Axiom

Pronunciation: /ˈæksiəm/ Explain

An axiom is a statement that is taken to be true without proof[1]. An axiom is taken to be self-evidently true, or obviously true. In contrast, a conjecture and a hypothesis are believed to be true, but are not self-evident.

In math, all proofs start directly or indirectly with one or more axioms. The word postulate means the same thing as axiom. An axiomatic system is a logical system that is based on axioms.

Examples

NameRepresentationDescription
Betweenness Assumption
Given collinear points A, B, and C, C is between A and B if AC + CB = AB.

Click on the blue points in manipulative 1 and drag them to change the figure. Notice that if C is between A and B that AC + CB = AB. If C is not between A and B then AC + CB > AB.

Angle Addition Postulate
If two angles are adjacent, they can be added together to form a larger angle. The measure of the larger angle is the sum of the measures of the two smaller angles.

Click on the blue points in manipulative 2 and drag them to change the figure. Notice that m∠BAC + m∠CAD = m∠BAD.

Table 1: Examples of axioms

References

  1. Mendell, Henry. Aristotle and Mathematics. sect 2. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. Last Accessed 8/6/2018. http://plato.stanford.edu/entries/aristotle-mathematics/#2.
  2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 3. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 8/6/2018. http://www.archive.org/stream/mathengineer00kellrich#page/3/mode/1up/search/axiom. Buy the book

More Information

  • McAdams, David E.. Euclidean Geometry. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. http://www.allmathwords.org/en/e/euclideangeometry.html.

Cite this article as:

McAdams, David E. Axiom. 7/10/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/axiom.html.

Image Credits

Revision History

6/15/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (McAdams, David E.)
1/1/2010: Added "References". (McAdams, David E.)
10/26/2008: Changed manipulatives from sketchpad to geogebra. (McAdams, David E.)
10/10/2008: Changed text to compare hypothesis and conjecture, expanded 'More Information'. (McAdams, David E.)
7/8/2008: Added axiomatic system. (McAdams, David E.)
4/7/2008: Added More Information. (McAdams, David E.)
3/25/2008: Added examples. (McAdams, David E.)
9/3/2007: Added synonym 'postulate'. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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