User:ArniDagur/sandbox

The number 𝜏 is a mathematical constant, the ratio of a circle's circumference to its radius, commonly approximated as 6.28319, and is equivalent to 2$\pi$. It is represented by the Greek letter "𝜏", though it is also sometimes spelled out as "tau".

Being an irrational number, 𝜏 cannot be expressed exactly as a fraction (equivalently, its decimal representation never ends and never settles into a permanent repeating pattern). The digits appear to be randomly distributed. In particular, the digit sequence of 𝜏 is conjectured to satisfy a specific kind of statistical randomness, but to date no proof of this has been discovered. Also, 𝜏 is a transcendental number; that is, a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of 𝜏 implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. Because its most elementary definition relates to the circle, 𝜏 can be found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses, and spheres.

Tau day is celebrated annually every 28th of June (6/28 in the U.S. calendar system) by those who advocate for its use over π.