# Math Project: Pi

## The History of Pi

1. Where did Pi originate from? (geometrically)

-Ancient Babylonians (the Greek letter representing this number was popularized by Euler in the 18th century).

2. Why was Pi necessary?

-To determine the ratio between the circumference and the diameter of the circle.

3. In what subjects is Pi used?

-Math, physics, and astronomy.

4. Which specific formulas use Pi?

-Circumference of a circle of a given radius.

-Area of a circle of a given radius.

-Volume of a sphere of a given radius.

-Surface area of a sphere of a given radius.

(Geometry)

5. What other cultures use Pi? What do these cultures use it for?

-Babylonians: Math

-Egyptians: Geometry (Pyramids)

-Chinese: Geometry (Polygons)

-Hebrew: Mathematics and Religious Testaments (Bible)

-Greek: Geometry

## The History of Tau

1. Where did Tau originate from? (geometrically)

-Egyptians

2. Why is Tau necessary?

-Tau helps calculating the circumference of a circle faster, easier, and more efficient. Tau also determines the ratio between the circumference of the circle to the radius.

3. In what subjects is Tau used?

-Math, Physics, and Biology.

4. What specific formulas use Tau?

-τ=c/r, τ =2(A/r^2), and the Euler's formula.

5. What other cultures use Tau? For what do these cultures use Tau for?

-Egyptians: Geometry (Pyramids)

## Arguments

1. Pi should be defined as C/D not C/r.

2. The area of a unit circle is pi, and confusion would occur if tau was used instead.

3. The only worse thing than multiplying a number by 2 is dividing the number by 2. In many equations the variable pi is shown alone and without a two in front of it, in these cases using tau would be a hassle and a waste of time. It would cause complexion in these already complicated, long equations. For example in the density function, f(x)= 1/pi(1+x^2), pi is multiplied by 1+x^2, however if tau was used it would be, f(x)= 1/ {[tau(1+x^2)]/2}, much more confusing and longer to solve.

4. Multiples of pi are very important in mathematics. The importance of tau comes from the fact that it is a multiple of pi, but other multiples of pi are just as important.

5. There may be a nice formula that uses tau, but that is because tau is a multiple of pi. In reality, there is also a nice formula for the multiple of 3 pi, but that does not mean we should start worshiping 3 pi also.

6. Changing pi to tau will cost lots of money, because calculators and textbooks would need to be updated which will cost millions of dollars. We can't afford to spend millions of dollars on just changing textbooks and calculators when we can just continue on using pi instead of tau.

## Possible Arguments for Tau

1. Tau makes some equations easier to do.

2. Pi is very confusing and and it's an unnatural choice for the circle constant.

3. 2 pi is used often, so it's easier to just use tau.

4. The value 3.14 is not the important value when it comes to circles.

5. Pi is only used for elementary geometry, while tau will be used for more advanced geometry.

## Rebuttals for Arguments of Tau

1. Tau only makes equations with 2 pi easier, but it makes all of the other equations more difficult. (Circle equations uses 2 pi often, while other equations don't).

2. Pi is not confusing for the circumference of the circle, because a division by 2 is only needed. Finding the area becomes confusing when tau is used.

3. Little amounts of equations actually need 2 pi, but there's many equations requiring the use of pi.

4. Pi is important in finding the area of the circle.

5. Pi is used in advanced mathematics such as trigonometry and physics.

## Opinionated Arguments

• Pi is the most efficient way of measuring a circle. Pi has been used as the radiant since the beginning of our education. We all know how to use pi and calculators have been fitted for pi, not tau. So, why change now?

## Survey Results

Survey: http://www.surveymonkey.com/s/NLD63HL

*The people surveyed were supplied with the Tau Manifesto, Pi Manifesto, and other reference materials.

*There were 20 people surveyed.

The survey results are shown in a circle graph.

## Interviews

"I chose pi, because I've been using pi since I was young, and I don't want to change something that I have been using for a long time. I didn't choose tau, because I'm not that familiar with tau, and it seems more confusing to understand.

"I chose tau, because looking through the reference materials makes me think that using tau will actually be easier and more efficient when trying to find mathematical equations. Using tau, I think, would make solving equations more interesting and a different experience.

Mathematical Pi Song