Pi

The mathematical constant ? is the ratio of a circle's circumference (Greek ??????????, periphery) to its diameter and is commonly used in mathematics, physics, and engineering. The name of the Greek letter ? is pi (pronounced pie), and this spelling can be used in typographical contexts where the Greek letter is not available. ? is also known as Archimedes' constant (not to be confused with Archimedes' number) and Ludolph's number.

Properties

π is an irrational number; that is, it cannot be written as the ratio of two integers, as was proven in 1761 by Johann Heinrich Lambert.

Related Topics:
Irrational number - Integer - 1761 - Johann Heinrich Lambert

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π is also transcendental, as was proven by Ferdinand von Lindemann in 1882. This means that there is no polynomial with rational coefficients of which π is a root. An important consequence of the transcendence of π is the fact that it is not constructible. Because the coordinates of all points that can be constructed with ruler and compass are constructible numbers, it is impossible to square the circle, that is, it is impossible to construct, using ruler and compass alone, a square whose area is equal to the area of a given circle.

Related Topics:
Transcendental - Ferdinand von Lindemann - 1882 - Polynomial - Rational - Constructible - Square the circle - Ruler and compass

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