Pasch's axiom

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In geometry, Pasch's axiom, is a result of plane geometry used by Euclid, but yet which cannot be derived from Euclid's postulates. Its axiomatic role was discovered by Moritz Pasch.

The axiom states that, in the plane,

given three noncollinear points a, b, c and a line X not containing any of these points, if X includes a point between a and b, then X also includes one and only one of the following: a point between a and c, or a point between b and c.

Pasch published this axiom in 1882, and showed that Euclid's axioms were incomplete.

Pasch's axiom is to be distinguished from Pasch's theorem.

[edit] References

  • Philip J. Davis and Reuben Hersh. The Mathematical Experience. Birkhäuser Boston, Boston, 1981. Page 160. [QA8.4.D37 1982]

[edit] External link

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