Pi approximation representation, illustration

Pi approximation representation, illustration

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Caption: Pi approximation representation, illustration. Pi can be approximated using a fraction, such as 22/7. This diagram shows the accuracy of the best approximations m/n for m from 1 to 10,000. Each dot represents a value of m, arranged on an Archimedean spiral, starting with m=1 (top) and ending at m=10,000 (centre). The colours encode the accuracy of the approximations. Pi (the sixteenth letter of the Greek alphabet) is the symbol used in mathematics to represent the constant of the ratio of the circumference of a circle to its diameter. It is a crucial element of periodic functions and is found in many formulae in trigonometry and geometry. The value of this ratio is approximately 3.14159. It has been calculated to over one trillion digits beyond its decimal point, though as an irrational and transcendental number it continues infinitely without repetition or pattern.

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