Brouwer fixed-point theorem

[ brou-er fikst-point thee-er-uhm, theer-uhm ]

noun

, Mathematics.

1. the theorem that for any continuous transformation of a circle into itself, including its boundary, there is at least one point that is mapped to itself.

Word History and Origins

Origin of Brouwer fixed-point theorem¹

Named after L. E. J. Brouwer

Example Sentences

Dr. Tanton chose Sperner’s lemma, which is related to the Brouwer fixed-point theorem that both Francis Su and Holly Krieger talked about on their episodes of the podcast.

From Scientific American

Dr. Krieger chose the Brouwer fixed-point theorem as her favorite theorem, which means for the first time on the show, we had a theorem repeat!

From Scientific American

A well-known result in topology called the Brouwer Fixed-Point Theorem states that any continuous transformation of a surface into itself has at least one fixed point.

From Project Gutenberg

A well-known result in topology called the Brouwer Fixed-Point Theorem states that any continuous transformation of a 2-sphere into itself has at least one fixed point.

From Project Gutenberg