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Steven Bogart, a mathematics instructor at Georgia Perimeter College, answers

By Steven Bogart

Succinctly, pi-which is written as the Greek letter for p, or π-is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To only 18 decimal places, pi is 3.141592653589793238.) Hence, it is useful to have shorthand for this ratio of circumference to diameter. According to Petr Beckmann's A History of Pi, the Greek letter π was first used for this purpose by William Jones in 1706, probably as an abbreviation of periphery, and became standard mathematical notation roughly 30 years later.

Try a brief experiment: Using a compass, draw a circle. Take one piece of string and place it on top of the circle, exactly once around. Now straighten out the string; its length is called the circumference of the circle. Measure the circumference with a ruler. Next, measure the diameter of the circle, which is the length from any point on the circle straight through its center to another point on the opposite side. (The diameter is twice the radius, the length from any point on the circle to its center.) If you divide the circumference of the circle by the diameter, you will get approximately 3.14-no matter what size circle you drew! A larger circle will have a larger circumference and a larger radius, but the ratio will always be the same. If you could measure and divide perfectly, you would get 3.141592653589793238..., or pi.

Otherwise said, if you cut several pieces of string equal in length to the diameter, you will need a little more than three of them to cover the circumference of the circle.

Pi is most commonly used in certain computations regarding circles. Pi not only relates circumference and diameter. Amazingly, it also connects the diameter or radius of a circle with the area of that circle by the formula: the area is equal to pi times the radius squared. Additionally, pi shows up often unexpectedly in many mathematical situations. For example, the sum of the infinite series

1 + 1/4 + 1/9 + 1/16 + 1/25 + ... + 1/n2 + ... is π ²/6

The importance of pi has been recognized for at least 4,000 years. A History of Pi notes that by 2000 B.C., "the Babylonians and the Egyptians (at least) were aware of the existence and significance of the constant π," recognizing that every circle has the same ratio of circumference to diameter. Both the Babylonians and Egyptians had rough numerical approximations to the value of pi, and later mathematicians in ancient Greece, particularly Archimedes, improved on those approximations. By the start of the 20th century, about 500 digits of pi were known. With computation advances, thanks to computers, we now know more than the first six billion digits of pi.

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Steven Bogart, a mathematics instructor at Georgia Perimeter College, answers

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Can you make a pictorial representation of the quadratic equation ax^2+bx+c=0

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Can you make a pictorial representation of the quadratic equation ax^2+bx+c=0

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https://sites.google.com/site/butwhymath/algebra/the-quadratic-formula

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Does 2 + 2 = 5 for very large values of 2?

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Does 2 + 2 = 5 for very large values of 2?

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http://www.straightdope.com/columns/read/1382/does-2-2-5-for-very-large-values-of-2

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Although I think this is just good math.

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NRICH - Mathematics Resources for Teachers, Parents and Students to Enrich Learning

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Why does every year have to have at least 1 Friday the 13th?  How many Friday the 13th's are possible in a year?

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Why does every year have to have at least 1 Friday the 13th?  How many Friday the 13th's are possible in a year?

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Are you spooked by Friday the 13th? How many of these cryptic Friday's are possible in one year?

Reference

The NRICH website publishes free mathematics resources designed to challenge, engage and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support for teachers by publishing Teachers' Resources for use in the classroom.

This task can be found at: https://nrich.maths.org/610

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Are you spooked by Friday the 13th? How many of these cryptic Friday's are possible in one year? The NRICH website publishes free mathematics resources designed to challenge, engage and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support for teachers by publishing Teachers' Resources for use in the classroom.

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more good questions: great ways to differentiate secondary mathematics instruction

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teaching methods & materials - mathematics

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mathematics - study and teaching (secondary)

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education / educational policy & reform / general

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education / teacher training & certification

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education / teaching methods & materials / mathematics

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More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction

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We know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategie...

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Praise for the First Edition! Resources for the Mathematics Educator Choice Mathematics: Teaching in the Middle School Teaching Children Mathematics Carolyn Chapman , Creative Learning Connections, Inc., and Rita King , King Learning Associates

Expanded to include connections to Common Core State Standards, as well as National Council of Teachers of Mathematics (NCTM) standards, this critically acclaimed book will help every teacher and coach to meet the challenges of differentiating mathematics instruction in the K-8 classroom. In this bestseller, math education expert Marian Small explains two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert with these strategies, Small also demonstrates more inclusive learning conversations that promote broader student participation and mathematical thinking required by CCSS. Specific strategies and examples for each grade band are organized around NCTM content strands: Number and Operations, Geometry, Measurement, Algebra, and Data Analysis and Probability.

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Good Questions: Great Ways to Differentiate Mathematics Instruction, Second Edition (0)

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Amazon.com: Good Questions: Great Ways to Differentiate Mathematics Instruction, Second Edition (0): 8601400117224: Marian Small: Books

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Marian Small

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When discussing fractions, why do we say "simplest form"? Is it really the simplest?

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When discussing fractions, why do we say "simplest form"? Is it really the simplest?

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Why do you reverse the sign when solving for x... 

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Why do you reverse the sign when solving for x... 

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-- Binary, base 10, 12 (hours), 16 (pounds), 60 (minutes).

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You can construct some great questions from this resource on the origins of symbols of operation. 

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You can construct some great questions from this resource on the origins of symbols of operation. 

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Cajori says, "There is clear evidence that, as a lecturer at the University of Leipzig, Widmann had studied manuscripts in the Dresden library in which + and - signify operations, some of these having been written as early as 1486."

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What is the difference between a number and a numeral? 

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What is the difference between a number and a numeral? 

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For instance, the number 5 is a concept used to describe five objects. One could express this concept by holding up five fingers or by saying the word "five." However, if one wrote down the number "5" that would be a numeral. Regardless of whether the person wrote that number using Roman (V) or Arabic (5) numerals or even letters (five), it would still be considered a numeral once it was written. \

Any written number can be a numeral, regardless of how many symbols or digits it takes to create that number. For instance, "5" is a numeral but so is "505" and "5,678,987." However, the word numeral can not be used interchangeably with digit. A digit is a single symbol used to make a number or numeral. The number 5 can be written with just one symbol or digit, while the number 505 needs three digits and 5,678,987 needs seven digits.
Learn more about Numbers

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What Is the Difference Between a Number and a Numeral?

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For instance, the number 5 is a concept used to describe five objects. One could express this concept by holding up five fingers or by saying the word "five." However, if one wrote down the number "5" that would be a numeral.

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What is the single most important object in mathematics? 

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What is the single most important object in mathematics? 

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Physics Forums - The Fusion of Science and Community

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For me it would have to be the set of complex numbers. What's yours?

Mathematics starts with the integers, so I would consider them the most important.

The concept of zero, hands-down.

The von Neumann hierarchy.

Well, the complex numbers include both of them (and also the reals).

From the empty set you can construct everything.

I second the empty set.

To be accurate math starts (in the standard construction) with the natural numbers and sets. From there you derive integers, then rationals, then reals, then complex, then quaternions, then octernian, etc.

Oh I'm totally all about Graham's number!

How many dollars I have.

The ideas of 'set' and 'function'.

the proof, Euclid I 47

The field of algebraic numbers.

So what's the LEAST important object in mathematics?

*insert offensive generalization about hygiene, women, etc.*.. oh snap!

1 is by far the most important.

To me its the idea that representation of any kind is abstracted to a mathematical quantity. This fact alone says a lot about the power of mathematics.

most important: equals sign?

I third the empty set.

Im gonna have to read about the empty set.

The most important thing in mathematics is the concept of numbers. And from there stems everything else.

But SPECIFICALLY, my absolute favorite is Euler's formula and his Identity.

[tex]e^{ix}= \cos (x)+ i \sin (x)[/tex]

[tex]e^{i\pi}+1 =0[/tex]

The most beautiful relationship ever.

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Single most important object in mathematics?

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For me it would have to be the set of complex numbers. What's yours? Mathematics starts with the integers, so I would consider them the most important. The concept of zero, hands-down. The von Neumann hierarchy. Well, the complex numbers include both of them (and also the reals).

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Math is often referred to as a universal language. Is mathematics taught the same way in most developed countries?

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Math is often referred to as a universal language. Is mathematics taught the same way in most developed countries?

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The study identified 75 variables in which there were differences in teaching patterns among the seven countries, but Hiebert says two of those stood out as the most common in the highest-achieving countries, but nearly absent in the United States.

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What are 5 common causes of math troubles in students? 

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What are 5 common causes of math troubles in students? 

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Do you often wonder why your child has such a hard time learning math? If she has trouble counting or remembering basic math facts, it could be due to a learning issue called dyscalculia. But other issues can also make it hard to work with numbers. Learn more about what might be causing your child's trouble with math, and how you can help.

What You Might Be Seeing

The signs of a math issue can vary depending on what's causing it and how old your child is. If dyscalculia is to blame, the symptoms may change over time as she uses math in different ways.
Math Trouble in Preschool or Kindergarten

Finds it hard to learn to count by 10s, up to 100

Has trouble pointing to and counting each object in a group

Has trouble understanding that a number can be used to describe any group with that amount in it-for example, knowing that 5 can be used for a group of 5 fingers, 5 bananas and 5 cats

Has difficulty recognizing and writing numbers up to 20

Skips numbers when counting, long after other kids the same age are able to count in order (children typically can count to 100 by 1s and 10s at end of kindergarten)

Doesn't tend to recognize patterns and may not be able to sort items by size, shape or color

Math Trouble in Early Elementary School (Kindergarten Through Second Grade)

Difficulty counting by 2s, 5s, and 10s

Unable to mentally calculate basic addition and subtraction problems

Difficulty recognizing basic mathematical signs such as plus or minus

Difficulty recognizing numbers, confusing 381 for 38 and 1 or 3, 8, 1

Math Trouble in Upper Elementary School or Middle School

Doesn't understand the concept of "more than" or "less than"

Struggles to learn and remember basic math facts, such as 5 + 5 = 10

Doesn't make the connection between related math facts or "fact families," such as 5 + 5 = 10, so 10 ‒ 5 = 5

Has trouble recognizing written numbers (also known as numerals)

Still uses fingers to count instead of doing the calculation in her head

Struggles to line numerals up neatly in columns when solving math problems

Doesn't know left from right

Avoids games that involve strategy like checkers or Sudoku

Has a hard time telling time

Math Trouble in High School

Has difficulty using math in real life, including things like budgeting or doubling a recipe to make it for more people

Has trouble understanding maps and charts

Hesitates to participate in activities that require a good sense of speed and distance, such as running track or learning to drive

If you've seen some of these signs in your child for at least six months, it's a good idea to talk to her teacher or doctor. Together you can come up with a plan for figuring out what's causing these problems and what may help.

"You may not know exactly what's causing your child's trouble with math. But even before you find out, there are steps you can take now to make things a little easier for your child."

What Can Cause Trouble With Math

For someone to do math well, many skills need to come together. These include language and memory skills, and the ability to picture things. If your child is doing fine in other subject areas and mainly seems to be struggling with math, then dyscalculia may be the cause of her issues. Here are some common causes of math trouble.

Dyscalculia: This brain-based condition makes it hard to work with numbers and number concepts. It may not be as well known as dyslexia, but it isn't uncommon. Research suggests that anywhere from 7 to 14 percent of people have it.

Dyscalculia isn't a sign of low intelligence. In fact people with this condition often do well or even extremely well in non-math areas.

Not all kids show the same signs of dyscalculia. Some may have a hard time learning to count or figuring out how many items are in a group. Others might struggle to remember math facts or use math-related vocabulary like "greater than" or "less than."

Dyslexia: This common condition is mainly known for its impact on reading skills. But it can also affect spelling, writing, speaking and math skills. If your child is having trouble learning to count and doing word problems, dyslexia could be the cause. Many kids have both dyslexia and dyscalculia.

Math anxiety: Children with math anxiety are so worried about doing math that it lowers their performance on math tests. Some kids may have both math anxiety and dyscalculia.

Visual processing disorder: You may see your child struggling to recognize patterns, line up math problems on the page and read maps or charts. These are all signs of a visual processing disorder.

Not paying attention to math isn't the same as not understanding it. If your child can't seem to focus on her math work, or makes a lot of careless errors, you might want to look into ADHD.

How You Can Get Answers

If your child is having trouble with math, there's a lot you can do to help. By knowing what's causing the issues, you and her teachers can find the most effective ways to build math skills and self-esteem. Getting answers make take a little work, but it's not as tough as you may think. Here are some steps you can take:

Talk to your child's teacher. This is a great first step toward finding out why your child is struggling with math. See what the teacher has observed in class and share what you've been seeing at home. You can ask the teacher for a list of the skills that students are expected to learn by the end of the school year. That can give you a sense of what your child needs help with and how far behind she may be. The teacher may try different strategies to help your child build math skills and understand concepts. You also can talk about whether your child might be eligible for a 504 plan. That plan would put some official strategies and accommodations into place.

Look into an educational evaluation. Either you or your child's teacher can request that the school evaluate your child for special supports or services. (The school can't do it without your permission.) If the school agrees, you won't have to pay anything. Depending on the results your child might be entitled to an Individualized Education Program (IEP). This plan will detail the free services and supports the school will provide to help your child learn math.

Talk to your child's doctor. This is another good place to start getting answers. The doctor will ask you to describe your concerns and help you find out whether certain medical conditions such as ADHD might be causing the issues. The doctor may also suggest you see a learning specialist to help figure things out.

Talk to a specialist. The professionals who focus on learning issues are called educational psychologists. They are trained to give specific tests that look at how children think and learn. These tests can help pinpoint which areas a child is struggling with. The specialists who can check for ADHD are a psychologist or neurologist.

What You Can Do Now

You may not know exactly what's causing your child's trouble with math. But even before you find out, there are steps you can take now to make things a little easier for your child. Here are a few options to consider:

Make math a game. Practicing math skills doesn't have to feel like homework. Doing it in a less pressured way may improve your child's understanding of numbers and reduce math anxiety. Ask your child to help you sort the laundry and pair up the socks. Or have her measure out ingredients to cook with or weigh things at the grocery store. Learn more about how games can help kids who struggle with math.

Check out apps and technology. Kids who have trouble with math facts and concepts can benefit from apps that boost math skills. Other types of assistive technology can help too. Using things like calculators may feel like "cheating." But if it's what your child needs to be able to manage the workload, it's simply another learning aid.

Boost your child's confidence. Struggling with math can affect your child's overall self-esteem and social life. Help your child recognize her strengths and build on them. Reminding her of what she does well can help improve her self-esteem and resilience.

Observe and take notes. The first step to finding help for your child is to observe her behavior and take notes on when she has difficulties. This can help you pick up on patterns and specific issues that you can begin to work on. Your notes will also be helpful when you talk to your child's teacher, doctor or other professional.

Try different strategies. There are things you can do at home to help your child build math skills. You may also want check out some of the advice from our experts in Parenting Coach. Get suggestions for helping your child with things like poor self-esteem and anxiety problems.

Connect with other parents. Although it may feel like you're the only family dealing with these issues, you're not. This site can help you find parents whose kids are struggling with math. These parents know what you're going through and can share insights and strategies.

Understanding what's behind your child's trouble with math is the best way to get support for her-and for you. The more you know, they better able you'll be to help her build her math skills and her confidence.

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Understanding Your Child's Trouble With Math

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Do you often wonder why your child has such a hard time learning math? If she has trouble counting or remembering basic math facts, it could be due to a learning issue called dyscalculia. But other issues can also make it hard to work with numbers.

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Math Facts for Kids is a fun resource that you can use to frame questions for your mathematical wonderings. 

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Math Facts for Kids is a fun resource that you can use to frame questions for your mathematical wonderings. 

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Math Facts for Kids

Check out our math facts for kids and enjoy exploring a wide range of fun trivia and interesting information.

Learn about numbers, geometry, math history, famous mathematicians and other topics related to the world of mathematics. Learn how to find the area of a circle, understand what a googol is, have fun reading famous, funny and inspirational quotes, learn what Albert Einstein thought about math and much more.

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Math Facts for Kids - Interesting Trivia & Information

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Math Facts for Kids Check out our math facts for kids and enjoy exploring a wide range of fun trivia and interesting information. Learn about numbers, geometry, math history, famous mathematicians and other topics related to the world of mathematics.

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What is thinking mathematics standards and what is content mathematics standards? 

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What is thinking mathematics standards and what is content mathematics standards? 

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early childhood education; mathematics education; activities; parent participation; parents as teachers;

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To a large extent, students and many of their teachers tend to define mathematics in terms of what they learn in math courses, and these courses tend to focus on #3. The instructional and assessment focus tends to be on basic skills and on solving relatively simple problems using these basic skills.

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A number divided by itself is 1 and you can not divide by zero. So what happens when zero is divided by zero, is it one or not possible? And why?

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A number divided by itself is 1 and you can not divide by zero. So what happens when zero is divided by zero, is it one or not possible? And why?

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Two times math doesn't work is square rooting negative numbers and dividing by zero. Why is it that square rooting negative numbers are called imaginary, but dividing by zero just can't be possible?

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Two times math doesn't work is square rooting negative numbers and dividing by zero. Why is it that square rooting negative numbers are called imaginary, but dividing by zero just can't be possible?

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Mathematics is the language of science and has enabled mankind to make extraordinary technological advances. There is no question that the logic and order that underpins mathematics, has served us in describing the patterns and structure we find in nature.

The successes that have been achieved, from the mathematics of the cosmos down to electronic devices at the microscale, are significant. Einstein remarked, "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?"

Amongst mathematicians and scientists there is no consensus on this fascinating question. The various types of responses to Einstein's conundrum include:

1) Math is innate. The reason mathematics is the natural language of science, is that the universe is underpinned by the same order. The structures of mathematics are intrinsic to nature. Moreover, if the universe disappeared tomorrow, our eternal mathematical truths would still exist. It is up to us to discover mathematics and its workings--this will then assist us in building models that will give us predictive power and understanding of the physical phenomena we seek to control. This rather romantic position is what I loosely call mathematical Platonism.

2) Math is a human construct. The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. It is a product of the human mind and we make mathematics up as we go along to suit our purposes. If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived. Mathematics is not discovered, it is invented. This is the non-Platonist position.

3) Math is not so successful. Those that marvel at the ubiquity of mathematical applications have perhaps been seduced by an overstatement of their successes. Analytical mathematical equations only approximately describe the real world, and even then only describe a limited subset of all the phenomena around us. We tend to focus on those physical problems for which we find a way to apply mathematics, so overemphasis on these successes is a form of "cherry picking." This is the realist position.

4) Keep calm and carry on. What matters is that mathematics produces results. Save the hot air for philosophers. This is called the "shut up and calculate" position.

The debate over the fundamental nature of mathematics is by no means new, and has raged since the time of the Pythagoreans. Can we use our hindsight now to shed any light on the above four positions?

A recent development within the last century was the discovery of fractals. Beautiful complex patterns, such as the Mandelbrot set, can be generated from simple iterative equations. Mathematical Platonists eagerly point out that elegant fractal patterns are common in nature, and that mathematicians clearly discover rather than invent them. A counterargument is that any set of rules has emergent properties. For example, the rules of chess are clearly a human contrivance, yet they result in a set of elegant and sometimes surprising characteristics. There are infinite numbers of possible iterative equations one can possibly construct, and if we focus on the small subset that result in beautiful fractal patterns we have merely seduced ourselves.

Take the example of infinite monkeys on keyboards. It appears miraculous when an individual monkey types a Shakespeare sonnet. But when we see the whole context, we realize all the monkeys are merely typing gibberish. In a similar way, it is easy to be seduced into thinking that mathematics is miraculously innate if we are overly focused on its successes, without viewing the complete picture.

The non-Platonist view is that, first, all mathematical models are approximations of reality. Second, our models fail, they go through a process of revision, and we invent new mathematics as needed. Analytical mathematical expressions are a product of the human mind, tailored for the mind. Because of our limited brainpower we seek out compact elegant mathematical descriptions to make predictions. Those predictions are not guaranteed to be correct, and experimental verification is always required. What we have witnessed over the past few decades, as transistor sizes have shrunk, is that nice compact mathematical expressions for ultra small transistors are not possible. We could use highly cumbersome equations, but that isn't the point of mathematics. So we resort to computer simulations using empirical models. And this is how much of cutting edge engineering is done these days.

The realist picture is simply an extension of this non-Platonist position, emphasizing that compact analytical mathematical expressions of the physical world around us are not as successful or ubiquitous as we'd like to believe. The picture that consistently emerges is that all mathematical models of the physical world break down at some point. Moreover, the types of problems addressed by elegant mathematical expressions are a rapidly shrinking subset of all the currently emerging scientific questions.

But why does this all matter? The "shut up and calculate" position tells us to not worry about such questions. Our calculations come out the same, no matter what we personally believe; so keep calm and carry on.

I, for one, believe the question is important. My personal story is that I used to be a Platonist. I thought all mathematical forms were reified and waiting to be discovered. This meant that I philosophically struggled with taking limits to infinity, for example. I merely got used to it and accepted it under sufferance. During my undergraduate days, I had a moment of enlightenment and converted to non-Platonism. I felt a great burden lift from my shoulders. Whilst this never affected my specific calculations, I believe a non-Platonist position gives us greater freedom of thought. If we accept that mathematics is invented, rather than discovered, we can be more daring, ask deeper questions, and be motivated to create further change.

Remember how irrational numbers petrified the bejesus out of the Pythagoreans? Or the interminable time it took mankind to introduce a zero into arithmetic? Recall the centuries of debate that occurred over whether negative numbers are valid or not? Imagine where science and engineering would be today if this argument was resolved centuries earlier. It is the ravages of Platonist-like thinking that have held back progress. I argue that a non-Platonist position frees us from an intellectual straightjacket and accelerates progress.

More information: Derek Abbott, "The reasonable ineffectiveness of mathematics," Proceedings of the IEEE, Vol. 101, No. 10, pp. 2147-2153 , 2013.

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Mathematics is the language of science and has enabled mankind to make extraordinary technological advances. There is no question that the logic and order that underpins mathematics, has served us in describing the patterns and structure we find in nature.

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We deal with numbers all the time. Not just while doing math lessons at school, but also while counting money at the shop, memorising the numbers of our favourite TV channels or even keeping tabs on the number of hours we spend in front of the Internet! But we are so used to numbers that it has never occurred to us to find out where these numbers come from.

For that, we must travel back in time. We must go back to 6th century India. It was around this time, that the great Indian astronomer Aryabhatta invented a set of numerals that is now used by people all over the world.

You might already have heard that zero was invented in India. But it is not so widely known that even the other numerals were invented in India only. This is because the figures written as 1, 2, 3 etc. are commonly known as 'Arabic'.

This would naturally make it seem that the number system originated in Arabia and not in India. Sounds rather mysterious no? That something that was invented by an Indian scientist should be known as Arabic? But there's quite an interesting story behind this.

Sometime in the year 771, Arab merchants took some Indian scholars to Baghdad (the present capital of Iraq) to help teach them the new set of numbers. After learning the numbers, the Arabs translated the numbers into their own script that is Arabic. Sometime later, the Arab traders carried a book of these numerals (in their language or script) to Europe, where the numbers were translated into Latin. As the world at large got these numbers from Arabia, these came to be known as Arabic.

In fact, it is interesting to note that there is another number system in use. This is the 'Roman' numerical system. The numbers in this system are written as I, II, III, IV, V etc. Although this number system is also a well-developed one, there's one problem in it. Since there is no symbol for zero in it, there is difficulty in carrying out addition, subtraction and other calculations.

Let's take an example. In the Arabic number system the calculation of 2076+600, can be easily computed by arranging the numbers in two vertical columns;

However, the same calculation is not so easy, when it comes to the Roman system. Why? Because under the Roman system the numbers are written differently. This is because M means a thousand, D stands for 500, C stands for a hundred, L for fifty, X for ten, V for five and I for one.

It is amazing what a big difference the seemingly simple and valueless number '0' can make. The small number '1' can be turned into a million! a billion!! Or even a trillion!!! - Thanks to the magical powers of zero.

Here are some more interesting facts. The script of the Arabic language (not mathematical) moves from right to left, unlike English, which moves from left to right. However, Arabic numbers are written from left to right. Why? Because they were borrowed from India!

Since the time they were invented, Arabic numerals have undergone only minor changes from the original Hindu manuscript. The numbers that have undergone slight changes include 4, 5, 6 and 7.

So that is the "number story" - how numbers were born in India, travelled to Arabia and then to Europe. And now? Well, the whole world is using them all the time. Rather interesting, no?

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We deal with numbers all the time. Not just while doing math lessons at school, but also while counting money at the shop, memorising the numbers of our favourite TV channels or even keeping tabs on the number of hours we spend in front of the Internet!

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I always wondered why we don't say oneteen instead of eleven and twoteen instead of twelve and threeteen in stead of thirteen. 

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I always wondered why we don't say oneteen instead of eleven and twoteen instead of twelve and threeteen in stead of thirteen. 

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How is it that mathematics describes nature so accurately? 

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How is it that mathematics describes nature so accurately? 

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How is it that mathematics describes nature so accurately?

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Answer (1 of 8): Mainly, because Mathematics has been hand-crafted and tailor-made to describe nature. It is specifically forged in a way that nature may be best described by it. See this function: It is called a Heaviside Unit Step function, written generally as u(t) in continuous time. It has...

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What is a good mathematics question? What does it accomplish?

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What is a good mathematics question? What does it accomplish?

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https://www4.uwm.edu/Org/mmp/PDFs/Yr5_PDFs/ThoughtProvokingQuestions-slides.pdf

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Cornell University's Mathematics Dept has a great project "GoodQuestions" that is sure to stimulate educator discussions about teaching.

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Cornell University's Mathematics Dept has a great project "GoodQuestions" that is sure to stimulate educator discussions about teaching.

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ConcepTests andJust-in-Time-Teaching. GoodQuestions is a pedagogical strategy that aims to raise the visibility of the key concepts and to promote a more active learning environment. The essence of the approach is to develop questions that

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What are some questions in mathematics that have subjective answers?

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What are some questions in mathematics that have subjective answers?

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What are some questions in mathematics that have subjective answers?

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Answer: Any deductive reasoning that involves the application of inference to sets of valid axioms, see Gödel's incompleteness theorems.

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What is mathematics? What are the branches within mathematics? 

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What is mathematics? What are the branches within mathematics? 

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Why are there three ways to symbolize multiplying -- X and * and ( )? But addition and subtraction have just their ➕and ➖?

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Why are there three ways to symbolize multiplying -- X and * and ( )? But addition and subtraction have just their ➕and ➖?