Tau vs. Pi
John Alberse, Brennen, Nishali, and John Scalley
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
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
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.
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
- 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
- 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
- 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
- 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.
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"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/>.