What is Tau (mathematical constant)?
{{about|the number|the Greek letter|Tau (letter)}} [[File:TAU constant.svg|thumb|right|Tau is an endless string of numbers]] '''Tau''' ('''{{tau}}''') ({{IPAc-en|'|t|ɔː|,_|'|t|aʊ}}) is a [[mathematical constant]] that is the [[ratio]] of a [[circle]]'s [[circumference]] to its [[radius]]. It starts as 6.283185307179586, and continues without end in a way that is not predictable. Numbers like this are called [[Irrational number|irrational]] numbers.<ref>{{Cite web|url=https://mathvault.ca/hub/higher-math/math-symbols/|title=Compendium of Mathematical Symbols|date=2020-03-01|website=Math Vault|language=en-US|access-date=2020-08-10}}</ref> The radius is the shortest connection between the center and the circumference of a circle. The [[circumference]] is the distance around a circle. Even though the radius and circumference are different for different circles, the number tau remains constant: its value never changes. This is because the relationship between the circumference and radius is always the same. ==Fundamentals== ===Definition=== {{tau}} is commonly defined as the [[ratio]] of a [[circle]]'s [[circumference]] {{math|''c''}} to its [[radius]] {{math|''r''}}: :<math>	au=rac{c}{r}</math> ===Approximate value=== Tau is often written as '''{{tau}}'''. It is also an [[irrational number]], meaning it cannot be written as a [[Fraction (mathematics)|fraction]] (<math>rac{a}{b}</math>), where 'a' and 'b' are [[integer]]s (whole numbers). This basically means that the digits of tau that are to the right of the [[decimal]] go [[Infinity|forever]]—without repeating in a pattern, and that it is impossible to write the exact value of tau as a number. Tau can only be [[approximated]], or measured to a value that is close enough for practical purposes. A value close to tau is 6.283185307179586476925287. [[Computer]]s can be used to get better approximations of tau. == Tau in real life == There are different ways to calculate many digits of tau. This is of limited use though. Tau can sometimes be used to work out