# Should Pi be replaced with Tau?

In mathematics, Pi (with a value of approximately 3.1415926…) is used in trigonometry. Pi is the ratio of the circumference to the diameter.  Tau, the proposed replacement, represents the ratio of the circumference to the radius.

## Pi should be kept

Introduction

Using Tau (τ) makes for simpler math and easier learning of trigonometry. It is fundamentally a better value to allow a user to understand the mathematical concepts.

Introduction

Pi (π) is in wide use and its replacement would put a learning burden on everyone who is already accustomed to the current system.  There are no real benefits from using Tau that would justify this change.

A circle is defined as having all points equidistant from a point, at a distance defined as the radius.  The radius is the defining property of a circle and the mathematical constant used should emphasize this.

The only way to measure most circles that exist in nature is by the diameter.  This makes using the diameter in Pi easier for real world applications, because conversions are not required.

Conversion from radians to tau is much easier than radians to pi. One circle has tau radians or two pi radians.  When performing trigonometry using pi, it is necessary to constantly consider the conversion factor of two, which tau eliminates.

Keeping radians simple is more important than keeping the area of a circle simple, because radians are used in trigonometry and therefore throughout mathematics and physics.

The use of Radians as a comparison point is arbitrary.  If the area of a circle was used instead of the angular measurement, then we would see how Pi is a much better unit for representing a circle.  (See area of a circle section below)

Current practice

Although Pi is conventionally used, teaching Tau may make trigonometry significantly easier and allow for a better understanding of trigonometry amongst students.

Current practice

Pi is in wide use.  Changing text books, scientific journals and other materials to Tau would be a large effort with negligible benefit.

Euler's equation

e^i π = -1 is derived from e^iθ=cosθ+i sinθ.  Solving using Tau we find that e^i τ = 1, which is just as beautiful an equation.

Euler's equation

Changing Pi would make Euler’s equation less attractive.  Substituting π with τ /2 changes e^i π = -1 to e^i τ /2 = -1.

Area of a circle

Changing the equation for the area of a circle to A = τ/2 r^2 tell us something about the nature of the calculation.  The τ/2  acts as evidence that the area equation can be derived, and makes the area of a circle look like other classically derived equations such as the equation for distance fallen (y =1/2gt^2) or the equation for the force of a spring (U =1/2kx^2)

Area of a circle

The equation for the area of a circle is A = π r^2.  Making this A = τ/2 r^2 makes the equation less nice.

Pi vs Tau

Should Pi be replaced by Tau?

1
6

Yes, replace Pi with Tau
2
3

No, keep using Pi
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References:

1. Vi Hart: Pi is (still) wrong: http://www.youtube.com/watch?v=jG7vhMMXagQ

2. Michael Hartl: The Tau Manifesto: http://tauday.com/tau-manifesto

3. The Pi Manifesto: http://www.thepimanifesto.com/

4. Numberfile: Tau Replaces Pi: http://www.youtube.com/watch?v=83ofi_L6eAo

5. Numberfile: Tau vs Pi Smackdown: http://www.youtube.com/watch?v=ZPv1UV0rD8U

• ### Roman

I like pie, yum!

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• ### Neil NP

Tau is like two pies! (Two half pies. Confused?)

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• ### Roman

Pumpkin PI = yum squared

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• ### Neil NP

Ever heard of Tautology? It's a formula that is true in every possible interpretation. That isn't relevant, but I thought it was interesting.

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