Formal Sciences

Mathematics

~500 BCE

Beginner

Pythagorean Theorem

a^2 + b^2 = c^2

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

By Pythagoras, Babylonian mathematicians

Formal Sciences

Pythagorean Theorem

~500 BCE · Pythagoras

Human Reviewed

84%

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Story PortalWho discovered this?Discover how Pythagoras and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — gps triangulation.Math PortalWhat does it derive from?Trace the mathematical lineage from quadratic formula.Future PortalWhere is it going?Spatial computing

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Why it matters: It enabled surveying, navigation, architecture, and the concept of distance in any dimension.

Discoverers: Pythagoras, Babylonian mathematicians (~500 BCE)

What does it mean?

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Why should I care?

It enabled surveying, navigation, architecture, and the concept of distance in any dimension.

Equation Compass

North — Prerequisites

Quadratic Formula

West — History

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$a$	Side A	m	Length of first leg
$b$	Side B	m	Length of second leg
$c$	Hypotenuse	m	Longest side opposite right angle

Worked Example

A triangle with legs 3 and 4 has hypotenuse c = √(9+16) = 5.

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Sources & further reading

Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

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