Tau (2π)
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Tau (τ) is a constant which has been proposed by mathematician Michael Hartl after an earlier proposal by Bob Palais as a replacement for the familiar circle-constant π. The value of τ is 2π[1], or approximately 6.28318531. The symbol τ was chosen as to stand for turn or τόρνος (tornos), since τ radians are equivalent to one full turn. The product 2π occurs very frequently in mathematics for many reasons, mainly that circles are usually defined by their radius rather than by their diameter[2].
Proposed advantages
Palais and Hartl claim a number of advantages of using τ instead of π.
- The so called "special angles", that need to be memorized when using π, simply become fractions of a whole circle, that is Template:Tfrac τ, Template:Tfrac τ, Template:Tfrac τ, Template:Tfrac τ and Template:Tfrac τ. It is easier to explain that Template:Tfrac of a pizza corresponds to Template:Tfrac τ than Template:Tfrac π[3]. Hartl describes the use of pi in this context as a "pedagogical disaster."
- In many formulae, such as normal distribution and Fourier transforms, the factor 2π can be eliminated, thus simplifying them[4].
- The periodicity of the cosine and sine functions is τ instead of 2π, which is not only a simpler notation, thus eliminating a possible source of errors, but also more intuitive[4].
- The formula for the circumference of a circle becomes simply τr, without introducing a factor 2.
- The formula for the area of a circle falls in line with the power rule for integrals (e.g. kinetic energy K = Template:Tfrac mv 2). Instead of A = πr 2, it becomes A = Template:Tfrac τr 2[4].
- Eulers identity is more straightforward expressed in τ it is in π: eiτ=1 instead of eiπ = -1, or as it's usually expressed, eiπ + 1 = 0.[4]
Other interesting facts
The famous Feynman point (six consecutive 9s early in the decimal digits of π) arrives one digit earlier in τ, and is seven digits long instead of six[5].
See also
References
- ^ Sequence OEIS: A019692 in the OEIS.
- ^ eg. x=r.cos(t), y=r.sin(t) or r2=x2+y2
- ^ Wolchover, Natalie (June 29, 2011). "Mathematicians Want to Say Goodbye to Pi". Life's Little Mysteries. Retrieved 2011-07-03.
- ^ a b c d Palais, Robert (2001). "π Is Wrong!" (PDF). The Mathematical Intelligencer. 23 (3): 7–8. Retrieved 2011-07-03.
- ^ Michael Hartl. "100,000 digits of τ". Retrieved 6 July 2011.
Further reading
- Hartl, Michael (June 28, 2010). "The Tau Manifesto". Tau Day. Retrieved 2011-07-03.
- "On National Tau Day, Pi Under Attack". Fox News Channel. NewsCore. June 28, 2011. Retrieved 2011-07-03.
- Springmann, Alessondra (June 28, 2011). "Tau Day: An Even More Fundamental Holiday Than Pi Day". PCWorld. Retrieved 2011-07-03.
- Palmer, Jason (28 June 2011). "'Tau day' marked by opponents of maths constant pi". BBC News. Retrieved 2011-07-03.
External links
- Vi Hart (Author). Pi Is (still) Wrong (flv). YouTube.