Theorems
Pythagorean Theorem
Also Known As Pythagoras' Theorem
Geometry
Citation Formats
General Reference
APA Style
BibTeX
Perhaps the most famous theorem in mathematics, relating the three sides of a right triangle. Tablets from Babylon show the relationship was known and used numerically well over a thousand years before Pythagoras; tradition credits his school with the first general geometric proof, though no writing survives to confirm this directly. Hundreds of distinct proofs are now known, including one attributed to United States President James A. Garfield.
Facts
Disputed
Proof YearThe relationship was used empirically by Babylonian and Egyptian mathematicians centuries earlier; whether Pythagoras personally, or a later member of his school, produced the first general proof is genuinely uncertain, since no writing by Pythagoras survives. StatementIn a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides: a squared plus b squared equals c squared. 1 Cross-Tradition Connections
In Branch
Proved By
Why this is disputed. Traditional attribution; independently confirmed proof authorship is not possible given the surviving record.
Sources
1. Wolfram MathWorld
Wolfram Research, Inc.
2. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsBiography of PythagorasQuote, Biography of Pythagoras
Although the theorem, now known as Pythagoras's theorem, was known to the Babylonians 1000 years earlier he may have been the first to prove it.
Pythagorean Theorem (Wikipedia)
Wikimedia FoundationProved By: Pythagoras, History sectionQuote, Proved By: Pythagoras, History section
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
Pythagorean Theorem (Wikipedia)
Wikimedia FoundationIn Branch: Geometry, IntroductionQuote, In Branch: Geometry, Introduction
the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
Dissenting Readings (1 dissenting reading)
Proved By: Pythagoras
Crediting Pythagoras alone with this theorem understates its independent discovery elsewhere. Chinese mathematical texts, most notably the Zhoubi Suanjing, preserve an independent geometric derivation of the same right-triangle relationship, there called the gougu theorem, on a timeline that historians of Chinese science place at or before the period conventionally assigned to Pythagoras, alongside the already-acknowledged Babylonian numerical knowledge of the relationship a thousand years earlier still. The theorem was discovered and used in more than one civilization independently; naming it for one Greek school, while a durable convention, is a convention, not a finding about priority.
A dissenting reading, from Joseph NeedhamMacTutor History of Mathematics Archive, University of St Andrews, School of Mathematics and Statistics
Reader Challenges (0 open reader challenges)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.
View At A Past Year
The atlas records no dated fact of its own for this entry, so there is no other year to choose.