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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 2π.
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.
τ is commonly defined as the ratio of a circle's circumference C to its radius r: A circle is defined as a closed curve formed by the set of all points in a plane that are a given distance from a fixed point, where the given distance is called the radius.
The distance around the circle is the circumference, and the ratio C/r is constant regardless of the circle's size. Thus, τ denotes the fixed relationship between the circumference of any circle and its radius.
When radians are used as the unit of angular measure there are τ radians in one full turn of a circle, and the radian angle is aligned with the proportion of a full turn around the circle: 1/8τ rad is an eighth of a turn; 3/4τ rad is three-quarters of a turn.
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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 2π.
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.
τ is commonly defined as the ratio of a circle's circumference C to its radius r: A circle is defined as a closed curve formed by the set of all points in a plane that are a given distance from a fixed point, where the given distance is called the radius.
The distance around the circle is the circumference, and the ratio C/r is constant regardless of the circle's size. Thus, τ denotes the fixed relationship between the circumference of any circle and its radius.
When radians are used as the unit of angular measure there are τ radians in one full turn of a circle, and the radian angle is aligned with the proportion of a full turn around the circle: 1/8τ rad is an eighth of a turn; 3/4τ rad is three-quarters of a turn.
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