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Pasch's theorem

Pasch's theorem proper noun: a result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d).

Proper noun

Pasch's theorem

  1. A result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d).

Origin of Pasch's theorem

Stated in 1882 by the German mathematician Moritz Pasch.

Questions about Pasch's theorem

What does Pasch's theorem mean?
Pasch's theorem means a result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d).
What part of speech is Pasch's theorem?
Pasch's theorem is a proper noun.

Words near Pasch's theorem in the dictionary

  1. pasch
  2. Pasch egg
  3. Pasch eggs
  4. Pasch of the Cross
  5. Pasch's axiom
  6. Pasch's theorem
  7. Pascha
  8. Pascha egg
  9. Pascha eggs
  10. paschal
  11. Paschal basket

Source and license

Adapted from Wiktionary: Pasch's theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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