In
geometry, Pasch's theorem, stated in 1882 by the German mathematician
Moritz Pasch,
is a result in
plane geometry which cannot be derived from
Euclid's postulates
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axiom ...
.
Statement
The statement is as follows:
ere, for example, (, , ) means that point lies between points and .
See also
*
Ordered geometry
*
Pasch's axiom
Notes
References
*
*
External links
*
Euclidean plane geometry
Foundations of geometry
Order theory
Theorems in plane geometry
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