# theorem

[ˈθiːərəm]

## theorem Definition

• 1a statement or idea that can be proven by a series of logical steps based on assumptions
• 2a mathematical proposition that can be proved from other propositions that have already been proved or are assumed to be true

## Using theorem: Examples

Take a moment to familiarize yourself with how "theorem" can be used in various situations through the following examples!

• Example

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

• Example

Fermat's Last Theorem was finally proven after centuries of attempts.

• Example

The theorem of calculus is a fundamental concept in mathematics.

## Phrases with theorem

• ### Bayes'theorem

a mathematical formula used to calculate conditional probabilities

Example

Bayes' theorem is used in many fields, including statistics and artificial intelligence.

• ### Euclid'stheorem

a geometric theorem attributed to the ancient Greek mathematician Euclid, stating that there are infinitely many prime numbers

Example

Euclid's theorem is one of the oldest and most famous results in number theory.

• ### Pappus'stheorem

a theorem in projective geometry that relates the areas of two triangles that share a common cevian

Example

Pappus's theorem has many applications in architecture and engineering.

## Origins of theorem

from Greek 'theorema', meaning 'a sight, speculation, theory'

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## Summary: theorem in Brief

A 'theorem' [ˈθiːərəm] is a statement or idea that can be proven through logical steps based on assumptions. It is often used in mathematics, such as the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Other examples include Bayes' theorem, Euclid's theorem, and Pappus's theorem.

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