Tau (mathematics)

The number $𝜏$ (/ˈtaʊ, ˈtɔː, ˈtɒ/ ^ⓘ; spelled out as tau) is a mathematical constant that is the ratio of a circle's circumference to its radius. It is approximately equal to 6.28 and exactly equal to 2 $π$ .

$𝜏$ and $π$ are both circle constants relating the circumference of a circle to its linear dimension: the radius in the case of $𝜏$ ; the diameter in the case of $π$ .

While $π$ is used almost exclusively in mainstream mathematical education and practice, it has been proposed, most notably by Michael Hartl in 2010, that $𝜏$ should be used instead. Hartl and other proponents argue that $𝜏$ is the more natural circle constant and its use leads to conceptually simpler and more intuitive mathematical notation.

Critics have responded that the benefits of using $𝜏$ over $π$ are trivial and that given the ubiquity and historical significance of $π$ a change is unlikely to occur.

The proposal did not initially gain widespread acceptance in the mathematical community, but awareness of $𝜏$ has become more widespread, having been added to several major programming languages and calculators.