# Pi vs. Tau

### By: Prad, Kaushik, Patrick, Chaitanya

## Pi

**A. From where geographically did the number originate? Why was it necessary?**

Originated in Ancient Civilizations like the Babylonians and Greek. It was first found in 1761 by Lambert who proved that Pi was the infinite ongoing irrational number. Also this number cannot be written as a ratio of integer numbers.

**B. In what subject (math and other) is it used? Which specific formula use it?**

It was necessary because it is the most basic level of finding the Circumference Radius, and Diameter of a circular object. Pi is used in Trigonometry, and Geometry. Also Pi can be used for Navigation, and other subjects that involve circles, or circular shapes. Specific formulas are: Area of a Circle=3.14*r to the power of 2, Circumference=3.14 times the Diameter.

**C. What other cultures use this number, and for what do they use it?**

Cultures that used, and still use Pi are the Greeks, Egyptians, and Babylonians. They were the people who first found out about this irrational number. In today's world India, China, and other developing countries also use Pi. They use it for the same things we do in America, like math, navigation, and traveling.

Extra Information:

Ancient civilizations knew that there was a fixed ratio of circumference to diameter that was approximately equal to three. The Greeks refined the process and Archimedes is credited with the first theoretical calculation of Pi. In 1761 Lambert proved that Pi was irrational, that is, that it can't be written as a ratio of integer numbers. In 1882 Lindeman proved that Pi was transcendental, that is, that Pi is not the root of any algebraic equation with rational coefficients. This discovery proved that you can't "square a circle", which was a problem that occupied many mathematicians up to that time.

Over the ensuing centuries, Chinese, Indian, and Arab mathematicians extended the number of decimal places known through tedious calculations, rather than improvements on Archimedes’ method. By the end of the 17th century, however, new methods of mathematical analysis in Europe provided improved ways of calculating pi involving infinite series. For example,Sir Isaac Newton used his binomial theorem to calculate 16 decimal places quickly. Early in the 20th century, the Indian mathematician Srinivasa Ramanujan developed exceptionally efficient ways of calculating pi that were later incorporated into computer algorithms. In the early 21st century, computers calculated pi to more than 2,700,000,000,000 decimal places, as well as its two-quadrillionth digit.

## Tau

**A. From where geographically did the number originate? Why was it necessary?**

Tau, was not created in a physical place, but it was created by a college professor in the year of 2001. The professor's name is Bob Palais, and he thought that Pi was an imposter of Tau, also that Tau is a better choice than Pi. Tau is a necessary number because the angles around the circle are fractions of how far around the circle's angle is.

**B. In what subject (math and other) is it used? Which specific formula use it?**

Tau is also used in Geometry, and Trigonometry. Also Tau can be used more efficiently in Trigonometry than Some specific formulas for Tau= 3.14*r to the power of 2/2.

**C. What other cultures use this number, and for what do they use it?**

No culture in the old times actually used Tau before because Tau was first recognized by Bob Palais in 2001. There is a group of people who support Tau, under a man called Michael Hartl. In todays time developing countries don't use Tau because it is not as known as Pi.

Extra Information:

Every June 28, math nerds makes his or her case for the abolition of arguably the most important irrational number in the world: pi. These men and women of the "tau" are adamant that pi, the ratio of circumference to diameter of a circle, should be replaced by tau, the circumference of a circle divided by the radius. They contend not that 3.14159265, the value of pi, is wrong, but that it's the wrong number to associate with a circle because "circles are more naturally defined by their radius than diameter.

Tau Day has been celebrated for at least 10 years. The underpinnings of the movement came from Bob Palais, a research professor of mathematics at the University of Utah. In 2001, he wrote an essay called "Pi is Wrong". In his opening salvo against Pi, he wrote "I am not questioning its irrationality, transcendence, or numerical calculation, but the choice of the number on which we bestow a symbol conveying deep geometric significant. The proper value, which does deserve all the reverence and adulation bestowed upon the current imposter, is the number now unfortunately known as 2π."

Michael Hartl announced “The Tau Manifesto” on what he calls Tau Day (6/28 for 6.28…). In this document, Hartl echoes the good points that Palais made and builds upon them to construct a strong case in favor of adopting a circle constant which is the ratio of a circle’s circumference to its radius, not its diameter. Inspired by Palais’ use of the word “turn”, he proposes calling this constant τ (tau).

## Pros and Cons

**Pros:**

- Pi is already in its simplest form.
- Pi is more commonly known so people may better understand you.
- Pi is a smaller number so it may be easier to use.
- Pi is used in many situations other than just finding the areas of shapes and stuff.
- Tau is the direct ratio of the radius of a circle to its circumference, and the radius of a circle, not the diameter of a circle (as used by Pi) is used to define the circle. The diameter is not a defining measurement for a circle and therefore Tau

**Cons:**

- Pi is harder to use while dealing with fractions because it is an irrational number.
- Pi is harder to use in complex geometry and trigonometry problems than it is in Algebra.
- Pi is only often used in subjects involving mathematics like Engineering and etc.
- Pi is losing its fame in important mathematics subjects like Geometry and Algebra and may soon be replaced if we don’t support Pi.