The children at St Matthews loved the Magical Maths performed today in assembly! Please sign up for the Magical Maths After School Club if they would like to explore the world of Magical Maths further!
Our children and parents enjoyed sharing the work that we do in our arithmetic lessons over a coffee and croissant. Thanks to everyone for making it such a success.
Our first café of the New Year got off to a fabulous start. Parents, brothers and sisters joined us to find out about the challenge of our maths sessions in school.
St Matthew’s opened its doors on 28th January to host a Y5 & Y6 Maths Café. Pupils, parents and siblings attended the café where refreshments and croissants were enjoyed over a puzzle or 2! The Y5 pupils used formal written


The most important thing when dealing with investment returns is to bear in mind that what is measured are past returns and that it is very unlikely that the past will be ever repeated in the future.
From a calculation point of view, it is important to keep in mind that investment returns are nothing more than growth rates of the capital invested over a certain time period expressed as a percent figure.
The rate of return can be calculated over a single period, or expressed as an average over multiple periods of time.
Average Return (Arithmetic Mean)
A simple average return is calculated by summing the returns for each period and dividing the total by the number of periods. The simple average return does not consider the compounding effect of returns. Because it does not take into account the compounding effect, average returns are the best tool for calculating an expected return over short periods of time.
N = number of periods and Ri is the return for period i.
The arithmetic return for a given period is the
Logarithmic or continuously compounded return
The logarithmic return or continuously compounded return for a given period is defined as:
Geometric average rate of return
The periodic average return that assumes the same return every period that results in the equivalent compound growth rate. The geometric return is the best tool for calculating an expected return over a long-term investment horizon
Geometric average rate of return, also known as the True Time-Weighted Rate of Return, over ‘n’ periods is defined as:
Compound Annual Growth Rate – CAGR
The CAGR is defined as the year-over-year growth rate of an investment over a specified period of time.
The compound annual growth rate is calculated by taking the nth root of the total percentage growth rate, where ‘N’ is the number of years in the period being considered. This can be written as follows:
Investors can compare the CAGR in order to evaluate how well one investment performed against other investment in a peer group or against a market index. The CAGR can also be used to compare the historical returns of stocks to bonds or a portfolio. But the CAGR does not reflect investment risk, it smooth out the return thus hiding the volatility.
Standard deviation is a widely used measurement of variability or diversity used in statistics and probability theory. It shows how much variation or “dispersion” there is from the average (mean, or expected value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
Where σ stands for standard deviation, is the observed values of the sample items and is the mean value of these observations.
The significance of standard deviation is that two-third of the times the annual return of the asset lies between +1 SD and -1 SD from mean, 95% of time lies between +2 SD and -2SD and 99% of time lies between +3 SD and -3 SD in a normal distribution.
The standard error is a method of measurement or estimation of the standard deviation of the sampling data associated with the estimation method. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate.
The standard error of the mean (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population. Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analyzed at the time.
Where, σ is the standard deviation of the population.
The smaller the standard error, the more representative the sample will be of the overall population. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.
Coefficient of Variation
The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from each other. It is also known as unitized risk or the variation coefficient. The absolute value of the CV is sometimes known as relative standard deviation (RSD), which is expressed as a percentage.
The coefficient of variation (CV) is defined as the ratio of the standard deviation σ to the mean µ.
It shows the extent of variability in relation to mean of the population.
In the investing world, the coefficient of variation allows you to determine how much volatility (risk) you are assuming in comparison to the amount of return you can expect from your investment. That is, lower the ratio of standard deviation to mean, better the risk-return trade-off.
Skewness is a term in statistics used to describe asymmetry from the normal distribution in a set of statistical data. When data is skewed to the right, the mean and the median of the set are both greater than the mode. Further, the mean is greater than the median in most cases. Conversely, when data is skewed to the left, the mean and the median are both less than the mode. In addition, as a rule, the mean is less than the median.
Positive skewness = Mode < Median < Arithmethic Mean, Negative Skewness = Mode > Median > Arithmethic Mean, Symmetrical = Arithmetic Mean = Median
The ratio of the third central moment to the cube of the standard deviation is called Pearson’s moment coefficient of skewness (or the coefficient of skewness) and is denoted by γ or g.
m3 = ∑(x−x̄)3 / n and m2 = ∑(x−x̄)2 / n
is the mean and n is the sample size, as usual. m3 is called the third moment of the distribution. m2 is the second moment of the distribution, that is, variance – the square of the standard deviation.
If skewness is positive, the returns are positively skewed or skewed right, meaning that the right tail of the distribution is longer than the left. If skewness is negative, the returns are negatively skewed or skewed left, meaning that the left tail is longer.
The other common measure of shape is called the kurtosis. As skewness involves the third moment of the distribution of statistical data, kurtosis involves the fourth moment. The classical interpretation of Kurtosis is that it measures both peakedness and tail heaviness of a distribution.
The reference standard is a normal distribution, which has a kurtosis of 3. In token of this, often the excess kurtosis is presented: excess kurtosis is simply kurtosis − 3.
- A normal distribution has kurtosis exactly 3 (excess kurtosis exactly 0). Any distribution with kurtosis ≈3 (excess ≈0) is called mesokurtic.
- A distribution with kurtosis less than 3 (excess kurtosis <0) is called platykurtic. Compared to a normal distribution, its tails are shorter and thinner, and often its central peak is lower and broader.
- A distribution with kurtosis more than 3 (excess kurtosis >0) is called leptokurtic. Compared to a normal distribution, its tails are longer and fatter, and often its central peak is higher and sharper.
The coefficient of kurtosis of a distribution is the ratio of the fourth central moment to the fourth power of the standard deviation.
m4= ∑(x−x̄)4 / n and m2 = ∑(x−x̄)2 / n
m4 is called the fourth moment of the data set. m2 is the variance, the square of the standard deviation. xi is the ith value, and is the sample mean.
The smallest possible kurtosis is 1 (excess kurtosis −2), and the largest is ∞. For a return distribution a negative excess kurtosis (platykurtic) is prefers over positive excess return (leptokurtic).
In probability theory and statistics, covariance is a measure of how much two variables change together. Variance is a special case of the covariance when the two variables are identical.
A positive covariance means that asset returns move together. A negative covariance means returns move inversely. Possessing financial assets that provide returns and have a high covariance with each other will not provide very much diversification.
Correlation is the degree to which two or more quantities are linearly associated. For two random variables X and Y, the correlation is defined by
Where, σ denotes standard deviation and Cov(X,Y) is the covariance of these two variables.
Correlation is computed into what is known as the correlation coefficient, which ranges between -1 and +1. Perfect positive correlation (a correlation co-efficient of +1) implies that as one security moves, either up or down, the other security will move in lockstep, in the same direction. Alternatively, perfect negative correlation means that if one security moves in either direction the security that is perfectly negatively correlated will move in the opposite direction. If the correlation is 0, the movements of the securities are said to have no correlation; they are completely random.
Coefficient of Determination (R-Squared)
The coefficient of determination is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.
With a value of 0 to 1, the coefficient of determination is calculated as the square of the correlation coefficient (R) between the dependent and the independent variable.
This measure represents the percentage of an investment movement that can be explained by movement in a benchmark index.
The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return (or risk premium) per unit of risk in a security or portfolio, named after William Forsyth Sharpe. It is defined as
where R is the security or portfolio return, Rf is the return on a risk-free asset, E[R − Rf] is the expected value of the excess of the investment return over the risk-free return, and σ is the standard deviation of the excess of the investment return.
The Sharpe ratio is used to characterize how well the return of a security or portfolio compensates the investor for the risk taken, the higher the Sharpe ratios number the better.
Like the Sharpe Ratio, the Treynor Ratio (sometimes called Reward-to-Variability-Ratio) is a measurement of the returns earned in excess of that which could have been earned on a security or portfolio that has no diversifiable risk (e.g., Treasury Bills or a completely diversified portfolio), per each unit of market risk assumed.
The Treynor ratio relates excess return over the risk-free rate to the additional risk taken; however, systematic risk is used instead of total risk. The higher the Treynor ratio, the better the performance of the investment under analysis.
R = Portfolio return
Rf = risk free rate
β = Portfolio Beta
Modigliani Risk-Adjusted Performance or M2 or M2 or Modigliani-Modigliani measure or RAP is a risk-adjusted performance measure. It contains the same information as the Sharpe Ratio, but, being a percentage return, is easier to interpret. It measures the returns of a security or portfolio, adjusted for the risk of the security or portfolio, relative to that of some benchmark (e.g., the market).
Di be the excess return of the security or portfolio (i.e., above the risk-free rate) for some period i.
It also defined a statistic called “RAPA” (Risk Adjusted Performance Alpha). Consistent with the more common terminology of M2, this would be:
Where, = Standard Deviation of Benchmark.
The beta coefficient is a key parameter in the capital asset pricing model (CAPM). Beta is that element of return variability from a portfolio which cannot be eliminated through diversification relative to one or several risk factors. It comprises the risk factors common to all assets in the investment universe. That’s why it is also the measure of systematic Risk.
Beta expresses the ‘sensitivity’ of the portfolio relative to the ‘market’. By definition, the “market” has a beta of 1.0. A portfolio that swings more than the market over time has a beta above 1.0. If a portfolio moves less than the market, the portfolios’ beta is less than 1.0. High-beta portfolios are supposed to be riskier but provide a potential for higher returns; low-beta portfolios pose less risk but also lower returns.
Where β is Beta, is the volatility of the portfolio, ρ is the correlation of returns of portfolio and the market and is market volatility.
Jensen’s alpha (or Jensen’s Performance Index, ex-post alpha) is used to determine the return of a security or portfolio of securities over and above the theoretical expected return. The security could be any asset, such as stocks, bonds, or derivatives. The theoretical return is predicted by a market model, most commonly the Capital Asset Pricing Model (CAPM) model. The market model uses statistical methods to predict the appropriate risk-adjusted return of an asset. The CAPM for instance uses beta as a multiplier.
In the context of CAPM, calculating alpha requires the following inputs:
Jensen’s alpha = Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)]
Tracking error is a measure of how closely a portfolio follows the index to which it is benchmarked. The most common measure is the root-mean-square of the difference between the portfolio and index returns
Where [Rp – RB] is the difference between the portfolio return and the benchmark return.
‘Var’ means variance and ‘SD’ stands for standard deviation.
Tracking Error of a portfolio constantly underperforming its benchmark is zero, for example, and therefore hardly a desirable result.
The Information Ratio (also known as Appraisal Ratio) is basically a risk-adjustment of Alpha. It measures the Alpha per unit of active risk, i.e. tracking error. It is defined as expected active return divided by tracking error, where active return is the difference between the return of the security and the return of a selected benchmark index, and tracking error is the standard deviation of the active return.
is the portfolio return, is the benchmark return
α = Active Return
ω= the standard deviation of the active return
Up and Down Capture Ratio
Up & down capture ratio show you whether a given security or portfolio has outperformed – gained more or lost less than – a broad market benchmark during periods of market strength and weakness, and if so, by how much.
The Up Capture Ratio measures the security or portfolio compound return when the benchmark return increased, divided by the benchmark’s compound return when the benchmark return increased. The higher the value, the better.
Ri are the fund returns when the benchmark returns are greater than or equal to zero
Bi are the benchmark returns when the benchmark returns are greater than or equal to zero
The Down Capture Ratio measures the security or portfolio compound return when the benchmark was down divided by the benchmark’s compound return when the benchmark was down. The smaller the value, the better.
Ri are the fund returns when the benchmark returns are less than zero
Bi are the benchmark returns when the benchmark returns are less than zero
A value of 100% for either ratio implies that the security or portfolio fully captures, or matches, the benchmark return during the period evaluated. A value of greater than 100% indicates that the security or portfolio captured more return than the benchmark (this is a positive for up-capture, however, a negative for down-capture). A value less than 100% means the security or portfolio captured less return than its benchmark (this is a negative for up-capture, however, a positive for down-capture).
Semi Variance (below-mean)
A measure of the dispersion of all observations that fall below the mean or target value of a data set. Semi variance is an average of the squared deviations of values that are less than the mean or target value.
n = the total number of observations below the mean
x = the observed value
= the mean value of the data set
Similarly, Semi volatility is defined as the volatility of returns below the mean return.
Downside Deviation/ Downside volatility/ Downside Risk
Downside volatility takes into account only those values of observed excess rates of return that lie below minimum acceptable return (MAR). In other words, Downside volatility is a generalization of the semi volatility as is defined as volatility below MAR.
Average Downside Deviation indicates the average size of the unacceptable returns. This statistic helps an investor judge the severity of the average ‘bad’ return. An investment that lost money twice as often as a second investment may still be preferable if it tended to lose far less than the second investment.
Downside Magnitude at the 99th Percentile
This is a worst-case scenario. An investment may lose money only occasionally, may average small losses when they do occur, and yet may prove unacceptable if the potential exists for huge losses. Downside Magnitude 99th Percentile answers the question: “When an investment is below the MAR, what is the worst case scenario?”
Lower Partial Moments
This measure of downside risk is colloquially known as “downside risk.” The main idea of the lower partial moment framework is to model moments of asset returns that fall below a minimum acceptable level of return.
LPM simply examines the moment of degree ‘a’ below a certain threshold ‘t’.
a = order of the lower partial moment
t = target return (Minimum accepted return)
LPM is a family of risk measures specified by ‘t’ and ‘a’. ‘T’ is often set to the risk free rate or simply to zero. By choosing the degree of the moment an investor can specify the measure to suit his risk aversion. Intuitively, large values of ‘a’ will penalize large deviations more than low values. Semi variance is a special case of LPM for which the degree of the moment is set to two.
Downside Potential/ Downside Factor
The possibility of making a loss in an investment
Downside variance eliminates positive returns when calculating risk. Instead of using the mean return or zero, measures the variability (volatility) from the Minimum Acceptable Return.
The Sortino ratio measures the risk-adjusted return of an investment and is similar to the Sharpe ratio, except it uses downside deviation for the denominator instead of Standard Deviation (SD). Standard deviation involves both the upward as well as the downward volatility. Whereas Downside Deviation only concerned about the volatility below MAR. The numerator is the excess return with respect to a Minimum Accepted Return (MAR) fixed by the investor.
R = Return of a security or portfolio
MAR = target return (Minimum accepted return)
DD = Downside Deviation
Downside Probability/ Downside Frequency
Likelihood or frequency of failure.
It calculates the probability that the portfolio would not achieved the target return (MAR).
While higher figure is considered bad, lower figure is considered favourable.
Downside frequency tells the user how often the returns violated the MAR (minimum acceptable return). This is important because in order to assess the likelihood of a bad outcome you need to know how often one occurred.
The chance that an investment return will equal or exceed the target return (MAR).
The opposite of downside probability is Upside Probability. Upside probability is how often the investment exceeded the MAR.
The average return above the target return (MAR), measuring how often and how far above the target return (MAR) a portfolio’s returns are likely to occur. Upside Potential, a term coined by Nobel Prize winner Daniel Kahneman, captures investors’ perception of risks concerning gains as opposed to risk concerning losses.
Upside Potential Ratio (U-P Ratio)
The ratio of Upside Potential to Downside Deviation at a given MAR, measuring how much upside potential is provided by a manager at a given level of downside risk.
The Omega Ratio is a risk-return performance measure of an investment. It is used to measure investment performance relative to a benchmark and also against an acceptable threshold level (MAR). Simply put, the Omega measure is a ratio of probability weighted returns above the MAR level to probability weighted returns below the MAR level.
The upside potential divided by the downside potential for a pre-defined MAR to produce a quality rating for the investment based on all return data in the period.
Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period and is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.
Maximum drawdown is highly dependent on the time interval chosen (annual, monthly, daily and so on) as well as the observation period.
P = Peak value before largest drop
L = Lowest value before new high established
Preservation of capital and a steady performance are important considerations in investing. Therefore, the maximum drawdown is highly relevant. A drawdown is measured from the time a retrenchment begins to when a new high is reached. This method is used because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the new trough is recorded.


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Even before the play starts, the audience are already grappling with the maths of finding their seats, amidst the rows of ascending or descending numbers, which is actually a kind of arithmetic progression. On a normal day, that may be the maximum amount of maths a theatregoer would encounter. But today, one of the protagonists of A Disappearing Number, Ruth Minnen (played by Koh Wan Ching) proceeds to give a lecture on her whiteboard, starting with the most basic of all arithmetic series: 1 + 2 + 3 + 4 + 5 + …
The theatre groans expectedly. Some laugh nervously. The mathematicians grin expectantly. As a maths major, I couldn’t wait to get beyond the maths to see how the maths plays out in the narrative – how would maths pan out in theatre?
A Disappearing Number is originally conceived and directed by Simon McBurney and devised by the original company of Complicité. Tonight, we are watching the version directed by Edith Podesta, with the cast comprising Koh, Pavan J Singh and Remesh Panicker, along with students from NUS Stage. This is the second production I’ve watched that is directed by Podesta, both coincidentally involving students. (The last one being Kaspar by NAFA students.) The story goes like this in the synopsis: In 1913, a clerk in rural India named Srinivasa Ramanujan sends a letter listing astonishing theorems to famed mathematician G. H. Hardy. In the present, Ruth, a math professor (played by Koh), and Al, a businessman (played by Pavan), fall in love over the concept of infinity.
Essentially, an equation is a relationship between two or more quantities. In A Disappearing Number, the director deals with sets and subsets of relationships, demanding us to juxtapose them side-by-side, or to see the symmetry and patterns between them.
The stage work is poetic to watch most of the time. In a bedroom scene with Ruth and Al deep in discussion, a series of snapshots showing moments of interaction between them, creates an illusion of infinity into a faraway convergent point. The multimedia (helmed by Brian Gothong Tan) seems to forebode the increasing infinite distance between the couple, likened to the infinite number of decimals in between two whole numbers. In fact, throughout the play, the director seems prudent in ensuring the twining of mathematical concepts and the plot. Just before Ruth announces her pregnancy to Al, they recall the lecture where Ruth illustrates how an infinite series can converge to 2; when Ruth insists on travelling to India on a Ramanujan pilgrimage and got into a squabble with Al, we recall a lecture explaining ‘asymptote’ as getting very close to but never arriving at, somewhat like the idea of ‘so near yet so far’. The use of ‘asymptote’ here forebodes Ruth’s not being able to get to Ramanujan, and Al never reaching Ruth. That perhaps explains why for most parts of the story, Al spends it with the ghost of Ruth, and Ruth with the ghost of Ramanujan.
Essentially, the play explores the emotions and relationships between two parties, but it does not come across clearly or strongly. For instance, the rare friendship forged between Ramanujan and Hardy is often obscured, like the many screens that hides Ramanujan in the background as his story is told. The feigned accented excitement in the voice of the actor playing Hardy only accentuates his selfishness to possess Ramanujan, rather than portray warmth and care for his friend. The story and staging tells less of how they became buddies, but more of the theorems that Hardy could extract from Ramanujan. I also could not feel emotionally invested for Ruth and Al’s failed relationship. It seems that the issues they grapple with as a couple are loudly announced and quickly glossed over. Al’s love for Ruth and Ruth’s infatuation for Ramanujan do not go beyond the superficial attraction to the mystery of the infinity concept. We see the maths in their daily interactions, but we don’t see the life stemming from maths.
Nevertheless, it has been an enjoyable evening for me, to see something familiar again, to be reacquainted with maths, and see it play a part in the stories people want to tell. Tan’s multimedia might have been distracting for some, but I think it plays out beautifully, visualising the abstract maths on stage in objects, images and mechanical movements. I also became a fan of Podesta’s work after seeing her treatment of text in Kaspar. Although this rendition of A Disappearing Number adheres closely to the original staging, I enjoy the director’s vision of the equations and nested repetitions.
A Disappearing Number
by NUS Stage, directed by Edith Podesta
Date: 15 Mar 2019
Venue: University Cultural Centre Hall
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The test scores prove that the faculty, staff and parents are doing something right.
The average test score of students in New York City was 29.6 percent at or above proficient in math and 26.5 percent at or above proficient in English Language Arts (ELA), with state scores averaging 31 percent in math and 31.1 in ELA.
The students of P.S. 122 scored 71 percent at or above proficient in math and 69.7 percent at or above proficient in ELA.
“It’s ironic that the city wanted to make major changes at this school a few months ago, and now these kids have blown away the city averages,” said Councilman Peter Vallone, Jr. “These scores are a testament to the teachers students and parents, and they prove that the program at P.S. 122 needs to be mirrored in schools across the city.”
Vallone presented the students, teachers and Principal Pamela Sabel with a City Council Citation in recognition of the school’s achievement.
“Everyone works very hard,” said Sabel. “We always have the highest expectations for our students and set high goals.”
Sabel said success at the school begins with its robust curriculum.
“A quality education is a well-rounded education,” she said. “It’s not all about test preparation.”


School of Mathematics
The 31st series of the Royal Institution Mathematics Masterclasses for young people in North-West Wales
will commence on January 10th, 2015, and will finish on March 7th with the presentation of certificates.
The Masterclasses are supported in 2015 by:
Visit the full News and Events page.
Having been a Department of Mathematics; then separate Departments of Pure and Applied Mathematics; and later a School of Mathematics; it's final form was as the Mathematics Division in the School of Informatics.
When the University was reorganised into Colleges in August 2006, what was left of Mathematics became part of the new School of Computer Science. The final cohort of Mathematics graduates obtained their degrees in July 2007.
When Mathematics was closed, the university expressed the hope that this was a temporary measure. The new vice-chancellor, Prof. John Hughes, has stated his firm intention to resurrect the School of Mathematics in due course.
A number of retired staff retain honorary research positions, and this site aims to be an archive of past and current research.


BMR Basal Metabolic Rate—The rate at which the body at rest uses energy (calories) to maintain vital functions, such as breathing. You can configure your BMR using the MIFFLIN ST. JEOR Equation. Female BMR = (10 × weight in kg) + (6.25 × height in cm) - (5 × age in years) - 161. *Of four equations tested, the Mifflin-St Jeor equation is more likely to estimate BMR to within 10% of that measured. Please note that this is a general equation and should be used as a ball park figure.
TDEE Total Daily Energy Expenditure—The number of actual calories used by the body in one twenty-four hour period for all activities and vital functions. This is your BMR plus whatever energy you expend during exercise and activity. TDEE (or TEE) results in more efficient tool for weight loss and management.
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CONTROL EQUASION = 41, 5'1", 105 lbs. BMR = 1081
Female BMR = (10 × weight in kg) + (6.25 × height in cm) - (5 × age in years) - 161
105 lbs = 47.6272 kilograms ( formula divide the mass value by 2.205 )
5'1" = 154.94 centimeters ( formula -> take the inches and multiply them by 0.08333333 THEN add the feet = 5.08333333 ( multiply the length (5.08333333) value by 30.48 )
41 = 41
FIRST CALCULATION ( weight ) -> 47.6272 x 10 = 476.272
SECOND CALCULATION ( height ) -> 6.25 x 154.94 = 968.375
THIRD CALCULATION ( age ) -> 41 x 5 = 205
ALL TOGETHER NOW -> 476.272 + 968.375 - 205 - 161 = 1078.647
TIMES ACTIVITY -> 1078.647 x 1.2 = 1294.3764
weight = lbs = 0kg
feet_and_inches = 0
centimeters = 0
BMR = -161;
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The biggest mathematical mystery in nature—Fibonacci numbers! Named after a famous mathematician, the number pattern is simple: 1, 1, 2, 3, 5, 8, 13. . . . Each number in the sequence comes from adding the two numbers before it. What's the mystery? The pattern crops up in the most unexpected places. You'll find it in the disk of a sunflower, the skin of a pineapple, and the spiral of a nautilus shell. No one knows how nature came up with the sequence. Sarah C. and Richard P. Campbell introduce the Fibonacci sequence through a series of stunning photographs in this ALA Notable Children's Book. Young readers will soon be seeing nature through new eyes, looking for Fibonacci numbers in daisies, pinecones, leaf patterns, seashells, and more.
About the Author
Sarah C. Campbell is the author of the Theodor Seuss Geisel Honor book Wolfsnail: A Backyard Predator. Her writing has appeared in a variety of publications, including Highlights for Children and the New York Times. She lives in Jackson, Mississippi.
Richard P. Campbell is co-photographer of the acclaimed children's nonfiction book Wolfsnail: A Backyard Predator. He lives in Jackson, Mississippi.
"Invaluable for visual learners." —Publishers Weekly
"Another beautiful photo-essay by the creators of Wolfsnail (2008). . . . Will be welcomed in elementary classrooms. (more about Fibonacci numbers, glossary)" —Kirkus Reviews
"Math teachers will appreciate the clarity of presentation, and the appended glossary and related miscellanea. Children who are ready to move beyond counting books and into brain-tickling areas of mathematics will welcome this introduction." —Bulletin of the Center for Children's Books


Main concepts of fuzzy geometry were introduced by Tim Poston in ,  A. The submitting author is responsible for securing any permissions needed for the reuse of copyrighted materials included in the manuscript. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Syst. The interrelation among these concepts and also their relations with the parallel existing concepts are established. By using the comment function on degruyter.
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42nd IMO 2001
A1. ABC is acute-angled. O is its circumcenter. X is the foot of the perpendicular from A to BC. Angle C = angle B + 30o. Prove that angle A + angle COX < 90o.
A2. a, b, c are positive reals. Let a’ = v(a2 + 8bc), b’ = v(b2 + 8ca), c’ = v(c2 + 8ab). Prove that a/a’ + b/b’ + c/c’ = 1.
A3. Integers are placed in each of the 441 cells of a 21 x 21 array. Each row and each column has at most 6 different integers in it. Prove that some integer is in at least 3 rows and at least 3 columns.
B1. Let n1, n2, … , nm be integers where m is odd. Let x = (x1, … , xm) denote a permutation of the integers 1, 2, … , m. Let f(x) = x1n1 + x2n2 + … + xmnm. Show that for some distinct permutations a, b the difference f(a) – f(b) is a multiple of m!.
B2. ABC is a triangle. X lies on BC and AX bisects angle A. Y lies on CA and BY bisects angle B. Angle A is 60o. AB + BX = AY + YB. Find all possible values for angle B.
B3. K > L > M > N are positive integers such that KM + LN = (K + L – M + N)(-K + L + M + N). Prove that KL + MN is composite.


If you are new to betting exchange sites, the first thing you will need is an explanation of how betting odds operate and how to understand betting odds.
Once you understand them, betting odds may help you determine how likely a result is and calculate your possible earnings. Odds tell us the probability of an outcome, which you can use to help you decide what to stake on that result.
Despite their intimidating appearance, they are straightforward to grasp once you apply some basic arithmetic. Below, we will go through them, with an example or two for each type, using an easy-to-understand stake and some simple probability maths.
What are Betting Odds?
Bookmakers employ betting odds to indicate the likelihood of a given result in an event. They calculate the probability that an event will happen and then adjust the potential winnings of a successful bet accordingly.
They are commonly expressed as fractions (2/1, for example) or decimals (3.0), but they can also be expressed with a plus or negative sign in front of a number (+200, for example), which is known as a moneyline or American odds. Betting markets may frequently supply you with many outcomes for any particular occurrence.
Betting odds, in addition to displaying probability, assist customers in calculating their possible rewards from a stake.
How do betting Odds Work?
Essentially, betting odds describe the probability of a result and are usually given in fractional or decimal form.
That depiction then informs us how much we might win from our stake if that particular scenario occurs as the outcome of a given event.
Learning to read odds is important if you want to know which bets are sensible to stake on! It might look intimidating now, but it all makes sense once you get used to reading odds.
How to Read Betting Odds
Understanding betting odds is crucial if you want to have a successful betting career. The good news is that reading odds is not difficult, and the maths is not too difficult. The odds vary in each country, but we will concentrate on a few important sorts: decimal odds, fractional odds, and American odds. Fractional odds and decimal odds are the preferred format of most bets in the UK.
Fractional Odds Explained
We may calculate our possible gains using fractional odds. The figure on the left reflects the possible profit if we stake the figure on the right.
A £1 wager on Team A to win at 2/1, for example, will earn £3 if successful. The first £2 is profit, and the last £1 represents the bettor’s risk – it is the amount of your initial stake.
Here are a few other examples:
10/1: A profit of £10 for every £1 invested.
5/2: A profit of £5 for every £2 wagered.
4/11: A profit of £4 for every £11 wagered.
The bet is called odds-on when the number on the left-hand side is less than the number on the right-hand side. When the contrary is true, it is called odds-against, and chances of 1/1 are called evens.
Decimal Odds Explained
Decimal odds give us our potential gains, including our original wager. To get the total returns, just multiply the bet by the odds.
A £1 bet on Team A to win at 3.00, for example, will earn £3 if successful. As with the previous bet with fractional odds, £2 of the returns are profit, and £1 is the bettor’s outlay.
Here are a few other examples:
10.00: A £1 bet would yield £10 plus the investment.
2.50: A £4 bet would yield £10, including the investment.
1.50; A £2 bet would yield £3, including the investment.
The decimal equivalent of 1/1 odds is 2.00.
This odds format can take a while to get used to, but understanding decimal odds is one of the most important parts of grasping how betting odds work.
You can bet on a team, a spread, a moneyline, or a total. These are in terms of 100, with a plus or minus for each. This is more common in America – hence the term “American odds”.
American odds are in blocks of 100 because it is a 1:1 ratio, which means that if your bet wins, you will get £1. There will be a mark next to the number. If it is a plus sign, you will win more than £100 on a £100 wager, and if it is a minus sign, you will need to stake more than £100 to win £100.
When you place a moneyline odds bet, you are betting on only one team to win. Assume the clubs are the Browns (+150) and the Steelers (-110). If you put a £100 bet and the Browns win, you will win £150. If the Steelers win, you must wager £110 to receive a £100 payoff from moneyline odds.
Spread betting assigns points to each team that must be met in order for you to win. Assume the odds are +3 for the Browns and -5 for the Steelers. This means that the Browns must win or lose by fewer than three points for you to win, while the Steelers must win by five or more points.
Total bets, commonly known as over/under bets, are wagers on the total number of points scored by both sides. If it states Browns Over 8, you must wager the given amount, and the aggregate score must be more than 8. If it states Steelers Under 8, you must wager the stated amount, and the overall score must be less than 8.
If American odds seem hard to understand, do not worry. You are unlikely to have to use this system in the UK!
Calculating Betting Odds
The bookmaker determines the odds. They will calculate the chances based on their prediction and evaluate the likelihood of an event occurring.
For instance, the chances for a nation winning the World Cup would most likely be around 80/1, indicating both the low likelihood of it happening and the big potential payment a bettor would receive if it did.
In order to be among the first to wager on a particular event of their choice, bettors can request odds on an outcome that is not yet offered by the bookmaker.
If the request is approved, the social media team will forward the bettor’s wishes to the traders upstairs, and the bettor will be able to place bets on their fully tailored odds on the day they requested them before anybody else.
Decimal odds let you know how much, including your deposit, a winning bet will pay you. To calculate your total returns, simply multiply your stake by the odds.
Therefore, if you placed a £1.00 bet on England to win the World Cup at odds of 10.00, you would receive £10.00 back, which would include your original £1.00 bet.
Here are some other examples:
6.00 – A £1 bet would result in a payout of £6.00.
2.50 – A £4 bet would result in £10.00.
1.50 – A £2 bet would result in £3.00.
You can calculate your potential winnings based on fractional odds. If you bet the number on the right, the number on the left represents the amount you stand to gain.
Thus, if you bet £1 on England to win the World Cup at a 9/1 odds and it is a winning bet, you will receive a payout of £9.00. Your initial £1.00 investment will also be returned, giving you a total return of £10.
Here are some other examples:
5/1 – For every £1 you bet, you will receive £5.
6/4 – You will receive £6 for every £4 wagered.
1/2 – For every £2 you bet, you will receive £1.
Comparing Sports Betting Odds in the UK
If you are searching for a place where you can evaluate various odds at once, an online sportsbook is the place to go! Not only will you avoid doing the majority of the maths, but you will also be able to add all of your favourite teams to your watch list.
They should include all of the popular betting options, and you may even gain access to additional features that will enhance your experience! Different firms will offer different choices, so look into them all!
Hopefully, our above example and explanations have given you a good sense of how betting odds work, both decimal odds and fractional odds. With a good understanding of how to read betting odds, how to calculate probability, and what the odds represent, your chances of a successful bet should be much higher, and your potential winnings improved.
Odds might look complicated, but they are actually much more simple than you might think at first glance. Essentially, the odds tell you how likely a certain event is to happen and how much money you could win if it happens. It is just probability maths applied to a practical situation.
The probability of an event happening is important information for anyone who wants to start betting on sports betting, as knowing the chances of a specific outcome can give you a rough idea of your potential profit and how likely you are to lose money, such as if that particular outcome does not happen.
Keep an eye out for customer offers when you gamble, as some sites will give new customers better deals on a certain outcome or stake!
What is Implied probability?
The translation of betting odds into a percentage is known as implied probability. It provides us with an estimate of how likely something is to occur.
The real likelihood of an event occurring is frequently smaller than the inferred probability. This is because betting odds include the bookmaker’s profit margin. Bookmakers provide odds that they feel are lower than the real likelihood of anything occurring. This is how they generate money in the long run.
The implied probability of an event is an important calculation – possibly even more so than the odds displayed on a bookmaker’s website.
We will calculate implied probability from fractional odds of 9/1 in this case.
Simply divide the number on the right by the total of both integers and multiply by 100. The number on the left-hand side is not needed to calculate implied probability.
As a result, if something has fractional odds of 9/1, it has a 10% implied chance.
Here are some more examples.
5.1% is equivalent to 1 divided by 6 times by 100.
40% is equivalent to 6/4 – 4 divided by 10, then multiplied by 100.
66.7% is equivalent to 1/2 – 2 divided by 3, then multiplied by 100.
In this example, we will use decimal odds of 10.00 to determine implied probability.
To do so, divide one by the decimal odds and multiply by 100…
As a result, if something has decimal odds of 10.00, it has a 10% implied chance.
Here are a few more instances.
6.01 divided by 6.00 and multiplied by 100 is 16.7%
40% is equivalent to 2.50 – 1 divided by 2.50 and multiplied by 100.
Are decimal odds or fractional odds better?
If you questioned a normal punter, most would probably prefer fractional odds simply because that is what they are used to betting with. Both odds work well enough, but there are some advantages to each.
While fractional odds are fine in most situations, when it comes to matched betting, decimal odds are the obvious winner. They are considerably easier to compare at a glance, which is crucial in the matched betting procedure. Betting exchanges also display their odds as decimals, so it makes logical sense to use decimal odds in most situations.
How do you convert fractional odds to decimal odds?
In general, you should not need to manually convert fractional odds to decimals. You will instead be able to pick your selection on the bookmaker’s website.
However, here is how it is done, just in case you have to convert fractional odds to decimal odds for any reason.
To convert 6/1 to a decimal, divide the left-hand side number by the right-hand side number and add one.
So 6÷1=6 and 6+1=7.00.
Here are a few more examples:
10/1: 10÷1-10 and 10+1-11.00
6/4: 6÷4=1.5 and 1.5+1=2.50
2/5: 2÷5=0.4 and 0.4+1=1.40
How do you convert decimal odds to fractional odds?
Just like the other way around, you are unlikely to have to convert betting odds from decimal to fractional. Let’s take a look at how to do this, just in case an unexpected situation arises.
To convert decimal odds to fractional odds, multiply by (x – 1.00) and multiply by 1.
6.00 odds, for example, 6.00 – 1.00 = 5.00 = 5/1
As in this more difficult example, you may need to simplify the fraction.
5.50 odds: 5.50 – 1.00 = 5.5/1 = 11/2
Where can I find fixed odds?
Baseball, football, hockey, and horse racing are among the sports with set odds.
What do betting odds mean?
Betting odds are the odds of a given team winning or certain events occurring.
What happens if you place a bet with negative odds?
If you bet on a team with negative odds, the payoff will be smaller than if you bet on a team with positive odds.
What are moneyline odds?
Money line odds, often known as American odds, are popular in, you guessed it, America. They are shown as positive or negative numbers, such as +500 and -200.
You will not need to utilise them for matched betting, but they are worth discussing because you will almost certainly come across them as an option at some time.
A rating of +500 indicates that you will gain £500 for every £100 bet. A -200 number indicates that you must invest £200 in order to win £100.


It’s National Tape Measure Day. As I look at the above picture I realize almost everything we touch, use, or like, has something to do with size. The tape measure, according to whether it is made of flexible metal, plastic or cloth, can tell us the of size a whole lot of things.
People need to know their measurements in order to buy clothing, especially out of a catalog. Men want to know ladies measurements to see if they “measure-up” to their ideal dream lady. Now that’s a sexist comment, but the truth. Ladies want to know how men “measure-up” in all sorts of situations. I’m not sure you can measure those situations with a tape measure, it has more to do with manners and sensitivities.
Builders have to know All the measurements in any building they build, whether it be the size of the doors to be used or the square footage of a closet. Everything has a measurement in the basic planning stages to figure out how much the planned building will cost to build. I know that because that is what my husband does at work. It’s detailed and exact.
I live in potato growing country and machines with varying size screens on conveyor belts are utilized to sort the potatoes. They don’t measure the potatoes individually, but the screens have specific measurements so the smallest fall through first, and then the next size, etc. Different sizes are used for different things.
Being a quilter, I measure the repeat of the design on a fabric. Some patterns call for a specific number of repeats to cut pieces to make a new pictorial. I also have to figure out exact measurements when I put a t-shirt quilt together because all the logos on the shirts are different sizes. In order to make an eye-pleasing mosaic it takes knowledge of the formulas of triangles and patience to get it right. I like the challenge.
This is my great-niece’s high school graduation gift. It’s not yet quilted. You can see the pieces are not all the same size or shape. Rulers help me with all the math, and a tape measure tells me how big the finished quilt is. Yes, I use all that “useless” math I learned in high school. In my life, a tape measure is a must.


3 edition of Hubbard, Intermediate Algebra found in the catalog.
Hubbard, Intermediate Algebra
July 27, 2004
by Houghton Mifflin Company
Written in English
|The Physical Object|
Find many great new & used options and get the best deals for Intermediate Algebra by Elaine Hubbard (, Hardcover) at the best online prices at eBay! Free shipping for many products! intermediate algebra free pdf books. The books listed below are for free. If the link doesn’t work, kindly report the book with the broken link through this form.
Elaine (Elaine Hubbard) Hubbard, Elaine Hubbard, Joel D. Hubbard Student Solutions Manual for Hubbard's Intermediate Algebra: Discovery and Visualization, 3rd 3rd Edition 0 Problems solved. Note: If you're looking for a free download links of Intermediate Algebra for College Students (6th Edition) Pdf, epub, docx and torrent then this site is not for you. only do ebook promotions online and we does not distribute any free download of ebook on this site.
Step-by-step solutions to all your Algebra homework questions Step-by-step solutions to all your questions SEARCH SEARCH. SUBJECTS. upper level math. high school math. science. social sciences. literature and english. foreign languages. other. Abstract algebra Algebra Algebra Textbook Solutions. x. Go. Don't see your book? Search by. Ronald D. Robinson is the author of Prealgebra ( avg rating, 0 ratings, 0 reviews, published ), Intermediate Algebra ( avg rating, 3 ratings, /5(3).
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Overall, a GREAT book for the Intermediate Algebra student. The information is layed out in a very easy to understand manner. Definitely recommend this book for a college student who wants to brush up before taking College Algebra. Would have gotten 5-stars, but the price of the book is s: 1.
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Elementary and Intermediate Algebra 2nd Edition by Elaine Hubbard (Author), Ronald Robinson (Author) out of 5 stars 2 ratings. ISBN ISBN Why is ISBN important.
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Textbook Site for: Intermediate Algebra: Discovery and Visualization Third Edition Elaine Hubbard - Kennesaw State University Ronald D. Robinson. Elaine Hubbard is the author of Intermediate Algebra ( avg rating, 3 ratings, 0 reviews, published ), Algebra Hubbard avg rating, 2 ratings, 0 revi /5(6).
This Guide is designed for students using a Texas Instruments TI Plus or TI graphing calculator in conjunction with the textbook Elementary and Intermediate Algebra: Discovery and Visualization, Third Edition, by Hubbard and Robinson.
ACE Practice Tests Take ACE Practice Tests and get your results immediately, to check your understanding. Textbook Site for: Intermediate Algebra: Discovery and Visualization, Third Edition Elaine Hubbard - Kennesaw State University Ronald D. Robinson ACE Practice Tests Click on a section title to take the ACE Practice Test Chapter 1: The Real Number System; The Real Numbers.
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Elementary and Intermediate Algebra: Discovery and Visualization, Third Edition, employs graphing technology as an integral part of a discovery-based learning approach.
This new edition offers expanded coverage of both modeling and data analysis. Developed for a one- Brand: Elaine Hubbard. Open Library is an open, editable library catalog, building towards a web page for every book ever published.
Intermediate algebra by Elaine Hubbard, Ronald D. Robinson,D.C. Heath edition, in EnglishCited by: 1. Intermediate Algebra is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course.
The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Elementary and Intermediate Algebra: Discovery and Visualization by Elaine Hubbard, Ronald Robinson and a great selection of related books, art and collectibles available now at Intermediate Algebra, Custom Publication: Discovery and Visualization by John H.
Hubbard and a great selection of related books, art and collectibles available now at The following PowerPoint slides correspond to chapters of Intermediate Algebra: Discovery and Visualization, Third Edition.
Instructors may download these slides for classroom presentations. Transition Guide This guide provides information to help users of. Pre-Algebra - Fractions Objective: Reduce, add, subtract, multiply, and divide with fractions. Working with fractions is a very important foundation to algebra.
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Beecher, Barbara L Johnson. Sell Elementary and Intermediate Algebra: Discovery and Visualization, by Hubbard, 3rd Edition - ISBN - Ship for free. - Bookbyte. Welcome. If you have a copy of Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, we invite you to write [email protected] with ``calculus book readers'' as the subject, to let us know what math course you are taking, or, if you are not using the book in a formal course, what your connection to mathematics is.
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April 2022 - March 2025 (projected).
University of Hannover
Summer Semester 22: Teaching assistant for second semester analysis and teaching assistant for elementary geometry for special education teachers.
Winter Semester 22/23: Making, presenting and correcting exercises for Riemannian geometry. Presenting calculus exercies to engineering students.
Summer Semester 23: Making and presenting geometry exercises for teacher students.
October 2019-March 2022
University of Oldenburg
Winter Semester 19-20: Teaching assistant for elementary PDEs.
Summer Semester 20: Co-organizing a student seminar in analysis.
Winter Semester 20-21: Teaching assistant for first semester analysis.
Summer Semester 21: Lecturing and solving the exercises for Complex Geometry. Supervising Bachelor thesis. Teaching assistant for second semester analysis.
Winter Semester 2022: Teaching assistant for measure and integration theory.


It was announced recently that Delta Airlines will use the upcoming Surface 2, which has Windows RT 8.1 installed on it, as their tool to replace their current 38 pound flight bags in the cockpit.
Here is the video detailing some of the benefits the electronic flight bag will bring to Delta’s cockpits.
The reason I wanted to share this was to highlight the sheer level of savings this change will bring to Delta as it seems to be a popular discussion point on this video over at YouTube. Many are referring to the 38 pound reference and saying it really does not make any difference in the long run because of future variables such as passengers bringing onboard more stuff, etc.
The reality is that even if passengers do bring more onboard the 38 pound flight bags are not coming onboard as they switch to Surface 2 so the weight savings is a reality.
Just how much of an overall weight savings does this equal up to once they completely shift over to the electronic flight bags?
To do the math we need the figures so lets do this like one of our old math problems we used to get in school.
In the video it is said that the Surface 2 will replace a 38 pound flight bag and that there are over 2,500 flights per day. At least one member of the cockpit crew brings a flight bag and typically both the pilot and co-pilot bring one.
So if we wanted to figure out the overall weight savings per year the equation would look like this:
38 (weight of flight bag) times 2500 (flights per day) times 365 (days in a year) = annual weight savings
38 x 2500 x 365 = 34,675,000
You can round it up and say there is an overall weight savings with this switch of 34.7 million pounds per year.
If both the pilot and co-pilot bring a flight bag onboard then you can multiply that number by a factor of 2. I would say that equates to a significant fuel savings.
Now if the airline would pass that savings along to the customer in lower ticket costs then it can be a Win-Win!


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1 cubic meter is equal to 4226.7528198649 cups, or 1000000 grams. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between cups and grams. Type in your own numbers in the form to convert the units! ›› Quick conversion chart of cups to grams. 1 cups to grams = 236.58824 grams US cup to Gram Conversion Chart - Rolled oats. Note: Fractions are rounded to the nearest 8th fraction. Values are rounded to 3 significant figures. US cups to grams of Rolled oats; 1 US cup = 89.9 grams: 2 US cups = 180 grams: 4 US cups = 360 grams: 5 US cups = 450 grams: 8 US cups = 719 grams: 1 / 16 US cup = 5.62 grams: 1 / 8 US cup . Here you can find the detailed conversions for different types of breakfast cereals such as: All Bran; Bran Flakes; 1.5 oz 1.7 oz. Bran Flakes. amount, in cups (c) ⅛ cup ¼ cup ⅓ cup ⅜ cup ½ cup ⅝ cup ⅔ cup ¾ cup ⅞ cup 1 cup. amount, in grams (g) 5 g 10 g 10. Measuring your ingredients by weight (grams) can help make your ingredient amounts are accurate. It's especially true in baking—think how much flour you can fit in a measuring cup depending on how much you pack it. These charts help you go between cups, grams, and ounces, depending on what your recipe calls for
US cups to grams of Honey; 1 US cup = 340 grams: 2 US cups = 680 grams: 4 US cups = 1360 grams: 5 US cups = 1700 grams: 8 US cups = 2720 grams: 1 / 16 US cup = 21.2 grams: 1 / 8 US cup = 42.5 grams: 1 / 4 US cup = 85 grams: 1 / 3 US cup = 113 grams: 1 / 2 US cup = 170 grams: 2 / 3 US cup = 227 grams: 3 / 4 US cup = 255 grams: 1 1 / 16 US cups. These US Cups to Ounces Cooking Conversions charts will help you convert from cups to grams and ounces. From my research, I have found that the United States is one of three nations (Liberia and Burma being the others) that have not adopted the metric system as their official weights and measures system Author Topic: How much are 1 Cup of Oatmeal in grams...roughly? (Read 24290 times) Stark. I measure out 1 cup to 1 1/4 cups and add about 1.75 cups of water and microwave it for 1.5 mins and eat it. Okay then. You're fine. That's about 55-70 grams of carbs. It's also about 8-10 grams of fiber,.
Conversion of cup amounts of CEREALS,QUAKER,QUICK OATS,DRY into g, gram measuring units. Exchange amounts between 0.5 cup and 1 or multiples of g, gram measure of CEREALS,QUAKER,QUICK OATS,DRY product One cup of oatmeal weighs 5.5 ounces. There are 111 calories in one cup of cooked oatmeal as well as 2 grams of fat, and 3 grams of dietary fiber
1.5 cup of rolled oats - US = 135.00 g ( grams ) of oats. Comment from/about : raw oats amount for cooking porridge. I asked how many cups of rolled oats are in 32 ounces. Conversion helpful. 32 ounces - oz net weight of rolled oats makes 10 cups of rolled oats. Comment from/about : Evelyn. Leave your commen 1.5 cups cooked oatmeal equals how many cups raw oatmeal? Three quarters of a cup. How many grams is a cup of broccoli? There are approximately 91 grams in one cup of chopped,.
200 grams of rolled oats equals how many U.S. customary cups? 200 grams of rolled oats = 2 U.S. cups + 3.5 tablespoons of rolled oats. 150 grams of rolled oats equals how many U.S. customary cups? 150 grams of rolled oats = 1.5 U.S. cups + 2.5 tablespoons of rolled oats US cup to Gram Conversion Chart - Peanut butter. Note: Fractions are rounded to the nearest 8th fraction. Values are rounded to 3 significant figures. US cups to grams of Peanut butter; 1 US cup = 240 grams: 2 US cups = 480 grams: 4 US cups = 960 grams: 5 US cups = 1200 grams: 8 US cups = 1920 grams: 1 / 16 US cup = 15 grams: 1 / 8 US cup How many grams are in one cup of flour? We all have to deal with the struggles of finding recipes where the ingredients are listed either in the metric syste..
50 grams of dates = 1 / 5 Imperial cup of dates. 25 grams of dates = 1 / 10 Imperial cup of dates. If you liked our article, please share with your friends! I hope that this helpful information could help you and you were able to calculate dates for your recipe Amount in grams Amount in ounces Amount in pound; 1 US Tablespoon of Yogurt is equal to: 15 grams (gr) 0.5 oz-1 US Teaspoon of Yogurt is equal to: 5 grams (gr) 0.2 oz-1 US Cup of Yogurt is equal to: 246 grams (gr) 8.7 oz: 0.5 lb: 1 UK Imperial Cup of Yogurt is equal to: 295 grams (gr) 10.4 oz: 0.7 lb: 1 Metric Cup of Yogurt is equal to: 260.
.5 cups of oatmeal -- enough to lower your cholesterol, according to the American Dietetic Association. It may be a bit much for breakfast,. Amount in grams Amount in ounces Amount in pound; 1 US Tablespoon of Rice is equal to: 13 grams (gr) 0.4 oz-1 US Teaspoon of Rice is equal to: 4 grams (gr) 0.1 oz-1 US Cup of Rice is equal to: 201 grams (gr) 7.1 oz: 0.4 lb: 1 UK Imperial Cup of Rice is equal to: 242 grams (gr) 8.5 oz: 0.5 lb: 1 Metric Cup of Rice is equal to: 213 grams (gr) 7.5. 1 cup flour: 120 grams: 4.2 oz: 1 cup whole wheat flour: 130 grams: 4.6 oz: 1 cup almond flour: 112 grams: 3.9 oz: 1 cup whole milk: 240 grams: 8.6 oz: 1 cup sour crea
.5 Imperial cups + 2 tablespoons of granola. Imperial cup equivalent to 150 grams of granola: 150 grams of granola = 1 Imperial cup + 3.5 tablespoons of granola. Imperial cup equivalent to 100 grams of granola:. There are 102 calories in 1 ounce, dry, yields of Oatmeal. Get full nutrition facts and other common serving sizes of Oatmeal including 100 g and 1 cup of cooked Amount in grams Amount in ounces Amount in pound; 1 US Tablespoon of Corn Syrup is equal to: 21 grams (gr) 0.7 oz-1 US Teaspoon of Corn Syrup is equal to: 7 grams (gr) 0.2 oz-1 US Cup of Corn Syrup is equal to: 334 grams (gr) 11.8 oz: 0.7 lb: 1 UK Imperial Cup of Corn Syrup is equal to: 401 grams (gr) 14.1 oz: 0.9 lb: 1 Metric Cup of Corn Syrup.
Cups to grams for common ingredients Please be aware that the list of ingredient options included in the converter and reference charts are approximations, meaning the result you receive will be an estimate Buy Oatmeal In Cups & More Groceries. Shop Oatmeal In Cups at Target.com. Shop Our Great Selection of Oatmeal In Cups & Save I went around the block on this and found many answers. Here is the final one. 1 poind of rice equals 2 1/2 cups of uncooked rice. 1 cup of rice equals 3 cups of cooked rice To make oatmeal, add 1.5 cups of milk to a utensil. Add a pinch of salt and two tablespoons of sugar and dissolve them in the milk. Add a cup of oat flakes and cook it with the milk. Add 50 grams of butter and let the oatmeal infuse for 15-20 minutes. Your oatmeal is now ready to be served Oatmeal makes a nutritious breakfast. A 1 1/2-cup serving of cooked oatmeal provides you with 8 grams of protein; 5 grams of fiber; 100 percent of the daily value for iron; 45 percent of the daily values for thiamin, vitamin B-6, niacin, folate, riboflavin and vitamin A; 30 percent of the DV for phosphorus; 20 percent of the DV for magnesium and calcium; and 10 percent of the DV for zinc
Looking to convert chocolate from cup measurements into grams (g) or ounces (oz)? Here you will find the detailed conversions for chocolate chips and grated chocolate. 1.5 oz 2.1 oz 2.3 oz 3.1 oz 3.9 oz 4.1 oz 4.6 oz 5.4 oz 6.2 oz. Grated Chocolate. amount, in cups (c) ⅛ cup ¼ cup ⅓ cup ⅜ cup ½ cup ⅝ cup ⅔ cup ¾ cup ⅞ cup 1.5 imperial cups to g conversion result above is displayed in three different forms: as a decimal (which could be rounded), in scientific notation (scientific form, standard index form or standard form in the United Kingdom) and as a fraction (exact result) Measure small amounts of dry and liquid ingredients, usually 3 tablespoons or less, in measuring spoons. They are sold in sets typically containing a 1/4 teaspoon, 1/2 teaspoon, 1 teaspoon and 1 tablespoon 1.5 Cups of butter to Grams of Butter Conversion breakdown and explanation 1.5 cup to g conversion result above is displayed in three different forms: as a decimal (which could be rounded), in scientific notation (scientific form, standard index form or standard form in the United Kingdom) and as a fraction (exact result) For example: 1.5 cups of dry oatmeal serves 3 people, using 3 cups of water. For steel cut oats, such as McCann's brand, the one serving is 1/4 cup of uncooked, steel cut oats. That's 1/4 CUP of STEEL CUT OATMEAL for every cup of water. The oats cook much longer, and expand and soak up the water
How much is 1.5 cups? What is 1.5 cups in grams of butter? This simple calculator will allow you to easily convert 1.5 cups to g 1/2 cup of dry oatmeal = 0.95 ounces/27 grams. 1 0. Jean. Lv 4. 5 years ago. To cook oatmeal all your adding is water you just times 4 (1/2 cups =2 cups) X 150 calories per 1/2 cup 150 x 4 = Water has no calories. (to make one serving it's 1 cup water and 1/2 cup oatmeal) 0 0. Anonymous Calories, fat, protein, and carbohydrate values for for 1 Cup Oatmeal and other related foods Oatmeal, Cooked The Quaker Oats, Co. 3/4 cup 116 calories 20 grams carbs 1.9 grams fat 5 grams protein 3 grams fiber 0 mg cholesterol 0.3 grams saturated fat 6 mg sodium 0 grams sugar 0 grams trans fa Flour Measurements Conversion in Cups, Grams, and Ounces. Here you can find the detailed conversions for: Plain Flour (all-purpose flour) Self Raising Flour (self rising flour) 1.5 oz 1.7 oz 2.2 oz 2.8 oz 2.9 oz 3.3 oz 3.9 oz 4.4 oz. Self Raising Flour (Self Riding Flour) amount, in cups (c) ⅛ cup ¼ cup ⅓ cup ⅜ cup ½ cup ⅝ cup ⅔.
1, 3/4, 1/2, 1/4, 1/3, 1/6 or 1/8 cup coconut oil in ounces (weight oz) or grams (g) - US cups to ounces or grams conversion. The below instruction table shows the cup in oz & grams for different quantities of coconut oil, useful when you are preparing different variety of recipes or your favorite recipes Five to 10 grams or more of soluble fiber a day decreases your LDL cholesterol. One serving of a breakfast cereal with oatmeal or oat bran provides 3 to 4 grams of fiber. If you add fruit, such as a banana or berries, you'll get even more fiber. Fish and omega-3 fatty acids Navigation: from unit menu • into unit menu • » converter tool « . Step 3 of 3 Convert amount of CEREALS RTE,MUESLI,DRIED FRUIT & NUTS measure. From cup to g, gram quantity. Amount: 1 cup of CEREALS RTE,MUESLI,DRIED FRUIT & NUTS Equals: 85.00 of g, gram in CEREALS RTE,MUESLI,DRIED FRUIT & NUTS TOGGLE: from g, gram to cup quantities in the other way aroun 1 cup sugar equals exactly 200 grams. Note To Converting 1 cup sugar in grams. Measuring your sugar by weight (200 grams instead of 1 cup) will provide much more accurate results in cooking. Please note that converting 1 cup sugar to grams can vary slightly by room temperature, quality of sugar etc. But by using 200 grams of sugar instead of 1.
We assume you are converting between cup [US] and gram [water]. You can view more details on each measurement unit: cup or gram [water] The SI derived unit for volume is the cubic meter. 1 cubic meter is equal to 4226.7528198649 cup, or 1000000 gram [water] . You can view more details on each measurement unit: cups or gram [water] The SI derived unit for volume is the cubic meter. 1 cubic meter is equal to 4226.7528198649 cups, or 1000000 gram [water] Eating oatmeal on a regular basis can do a lot for your body. Oats are packed with fiber (4 grams per 1/2 cup serving), which is one of the key nutrients you need to help you feel full and lose. Oatmeal is packed with soluble fiber, which reduces your low-density lipoprotein (LDL), the bad cholesterol. In fact, having 1 1/2 cups of cooked oatmeal provides six grams of fiber There are 145 calories in 1 cup of cooked Oatmeal. Get full nutrition facts and other common serving sizes of Oatmeal including 100 g and 1 oz, dry, yields
How much is 0.5 cups? What is 0.5 cups in grams of butter? This simple calculator will allow you to easily convert 0.5 cups to g This cooks like oatmeal and tastes like oatmeal, but without oats. Made with seeds and water, this low carb oatmeal has only 1.5 grams of net carbs and is quickly made with the stovetop or microwave. It's easy to adjust the thickness and sweetness to your liking, or add optional toppings for extra flavors I hope this helps make your life easier the next time you are reading a recipe :) Baking temperatures conversion table Fahrenheit Setting Celsius Setting Gas Setting 300 F 150 Gas Mark 2 (very low) 325 160 Gas Mark 3 (low) 350 180 Gas Mark 4 (moderate) 375 190 Gas Mark 5 (moderate) 400 200 Ga
Looking to convert carrots from cup measurements into grams (g) or ounces (oz)? Here you will find the detailed conversions. Skip to primary navigation; Skip to main content; Skip to 1.5 oz 1.8 oz. Grated Carrots. amount, in cups (c) ⅛ cup ¼ cup ⅓ cup ⅜ cup ½ cup ⅝ cup ⅔ cup ¾ cup ⅞ cup 1 cup. amount, in grams (g) 5 g 15 g 15. Sweet and tasty cranberries blended with crunchy almonds help to deliver 10 grams of protein and 40 grams of whole grains. All in a convenient on-the-go cup. Best With Less Sugar: Arrowhead Mills Organic Instant Oatmeal 100% commitment to quality. 47 grams of whole grains per serving and a good source of fiber Convert how many grams (g) from all purpose flour (APF) are in 1 US cup (us cup). This online all purpose flour (APF) conversion tool is for culinary arts schools and certified chefs. Convert all purpose flour (apf) measuring units from US cups ( us cup ) into grams ( g ), volume vs weights measures, including dietary information and nutritional values instantly


What you need to know: CNC Wood Turning Lathe Job Design Pattern Programming
In the previous article, we mainly talked about the . In this post, we are going to talk about several key points you should know in the programming process. You can work out the correct jobs only after you understand what is saying in this post.
Some users may encounter this error when initially using a cnc wood lathe, that is, the circle pattern in the balustrade is not completely machined. The part marked with a yellow circle as shown below:
Why does the wood turning job have this error?
The reason is probably caused by the fact that the operator did not properly set the shallowest cut depth when do programming. Exactly, the shallowest cut depth is the first point we are talking here.
Shallowest cut depth for computer wood lathe
Our blocks are square shape and we want to mill a complete circle in a square. How to do that?
First, we introduce a mathematical concept, which is the inscribed circle of the square. If a circle is exactly tangent to the four sides of the square, the circle is called the inscribed circle of the square, and the circle is just inside the square. The inscribed circle is the largest circle inside the square.
Same way, this inscribed circle is the largest circle we can mill from a square block with a .
So the question is how much cut depth do we need to set in order to machine this largest circle? We take an example to explain how to calculate this cut depth.
Suppose our block is a wooden square with a side length of 60mm. According to the common sense of mathematics, we can conclude that the inscribed circle diameter of this wooden square is also 60mm, and we can also calculate the diagonal length of the wooden square is 84.84mm. (Note: According to the Pythagorean proposition, diagonal length = side length multiplied by 1.414=60x1.414=84.84). Please refer to the following diagram:
From the figure we can see that in order to get a complete inscribed circle, a reasonable depth of cut should be (84.84-60)/2=12.42mm. This value is also the theoretical shallowest cut depth; In practice, we will set it to be slightly larger than the theoretical value (12.42) by 3 to 5 mm. If the shallowest cutting part does not reach this value when programming, there will be incomplete circumferential machining just like the above image shows.
Offset setup in cnc wood lathe controller
So, except this point, is there any other reason for the above error?
In this case, if the error occurs in the middle of the workpiece and does not appear at both ends, there is no other reason. If the error occurs at the end, we should also consider the offset parameter settings in the cnc wood lathe controller.
The correct offset value should be the exact tool spacing of the two wood lathe carbide tools
Deepest cut depth of programmable wood lath
In the drawing process, in addition to the shallowest cut depth, we must also well set the deepest cut depth. A reasonable setting should be less than a half of the diagonal of the square block. If using the above example, the corresponding deepest cut depth should be less than 42.42mm. If the deepest cutting point is equal to or greater than this value, the workpiece will be cut off.
As shown in the picture above (line in blue), a reasonable programming interval should be between the shallowest depth of cut and the deepest depth of cut. (12.42mm<reasonable interval<42.42mm)
If you have different opinions, please feel free to discuss.
Related Tutorials & Course:
How to make a design for broaching
Original post from Jinan EagleTec Machinery Co.,LTD.
Re-post please indicate the source.


It is important to know not only the distance between the two points but also the angle of the pipe with respect to the coordinate axes during creating and modifying a model. I would like you to add another item to the Tools menu called Angle Measurement or to extend the existing Measure Distance menu with angle measurement. This extension could be optional, the angle between the pipe axis and the coordinate axes would be calculated after filling in the check mark. Therefore, three new items (the angle alpha, beta and gamma) would be added to the existing three items (dx, dy, dz) in the result window.
PM Note - Enhancement 96025:Ability to measure angles of piping


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NRL TIPPING COMPETITION Round 14 2021 - Results Posted; Awards Presented
NRL ROUND 14 POLL 2021
13 members have voted
1. How many single figure victories (9 points or fewer) will there be in NRL Round 14?
0 - all the R14 margins of victory will be by 10 or more points
Just 1 or 2 games will produce a final score where the winning margin will be 9 points or fewer
3 or 4 games
5 or more games will produce final scores where the winning margin will be 9 points or fewer
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Table of Contents
The trick to brewing the perfect cup of coffee is finding the right ratios and balances. Coffee beans and water are the only two other ingredients that affect the taste of your cup of coffee. Ultimately, the very best cup of coffee comes from striking the right balance between the two. You may wonder how much coffee to use for 100 cups if you have experimented and did not get the right ratio. We will tell you exactly how much coffee to put into your coffee maker for 100 cups.
Different Strengths Of Coffee In A Maker
The ratio of water to coffee in a cup of coffee is the first thing coffee enthusiasts are likely to notice. From the first sip of coffee, one can usually tell which category the coffee belongs to.
The coffee is weak if it is too watery and tasteless, and it is made from too few coffee grounds. While weak coffee is brewed with a lot of water, strong coffee uses very little, and its taste and smell are unpleasant. The perfect combination of water and coffee creates a balanced cup of coffee.
Brewing Ratio That To Be Used In A Maker
The brew ratio describes the proportion of coffee to water used in the brewing of coffee. In addition to the choice of coffee and grind size, the brew ratio used to prepare your coffee can make all the difference in how it tastes.
You can control the quality of your coffee brew in a few different ways. In the scoop method, the amount of ground coffee is estimated by using the number of scoops. Scales offer the most accurate way to measure coffee and water since they reduce any chances of error.
A Golden Ratio For Brewing
Water and coffee should always be measured according to the Golden Ratio of 16:1. In other words, every part of coffee should be mixed with 16 parts of water. To mix the perfect coffee blend in your coffee maker, you only need a little mathematical understanding.
Scale For Measuring 100 Cups Of Coffee In A Maker
We will make 100 cups in this example. According to most coffee makers, a cup of coffee is around 6 ounces of liquid. 100 cups of coffee are equivalent to 600 ounces of coffee liquid. You now have to convert 600 ounces of liquid coffee to milliliters. In liquid measurement, 600 liquid ounces are equivalent to 17760 ml or just over a liter of coffee (29.6 ml = oz).
Now that we know how much water we will need, we can calculate the amount of coffee to use. For this, we use the 16:1 golden ratio between water and coffee. Calculate water weight in milliliters by dividing the total by 16. If we divide 17760 ml of water by 16, we get 1110 g (1 ml = 1 g). You can brew 100 cups of coffee using this amount of ground coffee.
Whenever you want to make a cup of coffee, you can utilize the following equation to figure out how much water and coffee to use:
- Water (oz): (number of cups) x 6
- Coffee (g): (number of cups) x 6 x 29.57) / 16
Scooping 100 Cups Of Coffee
Coffee scoops and cups of coffee are not standard units of measurement. A scoop of ground coffee weighs 10 g depending on its grind size. The amount of coffee in a scoop varies depending on the quality and fineness of its grind: the finer the grind, the more it weighs. It is because the smaller particles of the finer ground pack are closer together in the scoop. As well as the weight of each scoop varies.
The mathematical equation we used for the scale method for measuring coffee and water can be used for verifying this equation. To make 100 cups of coffee in a maker, 1110 g of coffee are needed. According to those calculations, we will need 11.1 grams of ground coffee per cup (1110 divided by 100). It is roughly equivalent to how much coffee you would scoop because we’re assuming a scoop is 10 grams.
Any approach may be used to achieve the proper balance for your coffee. It’s crucial to remember that the amount of coffee you scoop is proportional to the amount of coffee you brew. When you brew your coffee at home, investing in a scale can help you produce a great-tasting batch of coffee since you will be able to guarantee that you are using the correct amount of coffee.


Section 4: PRODUCT DEFINITION SECTION
|1-4||section4Length||unsigned||Length of section in octets (nn)|
|5||numberOfSection||unsigned||Number of section (4)|
|6-7||NV||unsigned||Number of coordinate values after template or number of information according to 3D vertical coordinate GRIB2 message|
|8-9||productDefinitionTemplateNumber||codetable||Product Definition Template Number (see Code Table 4.0)|
|10-xx||Product Definition Template (see Template 4.X, where X is the Product Definition Template Number given in octets 8-9)|
|[xx+1]-nn||pv||ieeefloat||Optional list of coordinate values or vertical grid information|
( 1) Coordinates values are intended to document the vertical discretisation associated with model data on hybrid coordinate vertical levels. A number of zero in octets 6-7 indicates that no such values are present. Otherwise the number corresponds to the whole set of values.
( 2) Hybrid systems, in the context, employ a means of representing vertical coordinates in terms of a mathematical combination of pressure and sigma coordinates. When used in conjunction with a surface pressure field and an appropriate mathematical expression, the vertical coordinate parameters may be used to interpret the hybrid vertical coordinate.
( 3) Hybrid coordinate values, if present, should be encoded in IEEE 32-bit floating point format. They are intended to be encoded as pairs.
( 4) Two distinct pressure-based hybrid coordinate formulations can be expressed in GRIB Edition 2. If the hybrid coordinate being used is based on pressure, then level type 105 (Code table 4.5) shall be used to specify the vertical level type. If the formulation is based on the natural logarithm of pressure then level type 113 (Code table 4.5) shall be used. In both cases Notes 1 to 3 (above) apply fully.
( 5) In the case of a generalized vertical height coordinate (fixed surface type 150), no pairs of coordinate values follow after the template, but six sets of additional information (each 4 octets long and encoded in IEEE 32-bit floating point format) follow, starting with the number of vertical levels and the identification number of the used vertical system in the additional GRIB2 message with the 3D vertical system. This identification number together with an UUID (Universally Unique IDentifier) in four parts allows a unique identification of the grid.
- [xx+1] - [xx+4] Number of vertical levels
- [xx+5] - [xx+8] Identification number of 3D vertical grid GRIB2 message
- [xx+9] - [xx+12] UUID part 1 of 4
- [xx+13] - [xx+16] UUID part 2 of 4
- [xx+17] - [xx+20] UUID part 3 of 4
- [xx+21] - [xx+24] UUID part 4 of 4