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-as of [11 APRIL 2024]–
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-the number π is a ‘mathematical constant’, the ratio of a circle’s ‘circumference’ to its ‘diameter’, commonly approximated as ‘3.14159’–
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*pronounced PI*
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(it has been represented by the greek letter “π” since the ‘mid-1700s’, though it is also sometimes spelled out as “pi” (/paɪ/).
(being an ‘irrational number’, π cannot be expressed exactly as a ‘fraction’
(equivalently, its ‘decimal representation’ never ends and never settles into a ‘permanent repeating pattern’)
(still, fractions such as ’22/7′ and other ‘rational numbers’ are commonly used to approximate π)
(the digits appear to be randomly distributed)
(in particular, the ‘digit sequence’ of π is conjectured to satisfy a specific kind of ‘statistical randomness’, but to date no proof of this has been discovered)
(also, π is a ‘transcendental number’; that is, a number that is not the root of any ‘non-zero polynomial’ having ‘rational coefficients’)
(this ‘transcendence’ of π implies that it is impossible to solve the ‘ancient challenge’ of ‘squaring the circle’ with a ‘compass’ + ‘straight-edge’)
(‘ancient civilizations’ required fairly accurate computed values for π for ‘practical reasons’)
(it was calculated to 7 digits, using ‘geometrical techniques’, in ‘chinese mathematics’, and to about ‘5 digits’ in ‘indian mathematics’ in the ‘5th century AD’)
(the historically first exact formula for π (based on ‘infinite series’) was not available until a ‘millennium’ later, when in the ’14th century’ the ‘madhava–leibniz series’ was discovered in ‘indian mathematics’)
(in the ”1900s’ + ‘2000s’, ‘mathematicians’ + ‘computer scientists’ discovered new approaches that, when combined with ‘increasing computational power’, extended the ‘decimal representation’ of π to many ‘trillions of digits’ after the ‘decimal point’)
(practically all ‘scientific applications’ require no more than a ‘few hundred digits’ of π (and many substantially fewer), so the ‘primary motivation’ for these ‘computations’ is the ‘quest’ to find more ‘efficient algorithms’ for calculating ‘lengthy numeric series’, as well as the desire to ‘break records’)
(the ‘extensive calculations’ involved have also been used to test ‘supercomputers’ + ‘high-precision multiplication algorithms’)
(because its most ‘elementary definition’ relates to the ‘circle’, π is found in many formulae in ‘trigonometry’ + ‘geometry’, especially those concerning ‘circles’, ‘ellipses’, and ‘spheres’)
(in more ‘modern mathematical analysis’, the number is instead defined using the ‘spectral properties’ of the ‘real number system’, as an ‘eigenvalue’ or a ‘period’, without any reference to ‘geometry’)
(it appears therefore in areas of ‘mathematics’ and ‘the sciences’ having little to do with the ‘geometry’ of ‘circles’, such as ‘number theory’ and ‘statistics’, as well as in almost all areas of ‘physics’)
(the ubiquity of π makes it one of the most widely known ‘mathematical constants’ both inside and outside the ‘scientific community’)
(several books devoted to it have been published)
(the number is celebrated on “pi day”, and ‘record-setting calculations’ of the ‘digits’ of π often result in ‘news headlines’)
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(attempts to memorize the value of π with increasing precision have led to records of over ‘70,000 digits’)
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*👨🔬🕵️♀️🙇♀️*SKETCHES*🙇♂️👩🔬🕵️♂️*
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💕💝💖💓🖤💙🖤💙🖤💙🖤❤️💚💛🧡❣️💞💔💘❣️🧡💛💚❤️🖤💜🖤💙🖤💙🖤💗💖💝💘
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*🌈✨ *TABLE OF CONTENTS* ✨🌷*
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🔥🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥🔥