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Try to explain (roughly) the difference between an axiom and a postulate.
A '''postulate''' is a statement that is assumed to be true without proof. [[Euclid]], the father of geometry, based ''The Elements'' on ten such statements, divided into five "[[axiom]]s" and five "postulates."<ref>Euclid. ''The Elements''.</ref> These are used as foundation for geometry<ref>"1.1: Definitions, Theorems, and Postulates." ''Beauty, Rigor, Surprise''.</ref> and occasionally applied to other sciences, such as [[special relativity]].<ref>http://casa.colorado.edu/~ajsh/sr/postulate.html</ref><ref>https://www.nobelprize.org/educational/physics/relativity/postulates-1.html</ref>
A '''postulate''' is a statement that is assumed to be true without proof. [[Euclid]], the father of geometry, based ''The Elements'' on ten such statements, divided into five "[[axiom]]s" and five "postulates."<ref>Euclid. ''The Elements''.</ref> These are used as foundation for geometry<ref>"1.1: Definitions, Theorems, and Postulates." ''Beauty, Rigor, Surprise''.</ref> and occasionally applied to other sciences, such as [[special relativity]].<ref>http://casa.colorado.edu/~ajsh/sr/postulate.html</ref><ref>https://www.nobelprize.org/educational/physics/relativity/postulates-1.html</ref>
In ordinary discourse about a subject in mathematics or science, the terms "axiom" and "postulate" are often not distinguished—they are the statements that one takes as true from the outset, that one does not need to prove. One then uses those to prove other statements. The difference is that postulates are initial statements relating to the subject matter, such as the geometrical postulates (including Euclid's fifth postulate, below) about angles and lines. Axioms, on the other hand, tend to be more universal statements about logic, such as "if X=Y, then Y=X".
==Euclid's fifth postulate==
==Euclid's fifth postulate==
Without the fifth postulate many familiar geometric ideas are no longer true, these include,
Without the fifth postulate many familiar geometric ideas are no longer true, these include,
* The sum of the interior degrees of a triangle are two right angle (180 degrees)
* The sum of the interior degrees of a triangle are two right angle (180 degrees)
== References ==
{{Reflist}}
[[Category:Mathematics]]
[[Category:Mathematics]]
[[Category:Geometry]]
[[Category:Geometry]]