these examples, the numbers simply provide symbols for the categories. In no sense can a doctor (professional: code = 1) be considered half of a bank manager (manager: code = 2), nor could a female be assumed to be twice a male (at least, not in the sense used in this categorisation exercise!). Nominal data cannot be added or subtracted or submitted to other logical operations. You may also see nominal data referred to as categorical data.
Usually, nominal categories are used to provide descriptive data. So, for example, we could identify the ratio or the proportion of women in a sample. (We will look at such frequency charts in the section on descriptive analysis.)
Another type of descriptive statistic that can be used to describe nominal data is the mode. This is a measure of the most populous category in a sample. N.B. a mean cannot be used with nominal data: a mean gender of 1.5 for a sample is meaningless.
4.2 Ordinal data
Sometimes the categories that one chooses for data are not simply arbitrary, but reflect some kind of order. Such data lies on an ordinal scale, but while the different categories have some form of order, they are not arithmetically related.
Look at question 5 on the questionnaire. Here there are five categories of educational achievement, and the fifth category (PhD or higher) is ‘greater’ in terms of achievement than the fourth category (Master’s degree), which in turn is ‘greater’ than the third, and so on. We can accept that there is an ‘order’ to these achievements.
However, ordinal data cannot be assumed to be additive, because the distances between items on an ordinal scale are not necessarily equivalent. This is actually made quite clear by the way we coded these achievements, which was in terms of the years of education needed post-16 to achieve them. The distances between the points on this ordinal scale are not equal.
This has implications for data analysis. We can do more with ordinal data than the frequency or proportion comparisons available with nominal data, but we cannot use the statistics that depend on additivity. Ordinal data can be described using ratios and percentages. As well as using a mode, it is also possible to calculate a median statistic for ordinal data. A median is the mid-point or middle value when all the observations are placed in order. It splits the observations into two equal-sized groups.
Most statistical tests for ordinal data avoid this problem of additivity in a clever way. What they do is rank the frequency of occurrence of different categories. In Table 7.2, the frequencies of different educational achievements for two samples have been ranked. The ranking can then be treated as an interval scale, and compared statistically, although in this case you could probably make some comment about the differences between these two samples simply by looking at the ranks.
Table 7.2 Ranking of ordinal data for two samples
|Urban Sample||Rural Sample|
|No qualification post-16||2||1||12||4|
|PhD or higher||3||2||0||1|
(Ranking: 1 is the lowest frequency and 5 is the highest frequency)
4.3 Interval and ratio data
Unlike the ordinal scale, an interval scale is one which shows the quality of additivity. This means that wherever one is along the scale then the gaps between the measurements are the same. In the questionnaire above, the first question provides interval data, because the distance between cases with age 10 and age 12 is the same as that between 13 and 15.
Sometimes one sees reference to ratio data. A ratio scale is simply an interval scale has a true zero point. Not all interval data have an absolute zero. For instance, Celsius temperature is an interval scale, but 0°C is not an absolute zero, but arbitrary (the freezing point of water). Ratio data, on the other hand, do have a true zero. For instance, height, age and income level all have a true zero.
4.4 Parametric and non-parametric statistics
Interval and ratio data can be manipulated by a wider range of statistics because they can be directly submitted to logical operations such as addition and squaring. At the simplest level, we can calculate averages using the mean. A mean is a measure of central tendency, and can be calculated by adding all the individual values and dividing this figure by the total number of individual cases.
Such tests are known as parametric (meaning ‘equal measures’). Parametric statistics are based on the assumptions of both additivity, and that the data follows a normal distribution (the distribution of data forms a bell-shaped curve with most points grouped towards the middle). Examples of parametric statistics are T-tests and analysis of variance (ANOVA).
Non-parametric statistics, unlike parametric statistics do not make any assumptions about additivity or the underlying distribution of data. Non-parametric statistics are therefore suitable for skewed interval data, and for ordinal and nominal levels of measurement.
Ordinal data can only be described in terms of a median (the value of the middle case) or a mode (the most frequent result). However, as was noted in 4.2, ordinal data can be manipulated to enable powerful statistical analyses to be undertaken.
Nominal data can only be described in terms of a mode (the most frequent result), and possible statistical analysis is quite limited. However, if an independent variable (cause) is nominal and the dependent variable (effect) is interval, a parametric test can still be used (see section 6.3 below).
SAQ 7.2 Kinds of data
You read an article in a journal which explores the effect of socio-economic status (a measure of social class based on occupational categories) upon amount of meat eaten per week. The investigator used the following coding frame for SES:Professional = 4Managerial = 3Skilled manual = 2Unskilled = 1The investigator took two samples of 100 subjects from different neighbourhoods, devised average SES scores for the two neighbourhoods, and recorded these results:
[table id=40 /]
The investigator concluded: ‘The higher the social class, the lower the meat eaten per week’. What do you think?
5. Rates and percentages
Rates and percentages are simple ways to compare data.
Percentages are a way of standardising data that is familiar to most people, enabling samples of different sizes to be compared. Percentages should not normally be used when there are fewer than 100 cases in total, as they may appear to inflate the number of cases studied. In such circumstances, use a proportion (for example 0.3 or 0.5, in place of 33% or 50%).
Another way of standardising data is through the use of a rate, which is like a percentage, although the denominator may be 1000, 10,000 or even 100,000.
Consider for example, a social survey on poverty. I would like to compare the levels of poverty in three areas of a city. As a proxy measure, I collect data on the number of people attending a food bank (a facility providing free food to people on low incomes) in each area. The survey shows that the number of registered food banks in area A was 80; in area B it was 42 and in area C, 240. These figures seem to tell a story, but to compare them we need to use a rate to express the number of users as a proportion of the number of people in each area. This rate is a more accurate indicator of the amount of poverty. This is illustrated in Table 7.3. Clearly, the rate was substantially higher in area C than in the other two areas.
Table 7.3 Food bank use rates
|Area||No. of food bank users||Area population||Rate/1000 population|
6. Statistical analysis
One of the advantages of quantitative data is that it enables the use of statistics, and a range of different statistical tests have been devised to allow you to analyse data and make judgements about its contribution to knowledge. The two main kinds of statistics are descriptive and inferential.
6.1 Descriptive statistics
Descriptive statistics provide a means to summarise data in terms of numbers. The simplest descriptive statistic is an average. Earlier we looked at an array of data in which values for each case are entered for a number of variables. From such an array or database it is possible to calculate simple descriptive statistics. For example, an average can be calculated (mean, median or mode, dependent upon type of data). As already noted:
A mean is a calculation of the arithmetic average of a set of data. It can be used for interval or ratio data.
A median is the middle value when the data values are put in ascending or descending order. It can be used for ordinal data.
A mode is the most frequent value in a set of data. It can be used for ordinal or nominal data. N.B. in multimodal data, there can be more than one mode, suggesting that the data are made up of more than one kind of case.
For interval data, a standard deviation ( a measure of the range of values) may also be calculated, as can other measures of distribution such as skew (data shifted to one side or other of a distribution) and kurtosis (how long the ‘tails’ of a distribution curve are).
Table 7.4 shows a typical frequency table and descriptive statistics for one of variables in the data set we looked at earlier: post-16 education. Note that the data is ordinal, and a mean is not calculated.
Table 7.4 Descriptive statistics for post-16 education
|5||PhD or higher||5||3.8|
Median = 2 Mode = 2
Such tables can be presented in a research report, summarising the values for each variable.
6.2 Inferential statistics
Inferential statistics allow us to draw conclusions about the meaning of data, and to test hypotheses (for instance, what effect an independent variable such as social class has upon a dependent variable such as attitudes to politics). They are associated with ideas of statistical significance which is a measure of how likely or unlikely it is that a finding occurred by chance.
This course cannot go into detail in terms of using statistical tests, which is a subject in its own right. However, we will quickly describe the different kinds of inferential statistics that are available, and then provide a guide to which kind of test can be used with different kinds of data.
(If you do not have expertise in statistics, it is good practice to consult a statistician when setting out to analyse your data, or even earlier, when you are designing the study, to make sure it will be possible to interpret the data you collect!)
There are four kinds of inferential statistics.
6.2.1 Contingency table
A contingency table gets its name from the extent to which variations in one variable is contingent upon another, for example a cause (independent variable) such as gender and an effect (dependent variable) such as voting intention (see table 7.5).
Table 7.5 Contingency table for gender and voting intention
|Left-wing||33 (66%)||25 (50%)|
|Right-wing||17 (34%)||25 (50%)|
|Totals||50 (100%)||50 (100%)|
Such associations between interval or ordinal data can be assessed by correlations, which are discussed in a moment. But all data, suitably transformed, can be evaluated by means of a contingency table, using one of a number of statistics, the best known of which is chi-squared. This is of use if both independent and dependent variables are nomimal. In the example just mentioned, data can be entered into a contingency table and chi-squared or another similar test used to see whether there is a significance (non-random) association.
Like contingency tables, correlations are concerned with the strength of associations between variables. Correlations are used when both variables are at least ordinal, and usually comprised of interval data.
An association between two interval variables can be represented visually in the form of a scattergram (see figure 7.3). In this example, we look at an imaginary data set that compares incomes (along the horizontal axis) and days spent on holiday per year (on the vertical axis)! There appears to be a strong positive association between these variables: as incomes rise, so do days spent on holiday. However it is not a perfect correlation: otherwise all the points would fall along a straight diagonal line.
Figure 7.3 Scattergram of income vs. annual holiday length
Statistical tests of correlation such as Pearson’s r assess whether this apparent association is significant statistically. They are relatively straightforward to interpret because they vary between fixed limits. A correlation of 1 is a perfect association (a straight diagonal line in the scattergram), down to 0 for no association whatsoever (random scatter) through to –1 for a perfect negative association (a diagonal line sloping from left down to right).
You can also do correlations if both variables are ordinal data, using a non–parametric test such as Spearman’s rho or Kendall’s tau.
6.2.3 Tests of differences in means or variances.
These are used to compare two or more groups of cases, subjects or samples, where the dependent variable is interval or ordinal, while the grouping variable (the independent variable) is categorical (nominal). For example, we can compare men and women (nominal) on the number of hours they spend a week on domestic tasks, childcare and so forth (interval).
This could be represented in a simple bar chart (see section 7). Tests of significance are used to assess if the differences between the means for the two groups are due to chance or due to the independent variable (gender).
The test used to assess two groups is the t-test, while for more than two groups use the F-test (also known as analysis of variance or ANOVA).
In the example of gender and hours of housework, these are independent samples. These tests can also be used for paired or matched samples. An example of this would be comparing the hours of childcare done by men who had full-time jobs with the hours they spent a month after they had lost their jobs due to redundancy. Here it is the same subjects in each of the two categories (working and non-working), so the data is paired.
There are also some tests that can be used if dependent variable data is ordinal, and these can be found in the guide to choosing tests in 6.3 below.
6.2.4 Multivariate analysis
It is possible to do more complex analyses to explore how a range of independent variables affect a dependent variable. The most common multivariate analyse is multiple regression. This is used when all independent variables are either interval data or dichotomous (two category) variables, and the dependent variable is interval data. For example, the dependent variable (outcome) could be days a year spent in paid work, and there could be a range of independent variables (causes) which we want to test to see which of them affects the outcome and to what extent. These might be variables such as gender, age, educational level, number of jobs held since 18, political attitudes, kind of diet, etc.
It is a sophisticated analytical tool (which must be done by computer) and will indicate the strengths of each independent variable in predicting the value of the dependent variable, and can rule out some variables as having little or no effect on an outcome.
There are other multivariate approaches such as logistic regression which are beyond the scope of this overview.
6.3 Choosing the right test
We have only scratched the surface of statistics here, and you should either take a specialist course or consult a statistician before deciding how to use statistics to analyse your data. The following table is a simple guide to the main statistical tests we have mentioned.
The top row of Figure 7.4 shows the type of data for the outcome (dependent) variable: nominal, ordinal or interval/ration. Each of the columns shows the tests appropriate to that kind of data. So when describing nominal data it is appropriate to calculate a mode; likewise when describing ordinal data, it is appropriate to use both the mode and the median, and so on.
The left-hand column shows the different kinds of statistics you might wish to use, ranging from descriptive to analytical statistics. Note that when it comes to associations, you need to choose a test according to whether the independent (causal) variable is nominal, ordinal or interval in character.
Figure 7.4 Choosing an appropriate statistical test
[table id=41 /]
SAQ 7.3 Which test?
Using Fig 7.4, work out which kind of statistical analysis should be used with the following studies.
[table id=42 /]
7. Presenting data
So far, we have considered how to manipulate data during analysis. Once analysis is completed, we will need to present it. The main ways to present data are:
A table provides a way to compare data easily and is useful where there are multiple categories. Any of the tables described earlier in this unit could be used in a research report to summarise data.
(For an example of a paper which should really have used tables to report an overwhelming mass of data, see Eaton, D.K. et al. (2006). Youth risk behavior surveillance – United States, 2005. Journal of School Health, 76(7), 353-372. This can be downloaded free at http://www.pactonline.org/docs/June%2006-Youth%20Risk.pdf).
7.2 Descriptive statistics
Data can be summarised in terms of simple descriptive statistics (e.g. an average such as a mean or a median value) or a range. These which may be coupled with tests of significance (see section 6 above).
7.3 Visual representations: figures and charts.
Figures are non-numerical representations of data (for example, a flow diagram showing how one variable affects another which in turn affects another).
Charts provide a means to visually represent numerical data such as frequencies. The chart used should be clear and should illustrate the data in a way that assists the reader to understand the findings.
7.3.1 Types of chart
Bar charts are a means to compare frequencies for discrete categories. Chart 7.1 displays the number of people in four socio-economic status (ordinal) categories.
Chart 7.1: Bar chart of proportion of meat-eaters by SES
Pie charts provide a more intuitive way to present percentages. Chart 7.2 shows the same data as chart 7.1, with different segments of the ‘pie’ representing proportions of the cases with each value.
Chart 7.2: Pie chart of proportion of meat-eaters by SES
Other more complex charts are available in statistical software packages or online.
This chapter covers a lot of ground and you may want to go over some of it a number of times. There are a number of key points with which you should now be familiar, namely:
- Quantitative data comes in three types: nominal, ordinal and interval.
- Each type of data requires a different sort of analysis and only certain types of statistical tests can be applied to particular data types.
- Data needs to be coded before it is entered into a computer, according to thought-through coding frames, and ensuring assumptions are not made about the type of data (e.g. interval rather than ordinal).
- Once analysis is complete, the findings of the analysis need to be presented in a clear way, using tables, statistical findings and visual representations, as appropriate.
Now please complete the following reflective exercise for your log book.
Reflective Exercise 7.1
[table id=43 /]
Bryman, A. and Cramer, D. (2011) Quantitative Data Analysis with IBM SPSS 17, 18 & 19: A Guide for Social Scientists. Hove: Routledge.
Kent, R.A. (2015) Analysing Quantitative Data: Variable-based and Case-based Approaches to Non-experimental Datasets. London: Sage.
Answers to SAQ 7.1
- Value (the variable is ‘family size’)
Answer to SAQ 7.2
The first thing you should have noted is that the investigator is using a confusing coding frame, in which a larger number represents ‘higher SES’, whereas conventionally, SES is described using Roman numerals with I = professional through to V = unskilled.
But the most remarkable thing about the study is the use of ‘mean SES’ scores. The investigator is treating the data as interval, whereas it is at best ordinal, and it arguably nominal, based on a set of occupational categories. (The dated term ‘lower classes’ should not be used to imply some kind of hierarchical order in these different occupational groups.) A mode may be the most appropriate summary statistic to use to describe the average social class for these groups.
The investigator is also confusing dependent and independent variable. In data analysis, the investigator should seek to examine the dependent variable (i.e. the outcome measure) by the independent variables. So in this example the investigator should display the mean meat eaten (the dependent variable) by each social-economic status grouping (the independent variable). If samples from the four socio-economic groups were compared on the amount of meat eaten (using an Analysis of Variance – see later in this chapter), it would be possible to discern if SES really had an effect on meat eaten.
Answer to SAQ 7.3
- Test of differences in means: independent samples, parametric data (T-test).
- Two-by-two contingency table (Chi-squared).
- Test of difference of means: related samples, non-parametric data (Wilcoxon).
- Test of differences in variance, parametric data, three independent samples (ANOVA).
- Non-parametric correlation (Spearman’s rho or Kendall’s tau).
- Correlation: parametric data (Pearson product-moment coefficient of correlation).


First we need to calculate the total water required. Let’s seen an example:
Consider we have 1.5 ha area and going to grow a cotton crop in the spacing of 1.5 m x 0.50m. We are going to use inline dripper having a discharge capacity of 2 LPH (litres per hour so how to calculate the water requirement in drip irrigation?
Taking the given parameters,
We need to calculate how many plants are there in a given area?
Convert ha to sq.meter
1.5 x 10,000 = 15000 Sq.meter
=15000 / 1.5 x 0.5 (crop spacing)
= 20000 plants can be planted in the field
We are going to provide 2 litres of water to each plant, so
Total Water Requirement = 20000 x 2 (Total plants x dripper discharge )
=40000 litres or 40 m3/hr
So, we need 40m3 / hr water to irrigate 1.5 ha of cotton crop using emitters in drip irrigation


Think-Tac-Toe is a puzzle where you are trying to discover the hidden locations of X’s and O’s in a grid by using number clues. The number in each square tells you the number of X’s in that square’s neighborhood. A square’s neighborhood is made up of the square itself and any squares with which it shares an edge or a corner.
Look at the #4 in the upper right hand corner of the Clues grid. It has a neighborhood of only four squares, so they must all be X’s (Step 1). Next, look at the #1 in the lower left hand corner. This square already has one X in its neighborhood, so there can’t be any more X’s. You can fill in O’s in the rest of its neighborhood (Step 2). Now, if you look at the #3 right above the #1 you can count the number of X’s already in its neighborhood. There are only two so far, so the square in the upper left must also have an X in it to make a total of 3 (Step 3). Similar logic will fill in the bottom right square, which completes this Think-Tac-Toe puzzle. There is only one correct answer. Try solving some more on the puzzles page!


A fifth grade science teacher from Frisco ISD’s Elliott Elementary School was honored in February by the Texas State Board of Education as one of eight state finalists for the 2014 Presidential Awards for Excellence in Mathematics and Science Teaching (PAEMST).
It is the second time Nancy Gardner has been named a finalist for the award, which is the highest recognition a mathematics or science teacher may receive for exemplary teaching in the United States. She was also named a finalist in 2012.
“Nancy’s passion for science is evident in her daily instruction,” said Elliott Principal Stacy Mills. “She is constantly reevaluating her own teaching practices and striving to instill that passion in her students. She knows which specific concepts they need help with and adjusts her support to personalize their instruction so that each student not only learns the concepts, but is also motivated and joyful about learning.”
Gardner is a graduate of Frisco High School. She joined the District in 2005 and was named Outstanding Elementary School Science Teacher by the Science Teachers Association of Texas (STAT) in 2008.
PAEMST recognizes kindergarten through sixth grade mathematics and science teachers whose innovative methods bring teaching to life in the classroom. The National Science Foundation administers PAEMST on the behalf of the White House Office of Science and Technology Policy.
To achieve recognition through the program, a teacher first must be nominated for the award. A state panel of master teachers, specialists, and administrators reviewed the applications and chose the most outstanding mathematics and science teachers for the National Science Foundation to consider for national awardee status.
After the initial selection process at the state or territorial level, a panel of distinguished scientists, mathematicians, and educators may select one mathematics and one


Quick income ratio (QIR) shows the ratio of operating cash flow adjusted for financial calculations to the similar financial results.
Alternative names of Quick Income Ratio:
- Quick Income Ratio
What Does the Indicator of QIR Show?
An enterprise is often financed by a loan or investment funds. In such situation, it is very important that it generates enough money not only to support current activity, but also to repay its debts. That is why it makes sense to conduct the analysis of operating income along with the financial costs like paid taxes and interest. The result represents the initial cash flow from the financial activity. Similar indicators refer to the financial performance. Comparing these metrics, it will be possible to determine the ability of an enterprise to pay interest and taxes in the future as well as understand better the level of the current solvency.
Formula of the Quick Income Ratio
QIR = (Operating cash flow + Percentage paid + Taxes paid) / (Net profit + Interest to be paid + Income tax + Depreciation)
Normative Value of the Quick Income Ratio
This indicator is calculated if the cash flow statement is composed indirectly. Cash flow statement prepared by a direct method does not provide the necessary figures. The normal situation is when the coefficient is approximated or equivalent to 1. Significant deviations, if any, require a detailed analysis.


ENGLISH LANGUAGE AND LITERATURE
English Language and Literature in Grade 9 includes a range of methodologies to teach literature, grammar usage, and writing, comprehension, speaking, and listening. In keeping with the American High School philosophy, students are expected to rely on a range of learning styles to maximize achievement across units of study. Writing is also emphasized. Students write from a variety of genres, modes, and organizational patterns; thereby developing skills in evaluating written work. Students are expected to read critically and improve oral and writing skills as they interpret literature and non-fiction texts. As such, the course objectives will help students with the Pre SAT training offered at school.
Algebra I is the introduction of variables, constants, expressions and equations. Topics covered are: solving equations, simplifying expressions, understanding order of operations, using properties (field axioms), arithmetic operations with positive and negative numbers, polynomials, factoring, graphing (linear functions), working with radicals and expanding arithmetic knowledge. Real-world applications of algebraic thinking are also introduced to the students.


Free printable 5 inch number stencils 1-10. Print these free number stencils which are suitable for many types of projects that require numbers in a stencil outline style. 1 to 10 numbers in 5 inch size.
1 to 10 number stencils can be printed below for free!
These numbers are excellent for kids activities, crafts and special projects where you need numbers that are in stencil outline format.
We also have printable stencils with numbers in other sizes / inches as well. Please see our Number stencils page.
Available in 5 inch print. View and print these free 1 to 10 numbers below.
Important print instructions for 5 inch number stencils.
For these numbers to print correctly at a 5 inch size height, please ensure your Laser/Inkjet printers DPI settings is set to 300 DPI. With your print settings adjusted to 300 DPI, these number stencils will print properly at a 5 inch height on paper.
Printable stencil templates measure 1700 x 1700 pixels each.
No of Printable number stencils: 10
Stencil size: 5 inch numbers
5 inch Number Stencils in Printable Format from 1 to 10
To download and print: 1. Place mouse over image 2. Right click 3. Select Save Image As
( You may also click the links below the number images and print the number in the new window )
Printable Number 1
Printable Number 2
Printable Number 3
Printable Number 4
Printable Number 5
Printable Number 6
Printable Number 7
Printable Number 8
Printable Number 9
Printable Number 10


Publications and Preprints
- Green currents for meromorphic maps of compact Kaehler
manifolds, J. Geom. Anal. 23(2), 970-998 (2013)
- Equidistribution toward Green current in big cohomology classes,
Internat. J. Math. 24(10) 135080 25pp (2013)
- (with S. Cantat)
Constraints on automorphism groups of higher dimensional manifolds, J. Math. Anal. Appl. 405 (2013) 209-213.
- Ergodic properties of random holomorphic endomorphisms of P^k, Int. Math. Res. Not. (IMRN) no. 4 (2015) 927-959.
- Equidistribution of zeros of random holomorphic sections, Indiana Univ. Math. J., 65 (2016), no 5, 1759-1793.
- Zero distribution of random sparse polynomials, to appear in Michigan Math. J.
- Asymptotic normality of linear statistics of zeros of random polynomials, to appear in PAMS.
- (with D. Coman and G. Marinescu) Equidistribution of zeros of random holomorphic sections and asymptotic normality, in preparation.
- (with T. Bloom and N. Levenberg) Pluripotential theory and convex bodies, submitted.


Java Tutors in Canyon, TX
Find Private & Affordable Java Tutoring in the Canyon Area!
Ali E. Private Java tutor in Canyon, TX
One of the greatest feelings for me is when I can teach someone something new and watch them become successful at it. Algebra, Calculus, Pre-Calculus, Statistics, Trigonometry, Math, Python Classes Taken: College Algebra, Pre-Calculus, Calculus 1, 2, and 3, Differenial...
Senior Mathematics Major at West Texas A&M University


Book Test No. 34
When is a book test not a book test? When it’s a card trick.
This is a method of forcing a number, and that is often used to predict a particular word on a particular page in a book. But I’ve recently shown you a book test, so for today’s video I decided to use playing cards. A grid of numbers from 1 to 16 is shown, and four are chosen, the other twelve crossed out. When the four chosen numbers are added together, they make 34. And the 34th card in a red-backed deck of cards s the only one with a blue back.
Another trick with arithmetic, but the maths is pretty easy for this one. (And since you know what the answer is, you can bluff your way through the sum if you need to.) You can download the grid and print it off here.
You can also view this trick on YouTube at https://youtu.be/hV4FMBQFuWM
You can see all the previous magic lessons here.


The Finite Element Method with An Introduction Partial Differential Equations by A.J Davies
Book Title : The Finite Element method with An introduction with partial differential equations
Author(s) : A.J Davies
Publisher : Oxford
Edition : Second
Pages : 308
PDf size : 1.82 MB
The finite element method is a technique for solving problems in applied science and engineering. The essence of this eBook is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson’s equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is also explained. The Finite Element Method with An introduction partial differential equations by A.J Davies book is written at an introductory level, developing all the necessary concepts where required. Consequently, it is well-placed to be used as a book for a course in finite elements for final year undergraduates, the usual place for studying finite elements. There are worked examples throughout and each chapter has a set of exercises with detailed solutions.


A person reading a totalizer must be careful to add the correct amount of zeroes or place the decimal point in the right place. If a mistake is made, the meter reading can be off by a factor of 10, 100, or even 1000 units.
Most totalizers have “multipliers”. Multipliers are always a multiple or fraction of ten which are used to multiply the direct reading of the totalizer
Gallons: A meter that totalizes in gallons will have a multiplier of times 10, times 100, or higher. That means that the meter is read not as gallons, but as tens of gallons or hundreds of gallons. In the example to the left, the correct reading is 9,254,500 gallons.
Acre Feet: A meter that totalizes in acre feet will have a multiplier of times .01, times .001, times .0001, or smaller. The digit counters on the right side are colored yellow to indicate where a decimal point should be placed when reading the totalizer. In the example to the left, the correct reading is 92.545 acre feet.


to use the LCD (Nokia 5110) to display info (speed, bearing, date, time, distance from a marked point). The exact opposite to the direct bearing followed to go somewhere new is called the back bearing. If I use ball of different diameters as a point here,can I find the diameter of the ball also simultaniously. The resulting distance equals sum of the difference of each element on the vectors. Calculate Bearing or Direction Between 2 Coordinates Good morning to all. EXAMPLE Find the distance between the following pairs of points. Points are designated by their distance along a horizontal (x) and vertical (y) axis from a Coordinate system, Arrangement of reference lines or curves used to identify the location of points in space. If the distance and circle reading to a third point are included in the sequence, thetotal station can display D13 and ∆h13 (radial MLM) or it can display D23 and∆h23. Read more about how to calculate Distance by Latitude and Longitude using C#. Distance Calculator to calculate the distance between cities, states or any two addresses. Find the distance between the starting point and the ending point. Given 2 point type SDO_GEOMETRY objects, how to calculate the bearing angle from the first point to the other? At the moment there is no built-in function to calculate bearing angle between 2 sdo_geometry objects. C Basic Declarations and Expressions: Exercise-15 with Solution. To list a bearing between two points using the Survey Command Window In Toolspace, on the Survey tab, right-click a named network Survey Command Window. I'm creating an algorithm on Matlab and need to find the distance between two points in spherical coordinates where I have (r1,theta1,phi1) for the first point and (r2,theta2,phi2) for the second point. @kirk_humphreys 7th graders used @desmos today to calculate linear/quad. A) You can calculate the elevation of land using the route elevation calculator. To measure the bearing from one point to the next, the protractor must be aligned so that 0° point to the top of the map (true north). Distance and bearing may be taken from topographical maps for quick analyses but great circle calculations are needed for more accurate work and are. We will look at polar coordinates for points in the xy-plane, using the origin (0;0) and the positive x-axis for reference. Using a magnetic compass to find north: The North N mark on the rotating part of the compass or the Red end on the needle or the Pointed end of the needle points towards magnetic north. The vectors determine the parallelepiped whose height is the distance between the two lines. Write the exact answer in radical form. Search this site Here is a useful utility for calculating the distance and compass bearing between any two points clicked on. Arc (End Points) Generates an arc between two points surrounding a central point. The formula for determining the slope between 2 points is: Slope = m = (Y 2 -Y 1 ) ÷ (X 2 -X 1 ) In the above graph we have 2 points where 'a' has the values of x=1 y=2 and the values of point 'b' are x=5 y=4. Another method for calculating the distance between two points that fall on the same line is to plot the points and. In the Survey Command Window, click Point Information menu Bearing. These two lines look this way: Now, where the two lines cross is called their point of intersection. If you're going to be working with spherical coordinates, two sites I've found invaluable are Aviation Formulary and Calculate distance, bearing and more between Latitude/Longitude points. • Bearing is defined by Webster’s to be “a support or supporting part” –A bearing is a component that allows for relative motion between parts • Your skeleton is the central structure that supports your body • Your body’s joints are bearings that allow different parts to move • Bearings can have many forms, but only two types of motions. It says as follows "If you want the the angle between the line defined by these two points and the horizontal axis: double angle = atan2(y2 - y1, x2 - x1) * 180 / PI;". EDM Calculator ™ is. say the call is from a point south 66 deg 48 min 00 secs west and you are at the ending point for this call. Distance Calculator. The following formula gives the distance between two points, (x1, y1) and (x2, y2) in the Cartesian plane: Given the center and a point on the circle, you can use this formula to find the radius of the circle. Now that we know how to leverage our newly learned GetDistance and GetDuration functions we can use them to measure the distance/duration for any routes, with any coordinates/addresses in between our starting point and our destination. Calculate the distance between 2 points in 2 dimensional space. The FreeVBCode site provides free Visual Basic code, examples, snippets, and articles on a variety of other topics as well. Math can be an intimidating subject. Vectors addition (A ± B) Two vectors A and B may be added to obtain their resultant or sum A + B, where the two vectors are the two legs of the parallelogram. Distance between two points in a three dimension coordinate system - online calculator Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!. Distance Calculator is use to calculate the distance between coordinates and distance between cities. Chris Veness's page also contains an Excel formula of the 'Haversine' equation (actually, using the "spherical law of cosines") for distances between points in kilometres:. Intersection of two lines. Then as you know two angles and one side. But, there is no reason to stop at three-dimensions. We use what's known as the distance formula to obtain the distance between any two points in space. Therefore, when calculating distance between points on a map using Northings and Easting values, the process is similar to calculating the distance between points on a Cartesian system. The next two points are the same, but they are about 14 meters southeast of the points above. longitude); auto time_s = (p2. 0 and newer versions Beginning with Tableau Desktop 10. This question is about finding bearings. A vector F along the line A-B and of magnitude F can thus be obtained from the relation. I m planning to calculate the GPS bearing between two points of a quadcopter. New coordinates by rotation of axes. 'OUTPUT: Distance between the ' two points in Meters. Draw a line between the intermediate elevation and the unknown point that you marked in step 3. Bore diameter max mm. For two points P 1 = (x 1, y 1) and P 2 = (x 2, y 2) in the Cartesian plane, the distance between P 1 and P 2 is defined as: Example : Find the distance between the points ( − 5, − 5) and (0, 5) residing on the line segment pictured below. How to calculate bearings between two points (in decimal degrees) using Excel. This script calculates distances, bearing and more between the two Latitude/Longitude points. Intersection of two lines. You're trying to get the X and Y co-ordinates of two points: Point1 and Point2. Amazing things about R is that there are more than 10,000 packages that are officially certified and available on CRAN (The Comprehensive R Archive Network) and a lot more on other places like Github. A B C 100 m 65° 55° Solution. I am trying to find the distence( in cm) between two points using image processing(one is fixed intentionally other point is not fixed and keeps varying). In this case a difference in 157 m is small (about 0. Outer diameter max mm. What really matters is the overall violent crime rate. 03 percent) compared to the distance between the locations. Calculation of angle between two planes in the Cartesian form: Let A 1 x + B 1 y + C 1 z + D 1 = 0 and A 2 x + B 2 y + C 2 z + D 2 = 0 be the equation of two planes aligned to each other at an angle θ where A 1, B 1, C 1 and A 2, B 2, C 2 are the direction ratios of the normal to the planes. ) using a counter than I calculate the previous elevation of previous point so that I can calculate the change in elevation Thanks So much, D. If two or more points are connected, a line or curve is formed. Cartesian, Compsys, Geodetic. Point P is in quadrant I, at coordinates (5,2). To simplify, we will examine two points on the cable: points 1 and 2. At the end, need to convert the result of ATAN2 back to degrees. There are always options to choose from: thinner treads and metal stringers, transparent railing, etc. The first method consists of converting the points to Cartesian coordinates, and then calculating the cord length (d) between the points (straight line distance through the Earth). New coordinates by rotation of points. Distance calculator helps you to find how many miles from a city to an another city on map. I implemented this, but I think the fact the I'm working in screen coordinates is causing a miscalculation, since the Y-coordinate is reversed. How to convert from Cartesian (x,y) coordinates to 360 bearing (where 360 and 0 = north) on *INFINITE FLAT PLANE* I am not a "math person" but I really want to know how to do this for finding my way around in a video game using the X,Y coordinates. for geocaching. Arc (End Points) Generates an arc between two points surrounding a central point. Cartesian Robot Design. • Bearing is defined by Webster’s to be “a support or supporting part” –A bearing is a component that allows for relative motion between parts • Your skeleton is the central structure that supports your body • Your body’s joints are bearings that allow different parts to move • Bearings can have many forms, but only two types of motions. Math can be an intimidating subject. The horizontal axis is called the x-axis, and the vertical axis is called the y-axis. Available with Production Mapping license. The Cartesian Coordinate System consists of two number lines perpendicular to each other at their 0's. The Bearing Distance Calculator function calculates the forward and backward azimuths between two specified coordinates as well as the distance. (This answer was prepared by Robert G. Other than the two ends, the beam has no vertical resting points. Calculate the area of the first trapezoid: To begin, you will want to find the area between X1 and X2. These two lines look this way: Now, where the two lines cross is called their point of intersection. Created to act as a math tool for both students and professionals, CalcuNation seeks the interaction of the user to create new calculators that help with everyday math problems. /** * Calculate the bearing between two positions as a value. Can someone show me how I would do this? It asks me to calculate the distance between the points F = (2,2) and M = (5,-4) in the cartesian plane. This is the snippet Calculate Distance Between 2 Points Given Longitude/Latitude (ASP) on FreeVBCode. Circular Curve Information: Angles Bearings & Arcs BEARINGS: the direction of a line speciﬁed by a given angle between the line and an established meridian, usually the north-south axis. Using the illustration below, we will first (1) “walk off” two distances, (2) sight the faraway object in our compass from both points, and finally (3) record the angle for both points to use in our distance calculation. Two points on N-Dimensional cartesian space It measures d istance between two points or vectors on N-dimensional space. a two-span steel plate girder bridge that spans over In terstate 5. Doing your assignments with regards to graphing can surely be very challenging. The ordinary compass cannot read directly the angle between two lines. If you are given a vector that is placed away from the origin of the Cartesian coordinate system, you must define the components of both points of the vector. The following formula gives the distance between two points, (x1, y1) and (x2, y2) in the Cartesian plane: Given the center and a point on the circle, you can use this formula to find the radius of the circle. We like to work with normalized bearings because they make for more efficient movement. ) sorting by distance 2. /** * Calculate the bearing between two positions as a value. When the two lines meet at a point, two angles (interior and exterior) and formed. Related Symbolab blog posts. The primary function of a bearing is to carry load between a rotor and the case with as little wear as possible. Inverses can be performed between two points or between a point and a line, the line being defined by two points. The Cartesian coordinates of two or three-dimensional vectors look just like those of points in the plane or three-dimensional space. Calculating Distance Between Coordinates Jan 16, 2008. x1 = x0 + distance*cos(bearing) y1 = y0 + distance*sin(bearing) Then create a new XY event layer using the new fields x1,y1. Taking and Following a Compass Bearing. AZIMUTH Calculates azimuth between points on a geoid az = AZIMUTH(lat1,lon1,lat2,lon2) computes the great circle bearing between the two points on the globe. Write a C program to calculate the distance between the two points. Add these two products and determine the arcsine of the sum. Cartesian; from René Descartes, a French mathematician, 1596 to 1650. Switch between inverse dimensions by clicking on the title. Call the point where the intersect the origin, and label it with the pair (0,0). image/svg+xml. Area of a triangle with three points. Greetings, does anyone have a calculation that calculates the new latitude and longitude based on a starting point, bearing and distance? I would greatly appreciate any help people might have. D Conversions between coordinate systems Cartesian ← Spherical x = r cosφ 2cos θ α = cosφ cos θ. For example, the vector AB has an ordered pair for point A and point B. Fortunately, there are online tools you can use, such as a graphing calculator. We use Cartesian Coordinates to mark a point on a graph by how far along and how far up it is: Example: The point (12,5) is 12 units along, and 5 units up Steps. Calculating the bearing between two points on a map is an essential navigation skill for piloting and land orienteering. What I wish to do is to select a point and then. I've got two sets of co-ordinates and need to find the bearing. The coordinates are numbers for a specific point on the screen. I have been trying unsuccessfully to calculate the "bearing" between 2 Universal Transverse Mercator points. Calculate the distance between 2 points in 2 dimensional space. We first find the distance between two points that are either vertically or horizontally aligned. Calculate distance, bearing and more between two latitude/longitude points Distance This page helps you to calculate great-circle distances between two points using the ‘ Haversine ’ formula. Given your two points. I assume you have the bearing and distances for each point in other fields. Cartesian to Polar coordinates. Calculate distance between two GPS coordinates 2 votes · 1 comment These functions compute the approximate distance in meters between two locations, and optionally the initial and final bearings of the shortest path between them. The library also has many other useful routines, and doesn't assume the gross simplification of a spherical Earth. In order to establish a point, you MUST have latitude and longitude coordinates in one form or the other. Where (x1, y1) is the heading point, (x3, y3) is the target point. Point of reverse curve - Point common to two curves in opposite directions and with the same or different radii L Total length of any circular curve measured along its arc Lc Length between any two points on a circular curve. Two points on N-Dimensional cartesian space It measures d istance between two points or vectors on N-dimensional space. Online version: Great Circle Calculator - 'As the Cocky Flies' Great Circle and Approximate Ellipsoidal [XLS 18. Is there anyone can tell how to calculate azimuth and distance of two points on earth, the points is in two-dimensional cartesian format, using spherical trigonometri for more accurate calculation. The surveyor's bearing and distance values, known as "survey pairs", found in the record of new roads, often use a notation and units not familiar to us 21 st century folks. Calculating distant between two coordinate points I request a template or formulas to calculate the distant between coordinate points (114,50 and 54,91 etc). In polar coordinates, the point is located uniquely by specifying the distance of the point from the origin of a given coordinate system and the angle of the vector from the origin to the point from the positive -axis. Distance calculator helps you to find how many miles from a city to an another city on map. Could someone explain why my code won't allow me to show the distance between two points?. The calculator will determine the straight line distance between the two points as well as present the coordinates of each point as entered in the standard. Click Image to Enlarge. Here's how they look on a graph: With just a quick glance, you can tell they are 3 units apart. Switch between inverse dimensions by clicking on the title. The Pythagorean Theorem, a 2 + b 2 = c 2 , is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse. Posts about Bearings written by corbettmaths. The previous chapter on vectors has initiated the study of this branch of mathematics. Learning how to calculate the break-even point is essential for determining when your business will become profitable. The function uses the Great Circle method of calculating distances between two points on the Earth. The Cartesian Coordinate System consists of two number lines perpendicular to each other at their 0's. There are two nearest-neighbor methods which map the points from one grid to the nearest corresponding point on the other grid, from either source to destination or vice versa. In these bearings, the roller is a cylinder, so the contact between the inner and outer race is not a point but a line. Coordinates Distance Calculator $0. Draw a line between the intermediate elevation and the unknown point that you marked in step 3. For example, the bearing of A from B is 065º. C :: Calculating Distance Between Two Points (x And Y Vars) Feb 23, 2013. The program should ask the user to enter two points then should calculate the distance between two points and print the distance on the screen. Write a program to determine whether the year is a leap year or not. UTM Coordinates Distance & Bearing The following outlines how to determine distance and bearing between UTM coordinates. The previous articles dealt with Setting the Map and Contour Interpretation. The distance is marked as d. Let the distance between point 1 and 2 be so small, that cable segment 1-2 is linear. It's a two-point function, it's like asking 'if you can add a third vector to a 2D vector?', and the answer's no, it's a 2D vector with only 2 vectors(and. I might have been able to google this and figure it out, but I'm having a hard time putting this problem into words. We could define vectors in four, five, or higher dimensions by just specifying four, five, or more Cartesian coordinates. Location android. Program INVERSE is the tool for computing the geodetic azimuth and ellipsoidal distance between two points given their latitudes and longitudes in degrees, minutes, and seconds. The coordinates are numbers for a specific point on the screen. This script calculates distances, bearing and more between the two Latitude/Longitude points. You can use this distance calculator to find out the distance between two or more points anywhere on the earth. I am a very recent convert to Civil 3d (within the last week, in fact!) -- I have been using LDD for many, many years. You can help protect yourself from scammers by verifying that the contact is a Microsoft Agent or Microsoft Employee and that the phone number is an official Microsoft global customer service number. Cartesian Coordinate System. Program INVERSE is the tool for computing the geodetic azimuth and ellipsoidal distance between two points given their latitudes and longitudes in degrees, minutes, and seconds. This distance is also the length of the line segment linking the two points. So for a line segment, use this formula to calculate the point that bisects a line segment defined by the two points. There are two nearest-neighbor methods which map the points from one grid to the nearest corresponding point on the other grid, from either source to destination or vice versa. The way I think about it is really to try to draw a right triangle where these points, where the line that connects these points is the. The hypotenuse of the triangle will be the distance between the two points. Distance between two points and the midpoint. How would I calculate XY coordinates given Angle and distance? Looking to put the formula into a spreadsheet. The cartesian system will be now broadened in scope to understand the three coordinates. An online resource that enables visitors to easily and quickly use maps in order to measure, search and overlay mark-up elements on maps for a wide range of useful applications. We could define vectors in four, five, or higher dimensions by just specifying four, five, or more Cartesian coordinates. You'll need to figure out the actual angle by checking which quadrant the second point is in with relation to the first point. Advanced Google Maps Distance Calculator. When it comes to calculating the distances between two point, you have the option of doing so in 1, 2, 3, or 4 dimensions. Description. So if the size between two points on the same line of latitude is 45 degrees it would calculate to 60 miles x 45 degrees = 2700 miles on Gleason's map. Taking a bearing refers to measuring the direction from one point to another, either in the field or on a map. Unlike a line, it does not extend off to infinity in both directions. Intersection of two lines. Find the course bearing from C to A. Now once you have the distance between the points you can estimate the average speed by dividing this distance by the time between the two position measurements like this: // // auto dist = distance_on_geoid(p1. Point 1: Point 2: Magnetic Declination:. Use the Bearing command to list the bearing from one point to another. Step 4: Calculate the altitude Calculate the altitude of the object, called H. And these coordinates are called Cartesian coordinates, named for Rene Descartes because he's the guy that came up with these. There are two ways of expressing the bearing of Y from X, namely true bearings and compass bearings. I want to be able to get the bearing between two points. The distance is marked as d. Spherical to Cartesian coordinates. If the end points of a line segment is (x 1,. Switch between inverse types by clicking on the title. Moveable Type Scripts: Calculate distance, bearing and more between Latitude/Longitude points About the Author Pearl Lewis has authored scientific papers for journals such as "Physica Status Solidi," "Materials Science and Engineering" and "Thin Solid Films" since 1994. The Bearing Distance Calculator function calculates the forward and backward azimuths between two specified coordinates as well as the distance. The Pythagorean Theorem, a 2 + b 2 = c 2 , is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse. The polar coordinates of a point describe its position in terms of a distance from a fixed point (the origin) and an angle measured from a fixed direction which, interestingly, is not "north'' (or up on a page) but "east'' (to the right). Switch between inverse types by clicking on the title. In a trig calculator (HP in my experience), simply subtract the easting of point A from the easting of point B, then subtract the northing of point A from the northing of point B, hit R-P (rectangular to polar) and you will get the direct distance, then the angle from North or East. which are not variables, are often called constants. Calculate with Geo Coordinates Calculators for the conversion of geo coordinates, as delivered by a GPS tool, for the distance of two point and for bearing. A bearing is used to represent the direction of one point relative to another point. The cosine of the angle between the two planes is given by:. ) Distance is always expressed in feet, regardless of map units. Calculate the distance between two addresses using Google Maps Geocoding API and PHP - Get distance between two addresses through PHP. The azimuth is reported from 0 to 360 degrees, clockwise from north, by convention. Figure 1: Standard relations between cartesian, cylindrical, and spherical coordinate systems. If we divide 225 by 45 (the number of degrees between directions in an eight-point compass rose), we get 5. For two points P 1 = (x 1, y 1) and P 2 = (x 2, y 2) in the Cartesian plane, the distance between P 1 and P 2 is defined as: Example : Find the distance between the points ( − 5, − 5) and (0, 5) residing on the line segment pictured below. It is essentially an equipotential line (a line in an two-dimensional field where the total hydraulic head or water level is constant for all points on the line). To distinguish between events happening at the same point in space but at different times we need to specify when an event happened as well as where it happened, so we add a time coordinate t. Extend the End Project reference bearing (Az) backward into the corridor. Calculate compass heading between 2 UTM grid points. Other than the two ends, the beam has no vertical resting points. Using a magnetic compass to find north: The North N mark on the rotating part of the compass or the Red end on the needle or the Pointed end of the needle points towards magnetic north. What can we do with this? Well, for starters, computing the distance between two points is easy: just use the Pythagorean theorem: dist = sqrt( (x1-x2)^2 + (y1-y2)^2). Between two points that are directly opposite each other, called antipodal points, there are infinitely many great circles, and all great circle arcs between antipodal points have a length of half the circumference of the circle, or , where r is the radius of the sphere. The point of intersection of the x-axis and the y-axis is called the origin. for geocaching. As an example let's use … Coordinate 1: easting = 420,760, northing = 5,449,670 Coordinate 2: easting = 420,710, northing = 5,449,630. mht Find file Copy path Fetching contributors…. Points and vectors may be entered via Input Bar in Cartesian or polar coordinates (see Numbers and Angles). I would like to measure the distance between the yellow points in this image: How can I do it? My goal is to cut the cube using the plane, but I must set a precise distance between the plane and the square's corner. Please note that in order to enter a fraction coordinate use “/”. SOLUTION: Calculate the distance between the pointsD=(-4,5) and K=(5,9) in the Cartesian plane. Pythagoras’ theorem is used to calculate the distance between two points when the line interval between them is neither vertical nor horizontal. ) Distance is always expressed in feet, regardless of map units. The polar coordinates of a point describe its position in terms of a distance from a fixed point (the origin) and an angle measured from a fixed direction which, interestingly, is not "north'' (or up on a page) but "east'' (to the right). Roller Bearings. 208 rule, which is considered by FCC as a valid approximation for distances less than 470 km. Great Circle Distances and Bearings Between Two Locations R. Sometimes you need to find the point that is exactly between two other points. The distance calculations and bearing are based on a true spherical model. The code has been written in five different formats using standard values, taking inputs through scanner class, command line arguments, while loop and, do while loop, creating a separate class. If you want to transform them directly, there are two ways: you can find two points on the plane (values which solve the normal form equation) and use them to span the plane. So, I have got two reference TLE from 2 different Satellite in LEO-GEO, which are as follows: (1st TLE for LEO, 2nd TLE for GEO) 1 44072U 19015A 19265. In other words, the distance between A and B. Just to note, I wrote most of this code using what I learned in class recently. It's an online Geometry tool requires coordinates of 2 points in the two-dimensional Cartesian coordinate plane. Pythagoras’ theorem is used to calculate the distance between two points when the line interval between them is neither vertical nor horizontal. A geodetic line is a curve on the surface of the earth. Age 14 to 18. I have also set many girders on point load posts in interior walls that someone might be in for a surprise if they think they could take out the wall. Python Exercises, Practice and Solution: Write a Python program to compute the distance between the points (x1, y1) and (x2, y2). Bullock If we’re given two points A and B on the Earth (assumed spherical with radius R), then how can we calculate the distance between the points and the direction (bearing) of one point from the other? Before we get much into this, let’s say a few things about our conventions. A polar coordinate system, gives the co-ordinates of a point with reference to a point O and a half line or ray starting at the point O. But simple Euclidean distance doesn't cut it since we have to deal with a sphere, or an oblate spheroid to be exact. We use what's known as the distance formula to obtain the distance between any two points in space. Hi, I want to know how to calculate a bearing between two points. The difference between the straight-line distance between the two sea level points and the distance along the surface of the Earth between those two points is: (d/24) * (d/R)^2. Advanced Google Maps Distance Calculator. Movable Type Scripts Vincenty formula for distance between two Latitude/Longitude points For the benefit of the terminally obsessive (as well as the genuinely needy), Thaddeus Vincenty ('TV') devised formulae for calculating geodesic distances between a pair of latitude/longitude points on the earth's surface, using an accurate. 208 rule, which is considered by FCC as a valid approximation for distances less than 470 km. @kirk_humphreys 7th graders used @desmos today to calculate linear/quad. Points can also be created using Point tools and vectors can be created using the Vector from Point Tool or the Vector Tool and a variety of commands. 00000 eqt 0. And to write the answer in radical form. Then multiply the cosine of L by the cosine of D, by the cosine of t. Calculate distance and true bearing between two latitude/longitude coordinates and show in Google Map : This service allows you to calculate the shortest distance over the earth's surface between two locations A and B. Apart from the stuff given above, if you want to know more about "Using pythagorean theorem to find distance between two points", please click here. To determine the direction from the starting point between two points on the earth, use the following formula: Note: 1) ln = natural log 2) if Δlon > 180° then Δlon = Δlon (mod 180). This article presents the formulae to convert between Cartesian and Spherical co-ordinate systems. Given your two points. The numerical distances in are determined by a numerical function for length. A Cartesian coordinate system is a special kind of mapping between points of these two structures. edit flag offensive delete link more. You can use OpenLayers. Taking and Following a Compass Bearing. This page shows how to calculate the geographic midpoint (also known as the geographic center, or center of gravity) for two or more points on the earth's surface. Cylindrical to Cartesian coordinates. Square both quantities in the parentheses. We already know where point A is, since we figured it out, so we only need to figure out where point C is, with respect to the origin. (This answer was prepared by Robert G. When working on problems in three dimensional space it is often required convert between two or more co-ordinate systems. Calculate the distance between two addresses using Google Maps Geocoding API and PHP - Get distance between two addresses through PHP. Cartesian Robot Design. Point P is in quadrant I, at coordinates (5,2). To determine a force’s moment, you use one of two different calculations, as you can see in the following list. What is the formula for the distance between two polar coordinates? Given in cartesian coordinates. The angles can be determined by observing the bearings of the two lines from their point of convergence. We can write the location of point C in Cartesian vector notation like so:. (see diagrams below) The triangle with angle θ can be bisected giving two right angled triangles with angles θ/2. Bullock If we’re given two points A and B on the Earth (assumed spherical with radius R), then how can we calculate the distance between the points and the direction (bearing) of one point from the other? Before we get much into this, let’s say a few things about our conventions. I guess you want to find the shortest distance along the surface of the sphere, not just the euclidean distance between the points. I would like to measure the distance between the yellow points in this image: How can I do it? My goal is to cut the cube using the plane, but I must set a precise distance between the plane and the square's corner. 4876'' N and 10° 27´ 5. Thank you beforehand!. A lug, also known as a lifting lug or a padeye, is essentially a plate with a hole in it where the hole is sized to fit a clevis pin. Thanks in advance. Angle, Azimuths and Bearings: (Chapter 7) In this chapter we will be most concerned with the calculation of line azimuth rather then bearings. Here is the easy way to calculate distances by latitude/longitude using Visual Basic. Example Two - Positive Gradient. These two lines look this way: Now, where the two lines cross is called their point of intersection. A point P in the plane, has polar coordinates (r; ), where r is the distance of. We define the angle coordinate for the point as follows. In addition, it can calculate a new point from origin using the given azimuth and distance. Let the distance between point 1 and 2 be so small, that cable segment 1-2 is linear. If we count off an eight-point compass rose's directions clockwise, starting with NE as 1, then 5 equals SW. So, thanks to the ability to reuse calculators logic, this calculator accepts coordinates of two points, sends them over to the loxodrome calculator, receives directional angle, sends it over to the compass point calculator and receives compass point. A better set of names would be:. The code has been written in five different formats using standard values, taking inputs through scanner class, command line arguments, while loop and, do while loop, creating a separate class. Switch between inverse types by clicking on the title. Generates a polygon based on a specified bearing line. The distance calculations and bearing are based on a true spherical model. This method is the fastest, but suffers from the problems discussed above. 1st Stanford in the Vale Scout Group. Calculating the bearing between two points Sometimes it is necessary to calculate the angle (bearing) between two points. If the lines are parallel the. If you're going to be working with spherical coordinates, two sites I've found invaluable are Aviation Formulary and Calculate distance, bearing and more between Latitude/Longitude points. There are four plate girders with simple spans of 44. I want to be able to get the bearing between two points. Calculate angle bearing by determining the difference between an object and the line heading North when the object is at the origin. DISTANCE BETWEEN TWO POINTS Distances are always positive, or zero if the points coincide. It can be a city, town, village or even the sea or ocean. Second one outputs compass point given course angle in degrees.


About the Formula Functions
Formula functions are logical and programmatic functions that can be included anywhere that a Formula Expression is defined.
The following conventions are used in these functions:
Element Description 'string' Strings must be enclosed with single quotes 'dString' Date strings must be enclosed with single quotes int An integer,for example, a number representing the number of days (or months or years) value An argument in date- and date/time-related Formula Functions, which defines a unit of time [ ,optional] Optional values are shown in brackets, as [ ,option1, option2]
See Date for details about these Day, Date and Time-related formula functions:
See Logical for details about functions resulting in TRUE/FALSE (YES/NO, 1/0):
See Math for details about mathematical functions:
See Text for details about text-related formula functions:
The Aggregate Functions are not available in every context, because of their potential impact on performance. They let you select a collection of records in an arbitrary object and perform a summary calculation on those records.


Your Body Mass Index is calculated as follows:
1) Establish your weight in kilograms (kg). To convert from pounds (lbs) to kilograms (kg) simply divide by 2.2.
2) Establish your hegiht in metres (m). If required, convert inches to centimetres by multiplying by 2.54. Then convert centimetres (cm) into metres (m) by dividing by 100.
3) Having obtained weight in (kg) and height in (m), use the following equation to calculate BMI.
BMI = Weight (kg) / Height² (m)
When you have your BMI, use the following table to see your results:
|Body Mass Index||Underweight||Healthy||Overweight||Obese|
|Men||< 18.5||18.6 – 24.9||25.0 – 29.9||> 30|
|Women||< 18.5||18.6 – 24.9||25.0 – 29.9||> 30|
Body Mass Index (BMI)
It is important to be aware that BMI uses total body weight and does not discriminate between fat and lean body mass. Therefore, BMI should ideally be used in conjunction with other body composition tests.


Thursday, February 12, 2009
What a better way to develop small motor skills then beading!! I found these great beads at Hobby Lobby and thought they would go great with our Valentine's theme!!
Once I got them home I noticed that the holes were VERY tiny.
So I set out some larger beads for the students who don't quite have those motor skills developed well enough.
The children LOVED the beads, and I was surprised at how many children tried it and worked REALLY hard to make these little beads work. What GREAT eye-hand-coordination!!
We also had some great math going on too.....check out the red/white pattern figured out all by herself!!
I'm a proud teacher!!


Keeping the “A” in STE(A)M
Please join us at Plains Art Museum’s next gathering in the Art & Business Breakfast series. This innovative program brings Fargo-Moorhead-West Fargo artists together with business and cultural leaders. Through presentations, conversations, and activities, we explore the connections art and business share.
STEM appears in 2005 when two US House members “set up the Science, Technology, Engineering, and Math, or STEM, caucus” in Congress. A few more mentions of STEM appear in 2006. And by 2008, STEM is making headlines. STEAM—the addition of ART—arrived around 2010-2011. But why has it been so difficult for the “A” to stay in STEM? What will it take keep it there? Join us as Lisa Parrish tells us why and how.
Parrish is founder of Musical Bridges, a Fargo-Moorhead based organization that connects cultures through music, uses STEAM concepts by relating Science, Technology, Engineering, Art, and Math to one another, demonstrating that the whole is stronger than its parts.
Registration required for this FREE event, generously sponsored by Heartland Trust Company.


We present the digital future of mathematics education! Our app Maphi makes learning mathematics a fun and painless experience. Maphi intelligently adapts to each ...
Edutapps is a german EdTech-Start-up. The founders are promoted by the Exist-Scholarship by the European Union and the German Federal Ministry for Economic Affairs and Energy.The app Maphi makes learning mathematics a fun and painless experience. The complementary App Maphi Classroom allows the seamless integration of Maphi into classroom environment and provides the teacher with advanced control, homework and supervision features.
Weender Landstr. 3-7
Topic: didacta DIGITAL
Hall 13, Stand C83


The central segment of the measurement model uses a series of cross-correlation calculations as shown in the equation below. This function essentially measures the similarity of two signals.
- where x and y are the two signals whose correlation is to be measured
- t1 and t2 are the period over which the correlation is measured
- and τ is an offset between the two signals under measurement
- (adapted from [Ifeachor and Jervis 1993])
This equation may be applied to any two signals, though for the purpose of our measurement model it is employed to analyse a pair of binaural signals (the signals that reach the ears of a listener or a head and torso simulator as discussed previously
). In this case, τ is usually measured over a range that is large enough to encompass the maximum interaural time difference that is caused by the physical separation of human ears, typically ±1 ms, though this can be specified in the measurement model.
The final output value is then commonly taken to be the maximum absolute value across the range of τ. However, we tend to use the maximum value, not the maximum absolute value for two reasons. Firstly, we believe that positive and negative output values relate to different perceived attributes and using the absolute value causes this difference to be lost. Secondly, the use of half-wave rectification as described previously
causes the range of results from the measurement to be between 0 and 1, meaning that the absolute and raw value maxima will be identical.
Also useful is the fact that the value of τ of the maxima relates to the interaural time difference of the sound. This can be used to predict the perceived location of the sound, though is not a full model of the perceptual process of localisation.
Both the maximum value of the calculation and the related value of τ are passed on for further processing in the measurement model.


Good maths and English skills are essential in daily life. Every job requires the ability to read, write and use numbers with confidence.
At Coleg Cambria, we are committed to helping your develop these skills and secure vital qualifications that will put you on the path to career and life success.
These free courses in maths and English are designed to inspire you to improve your current maths and English skills and help you to remember any areas that you may have forgotten.
Please select an option to access:
I am outside of the College network
I am inside the College network×
Comments or Suggestions


I’m a huge fan of math tricks, especially when it makes solving complex issues just a little bit easier. There’s a great trick that can be used to easily figure out how long it will take compounding interest to double your investment: it’s called The Rule of 72.
This is an easy trick. You simply divide 72 by your interest rate to solve for the number of years that it will take your initial investment to double in value.
Let’s take a look at a few examples. At my credit union the savings account pays 1% interest, so 72 divided by 1 is 72 – it will take an investment of $1,000 (or any amount) 72 years to double at a rate of 1 percent. On the other hand the current rate on the Orange Savings Account at ING Direct is 2.4%. So 72 divided by 2.4 is 30 – or in other words it will take 30 years for my investment to double if I were to place it in the Orange Savings Account.
See how much of a difference a small percentage increase can make? Let’s really have some fun with this now. If you could manage a return of 10% annually you could double your initial investment in 7.2 years! Or if you could manage a return of 15% you would be able to double your investment in 4.8 years!
The Rule of 72 can also be used to calculate a interest rate you’ll need to double your money in a certain amount of years. For example let’s say you want to double your money in 3 years. So divide 72 by 3 and you’ll come up with 24, which means you’ll need to earn a return of 24% in order to double your money in 3 years.


There is no any statistician that calculates standard deviation by hand in the real world. No doubt that its calculations are complex, and the risks of making the mistakes are too high. Suppose you want to reduce the chances of making mistakes in calculations. In that case, you can use the standard deviation calculator that can assist you in finding the standard deviation by a stepwise calculation. Because of its complexities, statisticians depend on spreadsheets & computer programs to determine their numbers. But if you want to understand the step-side procedure of determining the standard deviation, then go down.
What is Standard Deviation:
The standard deviation is a statistic, which finds the dispersion of the data-set relative to its mean. It is calculated by having a square root of the variance by finding data-set points relative to the mean. If the data points are further compared to the mean, then the deviation is higher within the limits of the data set.
You can say that the more the data spread out, the higher the standard deviation. Sometimes it becomes so challenging to determine S.D, but you have to worry now. You can use the online free standard deviation generator tool. The deviation generator helps you find the standard deviation, and this standard deviation calculator also measures the volatility or variability of the given data set.
How Does the Standard Deviation Relate to Six Sigma?
Before moving toward the calculation steps, it is imperative to understand the standard deviation. The deviation for the given data is also known as Sigma, which is represented by “σ”. The Sigma is considered a method in which the goal is to limit defects to the six sigma. And three of the sigma are above from mean, and the rest of the others are below the mean.
Anything beyond these limits requires some improvements. The improvements are because the three standard deviations contain about 99.9 percent of the data set. Six Sigma requires continuous refinement for considering the improvements, which fall within the 0.2 percent in the set. Don’t worry about the complex calculations for standard deviations. Use the standard deviation variance that tells how many standard deviations are there in the data sem, its sum, means, variance, coefficient of variance, and standard error of the mean.
How to Calculate Standard Deviation by Six-Step Method
You can use the two different formulas for its calculations. One of them is for determining the population data, and the other can be used to calculate the sample data. Using the formulas totally depends on analyzing the population data, which can either be sigma “σ” or estimating the population S.D from the sample data that is called s. Sometimes, it gets harder to calculate the deviation for the given data set, even when using the formulas for its calculations. Anyhow, you have the option to use the standard deviation calculator that lets you know how many deviations are present in a data set along with its step-by-step calculations.
Have a look at the below-listed steps for understanding how to calculate the standard deviation.
- First, you need to find μ by using the formula . In this step, calculate the mean for the set of data that is expressed as μ.
- Now, simplify ∣x-μ∣2 in the formula. To simplify the upper section of the formula, we find the distance at each point to the mean and then square each distance.
- After square distance values, add the four values that you find in step # 2.
- Now, divide the result that comes out in the 3rd step by adding the distances by the variable N. Here, “N” represents the total numbers of observations or data points.
- We are almost done, but you just need to square root the answer that we get in the previous step.
- After completing the procedure, recheck each calculation step to ensure the accuracy of the resultant value.
Instead of using the formulas for determining the standard deviation, you can consider the standard deviation calculator to make the calculation easier.
What Does Standard Deviation Tell You?
The standard deviation is a beneficial calculation of spread for the normal distribution. In this type of distribution, the data is symmetrically arranged with no skew. Most of the values are spread around the central region, along with the values tapering off as they go further away from the central point. It tells you how the data on average, is spread out from the center of the normal distribution.
There are many scientific variables that follow the normal distribution. It includes the variables like height, job satisfaction ratings, and standardized tests. If you have the standard deviations of different samples, you can compare the distributions using the statistical test to create inferences regarding large populations. It is possible that you might face a few complications during its calculation. In that situation, you can give try the standard deviation calculator for the calculations.
The Empirical Rule:
The standard deviation & the mean of the normal distribution tells you at which point most values appear in your distribution. The empirical rule lets you know that where the values fall. This rule is considered a quick way to get an overview of your data distribution and check whether the extreme values are following this pattern or not. For the non-normal distribution, the standard deviations are less appropriate for measuring variability. It can also be used in combination along with the other measuring values, such as range or interquartile range.
In this guidepost, we discussed standard deviation and the steps of calculation by using its standard formula briefly. We also mentioned what it tells us by describing the empirical rule. There is no doubt that step-by-step manual analysis for standard deviation is time-consuming and complex also. However, you can get rid of this issue by using the online standard deviation calculator free tool. On the other hand, if you want to do a manual analysis of normal distribution values, then this post will surely help you.


Today is April 15, 2017. Just recently I decided that I would build a green house. I made this decision after years of my vegetables getting rained out or ruined by a late frost. In the process, I wound up finding an answer to a question about music that has long been at the back of my mind.
When and by whom was music theory and musical instruments created?
The plans for my green house were being negotiated. I looked at dozens of pages online for ideas and decided it would be a hoop type. The dimensions would be 20 X 12.
This is where it all began, the revelation. The 20 X 12 dimension of the green house is a rectangle of course. So, how do I layout the rectangle in my yard so it is perfect and not out of proportion? I went back to google to begin my search. It did not take long to find my answer. The page I was on says this is very simple. The “Pythagoras Theorem” is how this is done. By squaring two sides of the rectangle, adding them and then calculating the square root of the sum will get the dimension of the diagonal distance. When laying out your rectangle if you get the diagonal distance correct, you have perfect rectangle.
The question now answered on how to create an accurate rectangle, another question arises. What or who is Pythagoras?
Pythagoras is the father of music and harmonics. He was a Greek philosopher, mathematician, astronomer and much more.
Born in 569 BC in Samos, Ionia Died: about 475 BC. His accomplishments are vast. All this time, I had no knowledge of this man, his connection to music and all his other discoveries and there he was right in my garden. There is a lot of documentation on his life and discoveries.. I would like to share…..