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Pi

The number π (/paɪ/ ⓘ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.

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Overview

Fundamentals

History

Modern quest for more digits

Role and characterizations in mathematics

Outside mathematics

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Pi

Nodes461
Edges460
Triples253
Avg. degree2
Density0.004338
Components1

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Pi

Top relations

related to Infinite series · 24
Pi → Although, An, Archimedes, Around, European, François Viète, Gottfried Wilhelm Leibniz, Gregory, Gregory's, In, Infinite, James Gregory, Kerala, Leibniz, Madhava, Nilakantha, Nilakantha Somayaji, Sangamagrama, Sanskrit, Several
related to Polygon approximation era · 23
Pi → AD, Almagest, Apollonius, Archimedes, Archimedes's, Around, BC, By, Cao Wei, China, Greco-Roman, Greek, In, Liu, Liu Hui, Liu Hui's, Perga, Ptolemy, The, This
related to Adoption of the symbol π · 18
Pi → Barrow, Before, Greek, Gregory, However, John Machin, Jones, Machin, Mathematics, Mr, New Introduction, Oughtred's Clavis Mathematicae, Periphery, Synopsis Palmariorum Matheseos, The, The Greek, Welsh, William Jones
related to Memorizing digits · 18
Pi → Akira Haraguchi, An, English, Guinness World Records, How, In, India, James Jeans, Japanese, March, One, Piphilology, Poems, Rajveer Meena, Record-setting, Such, The, When
related to Computer era and iterative algorithms · 16
Pi → Cook, ENIAC, First, Fourier, George Reitwiesner, John, Karatsuba, Levi Smith, Mathematicians John Wrench, Neumann, Such, The, They, Toom, Two, Using
related to history · 15
Pi → Although, Babylon, BCE, CE, Egypt, Giza, Great Pyramid, In, In Babylon, In Egypt, Indian, Rhind Papyrus, Shulba Sutras, Surviving, The
related to External links · 12
Pi → April, Archived, BibNum, December, Demonstration, Eric, Lambert, MathWorld, PDF, Search Engine, Wayback Machine, Weisstein
related to Approximate value and digits · 10
Pi → A000796, A063673, A063674, Approximate, Digits, Integers, List, OEIS, Some, The
related to Fourier series · 9
Pi → Among, Fourier, It, Nicolas Bourbaki, Periodic, R/Z, That, The, The Fourier
related to In popular culture · 9
Pi → Découverte, English, In, On, Palais, Paris, Perhaps, The, William Shanks

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Important terminology

displaystyle digits frac number circle used series infinite constant function one also formulae integral formula numbers complex algorithm value textstyle

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
.mw-parser-output .sfracinstance ofalthough fractions0.80text
number theoryinstance ofIt also appears in areas0.80text
statisticsinstance ofIt also appears in areas0.80text
and in modern mathematical analysisinstance ofIt also appears in areas0.80text
this was proposed as a definition of π by Karl Weierstrassinstance ofAn integral0.80text
who defined it directly as an integral in 1841.Integration is no longer commonly used in a first analytical definition becauseinstance ofAn integral0.80text
as Remmert 2012 explainsinstance ofAn integral0.80text
differential calculus typically precedes integral calculus in the university curriculuminstance ofAn integral0.80text
so it is desirable to have a definition of π that does not rely on the latterinstance ofAn integral0.80text
James Gregoryinstance ofAlthough infinite series were exploited for π most notably by European mathematicians0.80text
Gottfried Wilhelm Leibnizinstance ofAlthough infinite series were exploited for π most notably by European mathematicians0.80text
the approach also appeared in the Kerala school sometime in the 14th or 15th centuryinstance ofAlthough infinite series were exploited for π most notably by European mathematicians0.80text

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