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Yau left for the Ph.D. program in mathematics at University of California, Berkeley in the fall of 1969. Over the winter break, he read the first issues of the Journal of Differential Geometry, and was deeply inspired by John Milnor's papers on geometric group theory.[YN19] Subsequently he formulated a generalization of Preissman's theorem, and developed his ideas further with Blaine Lawson over the next semester. Using this work, he received his Ph.D. the following year, in 1971, under the supervision of Shiing-Shen Chern.
Xianfeng Gu and Yau considered the numerical computation of conformal maps between two-dimensional manifolds (presented as discretized meshes), and in particular the computation of uniformizing maps as predicted by the uniformization theorem. In the case of genus-zero surfaces, a map is conformal if and only if it is harmonic, and so Gu and Yau are able to compute conformal maps by direct minimization of a discretized Dirichlet energy.[GY02] In the case of higher genus, the uniformizing maps are computed from their gradients, as determined from the Hodge theory of closed and harmonic 1-forms.[GY02] The main work is thus to identify numerically effective discretizations of the classical theory. Their approach is sufficiently flexible to deal with general surfaces with boundary.[GY03] With Tony Chan, Paul Thompson, and Yalin Wang, Gu and Yau applied their work to the problem of matching two brain surfaces, which is an important issue in medical imaging. In the most-relevant genus-zero case, conformal maps are only well-defined up to the action of the Möbius group. By further optimizing a Dirichlet-type energy which measures the mismatch of brain landmarks such as the central sulcus, they obtained mappings which are well-defined by such neurological features.[G+04] 1e1e36bf2d


If you are an active day trader, you are probably aware that Fibonacci retracement and extension levels are some of the most important and useful tools in all of price action.
Day traders and technical analysts can use Fibonacci levels analysis to confirm an entry-level, target a take profit, and to determine your stop loss level.
In this guide we will explain exactly how to draw Fibonacci levels, so that you can make better decisions about when to get in and out of trades.
What are Fibonacci numbers and ratios?
Fibonacci sequence, also sometimes referred to as The Golden Ratio, is a series of numbers where each number is a sum of the previous two numbers.
For example, with the string 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, if we add 0+1, we get 1. If we add 1+1, we get 2. If we add 1+2, we get 3, and so on forever down the sequence.
The resulting sequence is known as the Fibonacci sequence and each of number in the sequence is called a Fibonacci number. The Fibonacci ratios are then calculated by dividing numbers across the sequence. These calculations then give us the following ratios that are used in the Fibonacci levels.
The ratios get translated into percentages – 23.6%, 38.2%, 61.8%, 78.6%, etc. – which are then applied to the chart to try and identify potential hidden support or resistance levels in the market.
The Fibonacci sequence was discovered in 1202 by an Italian mathematician known as Leonardo of Pisa, while considering a practical problem involving the growth of a hypothetical population of rabbits based on idealized assumptions.
This sequence governs many aspects of life; from the creation of flowers, the formation of waves, to proportioning of the human body. It also provides the information that traders and technical analysts need to formulate resistance and support levels which can be used within a risk management framework.
You can use Fibonacci retracement levels on their own or combine them with other trading methodologies.
The Fibonacci sequences were used to formulate other theories such as the Elliot Wave Principle and Dow Theory. You can also use Fibonacci ratios with other technical analysis tools.


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In modern spreadsheet applications, several spreadsheets, often known as worksheets or simply sheets, are gathered together to form a workbook.
A workbook is physically represented by a file, containing all the data for the book, the sheets and the cells with the sheets.
This electronic concept of cell references was first introduced in LANPAR (Language for Programming Arrays at Random) (co-invented by Rene Pardo and Remy Landau) and a variant used in Visi Calc, and known as "A1 notation".
Additionally, spreadsheets have the concept of a range, a group of cells, normally contiguous.
A spreadsheet may also refer to one such electronic document.
Spreadsheet users can adjust any stored value and observe the effects on calculated values.
Worksheets are normally represented by tabs that flip between pages, each one containing one of the sheets, although Numbers changes this model significantly.
Cells in a multi-sheet book add the sheet name to their reference, for instance, "Sheet 1! Some systems extend this syntax to allow cell references to different workbooks.
Besides performing basic arithmetic and mathematical functions, modern spreadsheets provide built-in functions for common financial and statistical operations.
Such calculations as net present value or standard deviation can be applied to tabular data with a pre-programmed function in a formula.
This makes the spreadsheet useful for "what-if" analysis since many cases can be rapidly investigated without manual recalculation.
Modern spreadsheet software can have multiple interacting sheets, and can display data either as text and numerals, or in graphical form.
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Does this sound confusing? Don’t run away just yet! It’s really simple.
Have you ever found a recipe that sounded great and you really wanted to try it, only the yield of the recipe served either more or less than you needed? I’m sure we have all come across this challenge. Sometimes we figure that it’s no big deal, I’ll eyeball it, or just estimate the measurements. This doesn’t usually work out as well as we expect. Especially when you are baking, it is important to use the correct measurements. Too much salt, too little baking soda for example can ruin a recipe. This is not only disappointing but can be costly if you have to start over with new ingredients.
There is a simple way to calculate a different yield for a recipe. You only have to calculate it once, just remember to write down the results and keep them with the original recipe so you have it in the future.
The first thing you need to do is calculate your conversion factor. To do this, you simply take the yield(servings) desired for your recipe, and divide it by the current yield of the recipe you are following. The result will be your conversion factor.
Yield Desired/Current Yield=Conversion Factor
If for example your current recipe makes 2 portions and you want to make 10 portions, the formula would be as follows:
So, 5 would be your conversion factor. To produce 10 portions, you simply multiply each ingredient in the recipe by 5 to arrive at the required amount of that ingredient. Below is an example of a three-ingredient recipe.
Ingredient Original Amount Conversion Factor New Amount
A 2 lb. 5 10 lb.
B 1 c. 5 5 c.
C 1 tsp 5 5 tsp
Once you get the formula down it’s really easy. Your recipe will be accurate and you wont have to throw any mistakes away and start over. This formula works with baking recipes as well as savory recipes.
And you thought you would never need all of those math skills you learned in school. Ha! 🙂


The candidates who registered for the Nov/Dec 2013 WASSCE Result should note that the results has been released and all candidates who are yet to check theirs, can do so by clicking on this link-> Waec Gce Nov/Dec 2013 Results
Meanwhile, the Statistics has been released and only 29% have complete papers.
Article Disclaimer: The article below is culled from Vanguard Nigeria.
The West African Examinations Council (WAEC) on Thursday released its November/December results with a total of 86,612 candidates, representing 29.17% of the total number of candidates who sat for the examination, obtained credits in five subjects and above including English Language and Mathematics.
Announcing the result at the WAEC office, Yaba, Lagos, Head of National Office, Mr Charles Eguridu said that a total of 308,217 candidates registered for the Nov/Dec 2013 WASSCE. 82 blind candidates registered and sat for the examination. From the figure, he noted, 17 candidates, representing 20.73% obtained credits in 5 subjects including English Language and Mathematics.
According to him, 296,827 candidates, consisting of 163,659 male and 133,168 female candidates sat for the examination. Out of the total of candidates, 299,784 candidates, representing 97.26% have their results fully released, while 8,433 candidates, representing 2.74% have a few of their subjects still being proceed.
Eguridu said: “Of the total of candidates that sat the examination, 120,115 candidates, representing 40.46%, obtained 6 credits and above; 161,721 candidates representing 54.48% obtained 5 credits and above. In addition, 198,832 candidates, representing 66.98% obtained credits and above in four subjects while 230,325 candidates representing 77.59 obtained Credits and above in 3 subjects. A total of 256,500 candidates representing 86.41% obtained credits and above in 2 subjects.”
When compared to the November/December 2011 and 2012 WASSCE (Private) results, Eguridu said, there is a marked decline in candidates’ performance.
He said: “In 2011 a total of 139,827 candidates, representing 36.07% obtained credits in 5 subjects and above including English Language and Mathematics.
Also in 2012, a total of 150,615 candidates, representing 37.97% obtained credits in 5 subjects including English Language and Mathematics.”
There was over 8% decline in candidates’ performance as only 29.17% obtained credits in 5 subjects and above including English Language and Mathematics in 2013 WASSCE.
Article Source: Vanguard


The new idea here is multiplication with 10 as a factor, either the multiplicand or the multiplier. Let's first look at the cases where 10 is used as the multiplicand, i.e., 10x1, 10x2, 10x3, .... These can be interpreted as one 10, two 10's, three 10's, ... respectively. In Grade 1, when students studied the numbers up to 100, this is something they should have encountered. Thus, they can use that particular prior knowledge to figure out what these facts will be, i.e., 10x1=10, 10x2=20, 10x3=30, ....
What about 10 as the multiplier, i.e., 1x10, 2x10, 3x10, .... These means, respectively, ten 1's, ten 2's, ten 3's, .... For adults, these are obvious and we might think they should be obvious to children, too. However, although young students can answer the problem on the left very quickly, many of the same students have much more difficult time with the problem on the right.
So, how can students think about problems like 3x10? Hopefully, when they were constructing their multiplication table, they have used the idea that when the multiplier increases by 1, the product increases by the multiplicand. For example, the answer for 3x6 should be 3 (the multiplicand) more than 3x5. This idea, then, can be used to think about 3x10. The answer to 3x10 should be 3 more than 3x9, which is a part of the basic fact they have learned in Grade 2. This idea is really a particular case of the distributive property, which students will formally study in Grade 4. However, the distributive property plays an important role as students think about how to multiply by larger numbers. Therefore, it may be useful if this idea is discussed explicitly in classrooms.
Some of us grew up memorizing the multiplication table up to 12x12. Even today, some teachers/schools/districts still make their students consider the multiplication table up to 12x12. Although it may have some usefulness in everyday situations to know the multiplication facts of 11's and 12's, there is really no particular mathematical reason for expanding the multiplication table to 12x12. Once students develop an algorithm for multiplying by 2-digit numbers, they can calculate anything beyond 10x10 using the algorithm. On the other hand, students can also use the property of multiplication and think of 11's and 12's as simply 10's and 1's or 10's and 2's. Thus, 7x12 can be thought of as 7x10+7x2 and 12x8 can be thought of as 10x8+2x8. Perhaps it is much more important for students to develop that form of flexible thinking than simply memorizing those facts.


This is the third book, Volumn two of a series that God has given me to write. It is religious/Pentecostal based. It will enlighten one on Christian relationships, both in the church and out. I recommend this book for young people, especially women, who wish to date and pursue godly relationships. It will give the seeker a view of the church experience as I have had the pleasure of seeing through my eyes. I try to paint a real picture of the Pentecostal Church scene throughout the pages as much as possible. I pray that with all of the other writings, television shows and movies alike, that this will be received as a partial if not whole description of what a Kingdom experience is like. I believe I've had the best of teachers, pastors, evangelist, etc. to befriend me and have lead me on this journey. I just would like to share that experience with someone who love to read as much as I do, and learn at the same time. One day, I fell in love with Jesus, and I've tried to share that experience throughout these pages. Many life lessons will be shared in a fictionary, interesting form. While writing this I have laughed, cried, sometimes almost went in as we say in the church. I had to stop writing and give God some real praise and worship from what He caused me to write on the pages. So my dear reader, take, read, enjoy and share with someone else. May this be a continued blessing in someones library. Prayerfully one day we will take the leap and put these writings in digital form. But for now, enjoy with it in your hand.
Real Analysis is a discipline of intensive study in many institutions of higher education, because it contains useful concepts and fundamental results in the study of mathematics and physics, of the technical disciplines and geometry. This book is the first one of its kind that solves mathematical analysis problems with all four related main software Matlab, Mathcad, Mathematica and Maple. Besides the fundamental theoretical notions, the book contains many exercises, solved both mathematically and by computer, using: Matlab 7.9, Mathcad 14, Mathematica 8 or Maple 15 programming languages. The book is divided into nine chapters, which illustrate the application of the mathematical concepts using the computer. Each chapter presents the fundamental concepts and the elements required to solve the problems contained in that chapter and finishes with some problems left to be solved by the readers. The calculations can be verified by using a specific software such as Matlab, Mathcad, Mathematica or Maple.
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“I found out I really loved business.”
Becky Blalock was earning $1.65 an hour working three jobs as a West Georgia College student when she heard of a professor paying $5 an hour for a research assistant. It was an assignment that would change her life.
Not only did the professor’s job help her pay for college, he recognized in her a proclivity for math and synthesizing large pools of data. She went on to a 33-year career at Georgia Power and Southern Company, retiring as chief information officer.
She published a book this year that synthesizes lessons from her career and those of 28 female executives.


ENSAE ParisTech is a unique scientific Grande École in the French system, on the cusp between the engineering and the business schools.
At ENSAE ParisTech, proficiency in mathematical tools is the basis for skills in both statistics and economics, the foundation upon which the students then choose to specialise. ENSAE ParisTech is part of CREST, the INSEE (National Institute for Statistics and Economic Research) research centre .
Made up of 9 laboratories, CREST has the general goal of actively participating in developing research in two main areas:
- the modelling of economic and social developments
- the design and implementation of statistical methods


If you don’t want to have the purchase term, utilize the removeO process. In that situation, the repeated factor is going to be the denominator of precisely the same number of fractions as its multiplicity. Its existence enables you to calculate the typical value of the definite integral.
To make it simpler to remember it’s commonly written in the next notation. Functions of this form are the exact same as the ones in case 3 only there’s a term in the denominator that’s repeated or is a constant multiple of another one. In this instance, a trigonometric identity will provide help.
Or you may use the standard program. This is due to the fact that the variable of integration is only a place holder. Locate an antiderivative of f.
A script tool icon ought to be present at the base of your toolbox. Since LaTeX provides a great amount of features, it’s tough to try to remember all commands. The function may be used to solve for different functions too.
You will observe that for the previous T you may use all eight approximate coefficients. Obviously in the event that you decrease the truth of the approximation should improve. To date, you’ve been solving indefinite integrals, and it might be difficult to imagine how all those calculations might be remotely linked to area.
The denominators is going to be the factors of the denominator. It is very important that you know about the standard trigonometric identities, as you often utilized these to rewrite the integrand in a more workable form. Sometimes an integrand might need a bit of algebraic manipulation to ensure it is integrable.
The New Fuss About Definite Integral Calculator
The trapezium or trapezoidal rule can be utilised as a means of estimating the region beneath a curve because the area below a curve is provided by integration. After the function takes on negative values, what’s approximated isn’t a true area below a curve, even though it can be interpreted as sums and differences of such locations. The tops of the rectangles are a significant way over the curve.
When rotated, it will appear similar to our preceding rotation but using a cylinder removed in the center. Let’s say we would like to discover the distance traveled online definite integral calculator over a rather small time interval. Instead of approximating the region under that portion of the curve, you need to find the specific area utilizing well-known geometric formulas.
The Secret to Definite Integral Calculator
Such a figure is known as a washer, or a donut. If you’re emotionally connected to the issue, it may be worthwhile to try setting this up differently. You could be presented with two primary problem types.
The Definite Integral Calculator Cover Up
Even in case you don’t consider yourself to be a terrific mathematician, practice will cause you to be a ton better at it. Practice is actually the best method to secure better at recognizing each type. You may want to review the rules for taking derivatives first.
However, it ought not be applied automatically. Be sure you specify the variable you desire to integrate with. Can figure out the definite integral.
A Secret Weapon for Definite Integral Calculator
MuPAD notebooks will be eliminated in a future release. If you discover this integral in an exam, for instance, you are going to have to use the formula twice. There is going to be homework for every single section covered.
Of course it can’t manage all potential integrands. Practice is also a rather important part of doing math homework. You should receive the same answers you got before.
The Death of Definite Integral Calculator
At times you might select a u simply to discover that you can’t make the substitution resemble a known integral. It is quite a bit easier to just try the proper substitutions. Variable substitution is useful for some integrals.
The Definite Integral Calculator Trap
Area is only an interpretation. In a computational context, integral is very likely to be an Operation in the place of a Representation.
It can be used to find areas, volumes, central points and many useful things. It stems from two different problems. Integration on the opposite hand is a significant bit harder, there are likewise some functions you won’t know how to integrate.
Zero might also appear to be a good pick because it appears like it’s in the center between negative infinity and infinity. Double Integral Calculator is a totally free software. Displays the on-line assistance for the calculator.
Students are permitted to use a calculator. The absolute most frequent dot symbols utilized in math notation can be found in LaTeX also. Again, the amount of fractions is going to be the very same as the variety of factors in the denominator.
Facts, Fiction and Definite Integral Calculator
There are lots of tools on the net that is able to make your math homework less stressful. Let’s look at some examples. Simply use our services and discover the indefinite integral online with no effort.
You’re likely to put those into your initial integrand so that you’re taking the integral over something that’s a purpose of u. The 2 methods for calling diff are the exact same, and are provided just for convenience. As someone might be thinking about, in general it could be not so simple to tell whether the graph of a single curve is above or below another.
Every year it’s the identical thing. It is a famous fact that a number of individuals can be helpful at writing novels and others are going to fix the math problems in a blink of an eye. So long as you understand which way you’re using and do it correctly, you will get the most suitable answer.
The Basics of Definite Integral Calculator
Mark the rows you want to display in a particular design. Each time a Monte Carlo simulation is made utilizing the very same sample size it will produce a slightly different price. Let’s say that given velocity, we would like to discover the distance traveled over a time period.
Whenever we are calculating area in a specific interval, we’re using definite integration. We’ve integrated the flow to have the volume. This means that every interval has just one velocity, and it’s constant.


Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure
In order to facilitate automated reasoning about large Boolean combinations of nonlinear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with interval-based arithmetic constraint solving. Our approach deviates substantially from lazy theorem proving approaches in that it directly controls arithmetic constraint propagation from the SAT solver rather than delegating arithmetic decisions to a subordinate solver. Through this tight integration, all the algorithmic enhancements that were instrumental to the enormous performance gains recently achieved in propositional SAT solving carry over smoothly to the rich domain of nonlinear arithmetic constraints. As a consequence, our approach is able to handle large constraint systems with extremely complex Boolean structure, involving Boolean combinations of multiple thousand arithmetic constraints over some thousands of variables.
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“Jimmy wants to determine the height of the tree on the corner of his block. He knows that a fence by the tree is 4 feet tall. At 3 pm, he measures the shadow of the fence to be 2.5 feet tall. Then he measures the shadow of the tree to be 11.3 feet. What is the height of the tree?” I hear from the other room. Homework is going on, and from her tone, I can tell my daughter is disgusted by the question being asked of her in geometry. “Ugh!” she says to no one in particular.
I remember this type of word problem as the bane of my existence in high school. “It’s 27.2,” I call to her, omitting the unit (because really, does it matter?). I am fully confident that I am not even close.
“What?” she says, a hopefulness in her tone that indicates she believes I might actually be supplying her with the right answer.
“I said, the answer is 27.2. I just did it in my head. Impressive, isn’t it?” I walk into the living room and smile at her. All three children are staring at me like I have three heads, maybe four. “What?” I look at them innocently. “I made it up. It’s called ‘creative mathematics.’ It’s a new thing I just invented.”
“Oh!” My daughter jumps up, completely on board with the new class I have just discovered. It would be kind of like creative writing, but on a math scale. “Where do I sign up? I could totally get into that class!”
Me too… and probably, many other people I know would also appreciate it. Word problems would be awesome! The question would no longer say, Calculate the height of the tree. It would now ask, How tall do you want the tree to be? Or maybe you could simply decide how tall you need the tree to be to suit your purposes. Of course, you would have to give the reasons to support your answer.
Creative mathematics would have nothing to do with calculations. It would be about problem solving and creating your world with the specifications that you find necessary. Plausible or not, you would be allowed to reimagine your world to suit your needs.
Granted, just like creative writing, creative mathematics would not fit every situation. For example, if you were putting new counters in your kitchen, you would need an accurate measurement rather than simply deciding how big you wanted your counter to be. However, such a mathematical option would allow the creative among us to enjoy math and take a break from the many long years of calculating the right answer and showing the work we did to get there.
In life—even in situations like medicine—there are very few “right” answers. Creative mathematics would honor that fact and encourage effective problem solving. Yes, in mathematical calculation, students would still be expected to find the right answer. But in creative mathematics… the sky’s the limit.
* this post is dedicated to the best math teacher I have never had. Once upon a time, a long time ago, she spent hours in daily telephone tutelage to move my sorry math-challenged self through high school calculus.
4 thoughts on “Creative Mathematics *”
Hey, loved this post and the idea of creative mathematics! Things would turn out to be so easy for our kiddos, were this to happen in actual 🙂
It would make things easier for parents, too! No more struggling to figure out each of the ten “new” ways to multiply two numbers….
LikeLiked by 1 person
The way my daughter describes mathematics is very similar to your creative math class. But I’m with J, “Ugh!” who can stand the 16 years of math it takes to get there?
LikeLiked by 1 person
Those many years… that’s why I am pretty sure I could make “creative math” fit any situation for which I require math. 😉


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DUBLIN – Students enrolled in the Science, Technology, Engineering, Arts, and Math (S.T.E.A.M.) Camp sponsored by Bladen County Schools spent a day in science, math, and writing laboratories at Bladen Community College in July.
Faculty members provided laboratory environments in which students could extract their own DNA, see their own cells under a microscope, build and test catapults, create a reaction that produces CO2, and much more.
“In the science portion of our camp curriculum, we provided several opportunities for students to see science in action and understand the importance of the scientific method,” remarked Lisa DeVane, BCC Department Chair for Math and Science. “Students also constructed fractals, which demonstrate mathematical sets of information that create a repeating pattern. It’s a fascinating geometric phenomenon.”
Dr. Joyce Bahhouth, BCC Dean of Arts and Sciences and Developmental Studies, conducted a writing workshop with S.T.E.A.M. participants. “Students were asked to write a story using a set of unrelated pictures they were given,” she explains. “This activity encourages original thinking, creative experimentation, and self-expression.”
Twenty-five students from the third to eighth grades are enrolled in S.T.E.A.M.
For information about the summer program, contact Bladen County Schools at 910-862-4136. For information about opportunities for school children to participate in activities at Bladen Community College, contact Lisa DeVane at 910-879-5509.
Cathy Kinlaw is the public information and marketing director for Bladen Community College.


If you’re one of the many who don’t understand the meaning of “percent” or what decimals are, don’t be embarrassed, just read on …
It’s a fact that a large proportion of the population doesn’t understand the meaning of “per cent” (frequently spelled as one word, “percent,” or indicated by the symbol %). This is not a reflection of their intelligence or knowledge. I’ve met extremely intelligent and knowledgeable people who simply don’t know what percent means. It’s an important concept in financial planning, so I’m going to explain it here, just in case you need it.
“Per” means “for each.” You’ve encountered this in many forms.
For example, “mph” means “miles per hour”; it tells you your speed, how many miles you will travel for each hour you travel, if you maintain that speed. Or “kph” for kilometers per hour.
It’s used for quoting prices. For example, flowers may cost $5 per dozen. If you want a dozen flowers, that’ll be $5. If you want two dozen, $10. If you want half a dozen, $2.50. And so on.
“Cent” is short for “a hundred.” It is derived from the same Latin source (“centum”) as “century.” Divide a dollar or a euro into 100 pieces, and each is one cent.
So “per cent” means “for each hundred.”
For example, if you are charged interest at 6% a year, it means you have to pay $6 of interest each year for every $100 you borrow. Borrow $200 and you pay $12 in interest. Borrow $50 and you pay $3 in interest. In both borrowing examples, whether you’re borrowing $200 or $50, the interest is $6 for each $100, or 6%.
Similarly if your bank credits you with 4% interest a year and you have $250 on deposit, you’ll get $4 on the first $100, another $4 on the second $100 and $2 on the remaining $50, for a total interest payment of $10, in that year.
OK, let’s try another example.
Here’s the first question in a financial literacy quiz offered by the FINRA Investor Education Foundation. (FINRA stands for the Financial Industry Regulatory Authority, in the US.)
“Suppose you have $100 in a savings account earning 2 percent interest a year. After five years, how much would you have? (A) More than $102 (B) Exactly $102 (C) Less than $102 (D) Don’t know.”
Well, 2 percent a year (as you now know) implies that you’ll get 2 for each 100, every year. So in the first year your $100 will get $2 interest added to it. And that’ll keep happening for five years. So you’ll clearly have more than $102 after five years. Easy, right?
Yet it’s unfortunate how many people can’t get it. To them 2 percent is like 2 units of currency on some foreign planet. Who knows how to translate that into dollars?
You can stop there, and that’s all you’ll need. Skip to decimals.
Or, if you’re enthusiastic and eager, you can take a step further along this path and explore a couple of unusual applications of percentages.
What is 0%? Well, it means zero for each 100. Aha, then it doesn’t matter how many hundreds are involved, the answer has to be zero! Kind of a trick question, going to this extreme.
What about 100%? OK, that’s 100 for each 100 — so it’s the whole thing. 100% of 72 is 72. 100% of 365 is 365. That’s another extreme.
Wait a minute, how about someone who “gives 110% effort” (as we often hear). Well, if you give your all, that’s 100%. So it’s impossible to give 110% effort! 110% effort is just an exaggerated way to say “Wow, what a huge effort!” But it may not be a good idea to correct someone who says they’re giving 110% effort, if you want to keep a friend.
Can you have a negative percentage? Sure. If you invest money and lose 5% of it, it means you have lost 5 of each original 100. So if you started with 300, you’ve lost 15 and you’re now left with 285. That’s often expressed as “earning a return of -5%,” even if it’s not the result you want!
One more notion: decimals.
You may not have heard the expression “place value,” but it’s an important concept that you already understand. If I were to say to you, “Write down the number five thousand and sixteen,” you’d write “5016” (with or without a comma after the 5, it doesn’t matter). The 5 indicates the value 5000 because it’s in the place for thousands; the 0 indicates that there are no hundreds; the 1 indicates that there’s 1 ten; and the 6 indicates that there are 6 ones. You have to put in the zero, even though there are no hundreds, because that place is reserved for hundreds. You put a value in each place. If you left out the zero and just wrote “516” that would be “five hundred and sixteen” rather than “five thousand and sixteen.” So the place in which a number is written signifies what value that number has.
OK, on to decimals. What would be the value of a number written to the right of the ones? Numbers that have one-tenth of the value. We indicate that by inserting a stop (called a “decimal point”) after the place for the ones. (In France they use a comma to indicate a decimal, instead of a stop: it has the same meaning.) And then to the right of that would be the place for numbers with one-hundredth of the value. You come across this all the time, without realizing it. With dollars, the first place after the decimal point indicates dimes and the second place indicates cents. So $1.06 means one whole dollar plus no dimes and 6 cents.
You can indicate percentages in exactly the same way. An interest rate of 1.06% simply means $1.06 for each $100. An interest rate of 0.06% means 6 cents for each $100.
Percentages and decimals are just ways of expressing fractions of something bigger.
I have written about retirement planning before and some of that material also relates to topics or issues that are being discussed here. Where relevant I draw on material from three sources: The Retirement Plan Solution (co-authored with Bob Collie and Matt Smith, published by John Wiley & Sons, Inc., 2009), my foreword to Someday Rich (by Timothy Noonan and Matt Smith, also published by Wiley, 2012), and my occasional column The Art of Investment in the FT Money supplement of The Financial Times, published in the UK. I am grateful to the other authors and to The Financial Times for permission to use the material here.


Literally, a stage is a level, degree, or period of time in the course of a process. The FORMAT methodology follows a stage-gate process, i.e. its activities are organized in stages, while gates represent the checkpoints distributed along the TF process. Stage can be performed using various techniques of methods, but it should produce a required output which is checked at Gate. Stage is represented by a rounded rectangle and a gate is represented by a diamond.
Context: Stage-Gates description of FORMAT methodology
A System is a group of interacting, interrelated, and interdependent elements/components performing a certain function.
The key idea of describing a system is that once the boundary has been described (a system is identified), then one describes: (a) the features of the system; (b) the features of the environment without the system which affect the system; (c) the interactions between system and environment.
In order to know anything, one has to make a distinction. Therefore, system is an artificial model to facilitate the learning process.
A system in border of some larger system. Sub-systems are parts (components) of a parent system.
Super-systems (context, holon)
A system that includes the analyzed system as a part. In other words, a super-system is a parent system for the examined system. For instance, the transport infrastructure is a super-system for a particular type of transport system.
Practical expression or relation between super-system and system:
- Super-system is a system that in order to work requires an existence of a system.
- There is a demand to a system that comes from a super-system.
Context: System operator, Law of system completeness
Simple logistic S-curve model
Simple (symmetric) logistic S-curve model is an equation suggested first time in 1838 by Pierre-Francois Verhulst as a model of population growth. The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops [ http://en.wikipedia.org/wiki/Logistic_growth ]. There are several logistic curves, one of the most popular equations is described below:
α – growth rate parameter, time required for growth trajectory from 10% to 90% of limit κ
characteristic duration (Δt); β – parameter specifies the time ™ when the curve reaches 0.5κ midpoint of the growth trajectory ™; κ – is the asymptotic limit of growth (κ) [Weisstein, E.W. Logistic Equation. (MathWorld A Wolfram Web Resource, 2003)].
This model describes a dynamics of growth under competition: Natural growth of autonomous systems in competition might be described by LOGISTIC EQUATION and logistic S-curve. Natural growth is defined as ability of a ‘species’ to multiply inside finite ‘niche capacity’ through time period.
For socio-technical systems the three-parameter S-shaped growth model is applied for describing “trajectories” of growth or decline through time.
Fisher-Prey transform is a change of variables that normalizes a logistic curve and renders it a straight line.
t – time; N(t) – size of population at t; κ – is the asymptotic limit of growth [P. S. Meyer, J. W. Yung, and J. H. Ausubel, “A Primer on Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software,” Technol. Forecast. Soc. Change, vol. 61, no. 3, pp. 247–271, 1999].
This transform facilitates comparison to other logistic growth processes, as soon as all the curves are normalized to limit of growth κ, more than one logistic can be plotted on the same chart. Therefore, competition of multiple systems over time can be simulated and analyzed.
Bi-logistic (component logistic models)
Bi-logistic is a model applied for a system that experiences growth in two discrete phases. In this model, growth is the sum of two discrete curves, each of which is a three-parameter logistic [P. S. Meyer, J. W. Yung, and J. H. Ausubel, “A Primer on Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software,” Technol. Forecast. Soc. Change, vol. 61, no. 3, pp. 247–271, 1999].
Multiple logistic (component logistic models)
Multiple logistic are models where growth is the sum of n simple logistics [P. S. Meyer, J. W. Yung, and J. H. Ausubel, “A Primer on Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software,” Technol. Forecast. Soc. Change, vol. 61, no. 3, pp. 247–271, 1999].
Logistic substitution model
“The logistic substitution model describes the fraction of the niche or market share of the competitors. The life cycle of a competitor can be partitioned into three distinct phases: growth, saturation, and decline. The growth and decline phases represent logistic growth processes, which as we will see, influences the saturation phase.”
The assumptions behind the logistic substitution model, as developed by Nakicenovic and Marchetti [Marchetti, C., and Nakicenovic, N.: The dynamics of energy systems and the logistic substitution model. IIASA Research Report RR-79-13. International Institute for Applied Systems Analysis, Laxenburg, Austria, 1979] are:
- New technologies enter the market and grow at logistic rates.
- Only one technology saturates the market at any given time.
- A technology in saturation follows a non-logistic path that connects the period of growth to its subsequent period of decline.
- Declining technologies fade away steadily at logistic rates uninfluenced by competition by new technologies.
Lotka-Volterra competition model
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. They were proposed independently by Alfred J. Lotka in 1925 and Vito Volterra in 1926, neither of whom were biologists [ http://en.wikipedia.org/wiki/Lotka-Volterra_equations].
Context: FORMAT methodology
 [P. S. Meyer, J. W. Yung, and J. H. Ausubel, “A Primer on Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software,” Technol. Forecast. Soc. Change, vol. 61, no. 3, pp. 247–271, 1999.]


|there exists, there are|
|IFF||if and only if|
|is defined as|
|≠||is NOT equal to|
|>||is greater than, e.g., 9 > 5, 9 is greater than 5|
|≥||is greater than or equal to|
|<||is less than, e.g., 3 < 6, 3 is less than 6|
|≤||is less than or equal to|
|is approximately equal to|
|rounded down (to the nearest integer/whole number);|
|9.5 = 9|
This particular convention will be used only in the special case of calculating the median when N/n is even.
In all other instances, the convention is that 1, 2, 3, or 4 round down to the next lowest number, while 5, 6, 7, 8, and 9 round up to the next highest number, e.g., 3.12 can be rounded to 3.1 or 3.0, 456 to 460 or 500, and 1,234 to 1,230 or 1,200 or 1,000, all depending upon the number of significant figures needed and allowed. For example, the number 11 has two significant figures, the number 2,003 has four significant figures, 2.3 has two significant figures, and 0.031 has three significant figures.
With regard to significant figures and performing calculations, a good heuristic to keep in mind is to add one (1) or at most two (2) significant figures to the number of significant figures in the data. Adding more results in false precision.


What are usually variables in math? In case you have a desire to become a math prodigy, it is crucially important to understand this question, and to be able to answer it in the affirmative.
Among the issues that people that are thinking about becoming a math prodigy have to help be aware of is they may be around reality math concepts prodigies. Is the truth from the matter that they may be that will type regarding math natural born player? The particular fact is usually you will find a write movie reviews range regarding folks who can head to school and work out a school diploma with mathematics without having ever calculus without knowing a little bit about arithmetic, or a student who can write a mathematics assignment.
People are going to be aware that there is a mathematics prodigy someone who had been born with an innate ability for mathematics. This specific person will become more prone in order to succeed in their area regarding study. Most people that are predisposed to excel in mathematics are currently going to be mathematicians, yes and professional mathematicians, mathematics prodigies.
Let’s take into consideration some of the things that anyone can consider because you start so that https://chemistry.uni.edu/ you can consider figuring out ways to deal with factors in mathematics. Here are a few suggestions.
You may be a math prodigy when you’ve got an innate ability to solve problems quickly and efficiently. There really are a number with individuals that become proficient inside many of the facets with mathematics.
If you have a substantial quantity of knowledge of properties of variables you might be a math prodigy. This knowledge would be a substantial asset to you if you were going to be working to come up which you would be asked to fix.
You might be a math prodigy when you have an interest in mathematical equations and proofs. Whenever you actually using them to solve problems and have an interest in numbers, you are likely to become extra apt to discover that you’re likely to possess a fascination with exact issues.
You may be a math prodigy if you are logical and patient. The thinking skills that you create in your math classes and the patience can be very crucial within various strategies.
If you are an intuitive problem solver you may be a math prodigy. You’re going to be able to become https://www.grademiners.com/ confident in the knowledge that you grow as you go along on your mathematics courses when you have an intuitive feel for the issues you will be required to resolve.
If you are interested in the solution to the difficulties of our lives, Last, you may be a math prodigy. Whenever you can utilize your mathematics skills to design a remedy for a problem that you will face, you are going to be in a position to become successful in your mathematics courses.
You may be a math prodigy if you’re going to become an inspiration to others that are likely to be attempting to address problems which are larger than you, but smaller on your own. This kind of fact is a one. Your concept of which you are likely in order to be able to be a motivation for others is which is valuable throughout accomplishing the particular objectives that you have fixed on your own.


AP Calculus BC Test Preparation
AP Calculus BC reviews and extends concepts from AP Calculus AB using a curriculum more extensive than AP Calculus AB. Since the BC exam covers more material than the AB test, it often offers students higher course placement, more course credit, and a greater chance of acceptance at competitive colleges. AP Calculus BC test preparation can be a great option for tutoring.
Our course covers the study of functions, graphs, limits, derivatives, definite integrals, polynomial approximations and series, and their various applications. Vectors, polar graphs, and parametric equations are also included. We emphasize a multi-representational approach to problem-solving and focus on developing students’ understanding of Calculus concepts.
Online AP Calculus BC Test prep
Our online tutors are trained to prepare students effectively for the AP Calculus BC Test. Our program identifies a specific area in need of improvement and works on those so that better knowledge and skills lead to higher scores.'
AP Calculus AB Test Preparation
Our math curriculum covers all of the AP Calculus test preparation material outlined by the College Board to prepare students for the AP Calculus AB exam. Emphasis is given to understanding and problem solving, gaining experience in the use of Calculus methods, and learning how Calculus may be used in practical applications. The course uses tests and homework from the AP Exam.
AP Statistics Test Preparation
Statistics has the power to improve decision-making accuracy, to test new ideas, and to form the mathematical basis for quality control. It is an analytical tool used in Education, the Social Sciences, and Business Administration, and is often a required subject for many College Majors.
AP Statistics introduces students to the concepts and tools for collecting, analyzing, and drawing conclusions from data. We expose our students to four broad conceptual themes, helping them to master the concepts and techniques of Statistics and equipping them to communicate methods, results, and interpretations using the vocabulary of Statistics.
We encourage our students to familiarize themselves with the form and notation of formulas. We expose them to multiple-choice questions, open-ended free-response questions, and investigative tasks involving more extended reasoning.
Any student with concerns about the information and skills needed for success on the AP Statistics Test can benefit from our online tutoring program. The tutors at YG provide effective help for learning this branch of Applied Mathematics. This program identifies specific areas that are a matter of concern and works on those so that test scores will rise.


Sometimes rather difficult steps are required to solve the most difficult binary puzzles. Consider for example the blue cell in the puzzle below. Do you see which number should be placed here?
Especially for starting binary puzzlers this is not easy to see. We will give a step by step explanation.
Two zeros and two ones are missing in the fifth row. Because at most two equal numbers are allowed to be placed next to each other, there are four possibilities for the fifth row:
Because each row of the puzzle has to be unique, and because the second possibility above is equivalent to the second row of the puzzle, this possibility can be crossed out. The three remaining possibilities for the fifth row are:
Maybe it's already clear now which number has to be placed in the blue cell. Regardless of the possibility we choose, there will always be a one in the fourth cell of the fifth row. We can thus fill in a one in the blue cell.
BinaryPuzzle.com © 2011-2017


cement formulas cement
15 rows C 2 S 2CaO SiO 2 dicalcium silicate belite C 3 A 3CaO Al 2 O 3 tricalcium aluminate C 4[email protected]
4 12 33 100 x 33 33 cubic feet 33 x 037 122 cubic yards now the formula is ideal for solving for volume and then converting it to cubic yards for concrete the procedure for volume is as follows length x width x thickness you need to divide the total cubic yards that the yield needs to determine the number of concrete bags.
About surecrete design products concrete calculator entering depth of concrete height thickness number in inches diameter inches entering width depth area across the number of feet volume hole diameter length beginning length of the slab number of feet diameter number cubic yard concrete column calculator soon to come.
An online concrete calculator which estimates the amount of concrete required for your project using various shapes slab post hole blockfill.
concrete calculating formula heres how you make it clear how much concrete is needed for the job find out the thickness of the layer you will need find out the width and length of the area you will need to pour that layer on find out the square footage by multiplying the two measurements width and length youll get a measurement in inches now transfer it to feet.
how to calculate concrete determine how thick you want the concrete measure the length and width that youd like to cover multiply the length by the width to determine square footage convert the thickness from inches to feet multiply the thickness in feet by.
know that the formula for calculating concrete consists of the following length x width x height27 x 105 total concrete needed plus 5 percent extra the length width and height are measured in feet generally you should purchase 5 percent more concrete than you need to complete your concrete project to ensure that you have enough to.
concrete calculator use steps to use this calculator are mentioned below this online concrete volume calculator is extremely easy to use select the concreting member for which you require the concrete next select the unit of measurement and the concretemix ratio.
Calculate cement concrete mix design or estimate how much cement concrete volume is required for your construction using our free online calculator know exactly how many bags kg and ton of cement sand and aggregate is needed of specific cement sand and aggregate ratio m20 m15 m10 m75.
Calculator formula for a concrete wall calculating concrete yardage for a wall uses the same formula as a slab example height 8 length 40 thickness 8 convert thickness to feet 8 12 0667 feet volume in cubic feet 667 x 8 x 20 21344 ft volume in cubic yards 21344 ft 27 79 yd.
Concrete calculation formula calculate the slab volume slab volume length x width x height thickness calculate the number of bags number of bags density of the concrete volume of the slab weight bag the loss is then calculated by adding the defined to the total.
Concrete calculator an easy to use tool for determining how much concrete you need for your project concrete calculator call for immediate assistance 407 7089175 slabs square footings or walls length width thickness or height quantity hole column or round footings.
Concrete calculator the concrete calculator estimates the volume and weight of concrete necessary to cover a given area purchasing slightly more concrete than the estimated result can reduce the probability of having insufficient concrete slabs square footings or walls hole column or round footings circular slab or tube.
Concrete cost per square foot you can estimate an average cost of 425 625 per square foot to have a regular concrete floor slab poured thus if you require a more accurate number of your projects cost please request a free estimate from the local contractors in new york city bagged concrete.
Concrete cubic yards formulas use the following formulas to calculate the concrete needed for various types of pours square and rectangular areas the volume for a rectangular space is equal to the length times the width times the height for slabs substitute the.
Concrete formulas 149 a 28day compressive strength of 6000 lbin2 41 mpa and 082 for 2000 lbin2 14 mpa airentrained concrete wc ratios vary from 040 to 074 for 5000 lbin2 34 mpa and 2000 lbin2 14 mpa compressive strength respectively be certain to refer to the aci code for the appropriate wc value when preparing designs or.
Concrete formulas 149 a 28day compressive strength of 6000 lbin2 41 mpa and 082 for 2000 lbin2 14 mpa airentrained concrete wc ratios vary from 040 to 074 for 5000 lbin2 34 mpa and 2000 lbin2 14 mpa compressive strength respectively be certain to refer to the aci code for the appropriate wc value when preparing designs or concrete analyses.
Concrete ingredients calculation for cement sand and coarse aggregate this is a volumetric calculation assuming we need 2 m 3 of concrete for m20 concrete mix mix ratio m20 1 15 3 total part of the concrete 1153 55 parts therefore cement quantity cement part concrete parts concrete volume.
Concrete slabs calculator input length width and depth of the area click the button to calculate the volume of concrete and manhours not including mixing needed for this job this calculator is to be used as an estimating tool only shop concrete mix.
Formulas for lightweight concrete fernando martinez lewels has a msce degree from the university of texas at el paso he is now working with the agartif company in chihuahua mexico about 170 miles from el paso texas this company has developed a type of lightweight aggregate that provides material for all types of construction needs at.
Fundamental formulas for cement kiln process ulang the cement manufacturing process advancing mining cement manufacturing is a complex process that begins with mining and then grinding raw materials that include limestone and clay to a fine powder called raw meal which is then heated to a sintering temperature as high as 1450 c in a cement.
In the cement industry one such initiative was the release of cement formula handbook in 2009 this cement formula handbook was extensively circulated among the industry the response for the handbook has been very encouraging and received positive feedback from.
heres the list of ingredients that youll need cement sand and rock and heres where the 123 comes in use onepart cement twoparts sand and threeparts rock when we mix it we use a shovelful of cement two shovelfuls of sand and three shovelfuls of rock half to threequarterinch rock is best gravel will weaken the concoction.
a type of lime cement precursor to portland cement was invented in 1756 by engineer john smeaton although different from todays portland cement the resulting mix was quite strong smeaton used his formula in the construction of a lighthouse.
by analyzing concrete used to build 2000yearold roman structures a team of scientists may have found a longerlasting greener alternative to modern cement.
the formula for concrete mix is one part cement two parts sand and three parts gravel or crushed stone if hand mixing its inadvisable to exceed a water to cement ratio of 055 which translates to 55 pounds of water for every 100 pounds of cement when mixing concrete its necessary to ensure that there is an adequate amount of aggregate.
the formula for concrete calculations is length x width x depth divided by 27 the result of this formula provides the number of cubic yards of concrete needed the measurements must be in feet in order for the equation to work concrete is comprised of several components including water portland cement and aggregate which is granular.
casing capacity 08679 ft3ft step 2 determine the slurry volume ft3 slurry vol ft3 500 sk x 115 ft3sk slurry vol 575 ft3 step 3 determine the amount of cement ft3 to be left in the casing cement in casing ft3 3000 ft 2900 ft x 08679 ft3ft cement in casing ft3 8679 ft3 step 4.
Our concrete calculator provides you an easy way to calculate concrete volume and estimated cost of concrete slabs footers walls columns steps stairs curbs and gutters in cubic feet cubic yards and cubic meters and inches it makes your construction project planning and budgeting more accurate.
Portland cement you can buy this in a 94lb bag sand course or fine will work course sand will give you a stronger mix aggregate stone you can use 38 12 or 15 stone for aggregate water clean cool water is best.
Prism cement prism cement a division of prism johnson limited is one of indias leading integrated building materials company with a wide range of products from cement readymixed concrete tiles and bath products prism johnson limited is an ims certified company iso 90012008 iso 140012004 iso 180012007 sa 80002008 amp iso 500012011.
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Alexander Rinnooy Kan
Een steeds ingewikkeldere wereld goed begrijpen en helder uitleggen.
Mr. Alexander Rinnooy Kan was born in the Netherlands. Mr. Rinnooy Kan has degrees in Mathematics from Leiden university and Econometrics from Amsterdam University, and a Ph.D. in mathematics from the University of Amsterdam.
He was employed as mathematics editor at the Spectrum Encyclopaedia for the period of a year, and at the University of Delft for three years. In 1977 he moved to Erasmus University in Rotterdam, where he became a professor in operational research in 1980, Director of the Econometric Institute in 1983 and Rector Magnificus in 1986. In the meantime he was also a guest lecturer at Berkeley, California and MIT, Boston, among others.
In 1991 he became Chairman of the Confederation of Dutch Industry VNO, which became VNO-NCW in 1995, Mr. Rinnooy Kan was a Member of the Executive Board of ING Group from 1996 to 2006. Subsequently, he was appointed as Chairman of the Social and Economic Council of the Netherlands, a post which he occupied until September 2012.
Aside from his current job, Mr. Rinnooy Kan is a member of several advisory boards and committees.
Mr. Rinnooy Kan has published ten books and 150 articles.
As of September 2012, he is University Professor of Economics and Business at the University of Amsterdam.


Morris Kline con Mathematics for the Nonmathematician (Dover Books on Mathematics) (English Edition)
Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.
In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.