Tau vs. Pi

John Alberse, Brennen, Nishali, and John Scalley

Background Information

1) Geographic Origin, why it was needed.

a) Pi- The notation of π was first used by William Jones in 1706, which became standard. The origin of pi goes back to the Greeks who used it as apart of their alphabet but it was later used for math.
notation, in Wales. However, the number has been used for at least 4,000 years in Babylon and Egypt,
and later in Greece with Archimedes.

b) Tau- Bob Palais of the University of Utah was the first to bring Tau to a wide audience and to identify the issues in his paper
, “π is wrong”. Taught also comes from Greek alphabet and shouldn't be confused with Latin alphabet.

2) Subjects and professions used for, why is it needed.

a) Pi- Based off of Greek Alphabet. Trig in Euclidian geometry, for Spherical Geometry as well for
use in global maths. Physics


π = C/D

Area of a Circle = πr^2

Circumference of A Circle = 2πr

SIN(0) = 0, SIN(π/2) = 1, SIN (π) = 0, SIN(3π/2)

e^iπ = -1

b) Tau- Based off of Greek Alphabet. Trig, spherical. Physics. Engineering


Π = C/r

Area of a Circle = (1/2)τr^2

Circumference = τr

SIN(τ/4) = 1, SIN(τ/2) = 0, SIN(3τ/4), SIN(τ) = 0

e^iτ = 1
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Arguments for Tau

When using radians and dealing with circumfrie, tau is superior as it is far simplified. For example, finding the SIN and COS of pi requires ludicrous amounts of nonsensical equations: while τ/4 radians is one quarter rotation of a circle, to find one quarter of a circle with pi, the equation is π/2 radians, which is an odd disconnect between the equation and the result of the equation. Because tau is equivalent to one full rotation and pi is equivalent to 1/2 of a rotation kids often forget that one full rotation is equivalent to 2 pi not 1. So, whenever pi/ 2 is stated they say it is 1/2 the rotation instead of 1/4.
Similarly, Euler’s Identity is e^iπ=-1. But, if tau is used to replace pi, e^iτ = 1. A far easier number to use than -1, tau is obviously superior in this scenario. This makes sense,because a rotation in the complex plane by one turn is 1.This same trend follows in most of higher level mathematics.
In the job world of engineering tau helps represent the the inverse of time.

Rebuttal against pi

The principal argument used to support the idea of pi is that it is the best for use when calculating area or volume. The tauists will concede this advantage that pi holds over Tau: the beauty that a unit circle has an area of pi is irrefutable.
However, tau has more benefits in higher level mathematics, which deal more frequently with radii and circumference than area, in such equations as SIN, COS and TAN, as shown in the previous argument.

Our Solution

Many traditionalists which support pi and many radicals that support tau are refusing to concede even the slightest ground in this war over notation. However, it must be said that pi has an advantage in regards to area, and so lower level maths, while tau makes more sense to use in higher level maths dealing with circumference.
So, it only makes sense to use both notations: Pi for area, and tau for equations such as SIN and COS. It makes no sense to not compromise from either side, as both must concede the other has an advantage in some areas. Ergo, those areas should simply use the better notation. This will not destroy pi’s long history, it will simply add another, equally important addition to that history.

Arguments for Both

  • Arguments for Tau and Pi

  • Tau
    • Pros
      • COS and SIN are simplified with a more clear correlation between the equation and the meaning of the equation
      • Euler’s Identity results in positive 1 rather than negative 1.
      • Higher level maths tends to benefit from Tau as opposed to pi
    • Cons
      • When discussing area, the equation and the result of the equation have a disconnect.
      • Lower level maths are made unnecessarily complex by tau, requiring half tau often.
      • Non-traditional, the transition would be difficult
  • Pi
    • Pros
      • Tradition
      • Area of a circle is simplified by using pi as opposed to tau
      • The area of a unit circle is pi
      • Lower level maths are easier
      • Cons
      • Radii and circumferences are more complex than need be
      • The results of SIN and COS of pi are nonsensical rather than straightforward.
      • Higher level maths made more difficult
      • Euler’s identity results in negative 1, rather than positive.


"Tau Day | No, really, pi is wrong: The Tau Manifesto by Michael Hartl." Tau Day | No, really, pi is wrong: The Tau Manifesto by Michael Hartl. N.p., n.d. Web. 8 Jan. 2013. <http://tauday.com/>

"The Pi Manifesto." The Pi Manifesto. N.p., n.d. Web. 8 Jan. 2013. <www.thepimanifesto.com/>.

"DailyTech - Mathematics Upstarts Look to Replace Pi With New Circle Constant." DailyTech. N.p., n.d. Web. 9 Jan. 2013. <http://www.dailytech.com/Mathematics+Upstarts+Look+to+Replace+Pi+With+New+Circle+Constant/article21125.htm>.

"Forget Pi, here comes Tau." Math-Blog: Mathematics is wonderful!. N.p., n.d. Web. 9 Jan. 2013. <http://math-blog.com/2010/06/28/forget-pi-here-comes-tau/>.