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# Pi
Pi is one of the most important and famous [numbers](number.md), equal to approximately 3.14, most commonly defined as the ratio of a circle's circumference to its diameter (but also definable in other ways). It is one of the most fundamental mathematical constants of our universe and appears extremely commonly in [mathematics](math.md), nature and, of course, [programming](programming.md). When written down in traditional decimal system, its digits go on and on without end and show no repetition or simple pattern, appearing "random" and [chaotic](chaos.md) -- as of 2021 pi has been evaluated by [computers](computer.md) to 62831853071796 digits. In significance and properties pi is similar to another famous number: [e](e.md).
Pi is one of the most important and famous [numbers](number.md), equal to approximately 3.14, most popularly defined as the ratio of a circle's circumference to its diameter (but also definable in other ways). It is one of the most fundamental mathematical constants of our universe and appears extremely commonly in [mathematics](math.md), nature and, of course, [programming](programming.md). When written down in traditional decimal system, its digits go on and on without end and show no repetition or simple pattern, appearing "random" and [chaotic](chaos.md) -- as of 2021 pi has been evaluated by [computers](computer.md) to 62831853071796 digits. In significance and properties pi is similar to another famous number: [e](e.md).
Pi is a [real](real_number.md) [transcendental](transcendental.md) number, i.e. simply put *it cannot be defined by a "simple" equation* (it is not a root of any [polynomial](polynomial.md) equation). As a transcendental number it is also an [irrational](irrational.md) number, i.e. it cannot be written as an integer [fraction](fraction.md). Mathematicians nowadays define pi via the period of the [exponential function](exp.md) rather than geometry of circles. If we stick to circles, it is [interesting](interesting.md) that in [non-Euclidean](non_euclidean.md) geometry the value of "pi" could be measured to different values (if we draw a circle on an equator of a ball, its circumference is just twice its diameter, i.e. "pi" would be measured to be just 2, reveling the curvature of space).