Ruler Postulate

Pronunciation: /ˈrul.ər ˈpɑs.tʃə.lət/ Explain

Click on the blue points and drag them to change the figure.

Every point on a line can be paired with a number.
Manipulative 1 - Ruler Postulate Created with GeoGebra.

The ruler postulate states that:

  1. Every point on a line can be paired with a real number.
  2. The number associated with a point A on the line is called the coordinate of A.
  3. Two arbitrary points can be paired with the numbers 0 and 1, defining the length of a unit.
  4. The distance between any two points A and B is designated AB.
  5. The distance between two points is taken to be positive. Note that a directed distance can be positive or negative.
  6. The distance between two points A and B can be found by taking the absolute value of the difference of their coordinates.

This postulate allows mathematicians to define coordinate systems. Coordinate systems allow us to graph mathematical models. Notice that this postulate does not define a unit of measure, it only tells us that a unit of measure is defined by assigning the values of 0 and 1 to two points. The 'ruler' used may be a metric ruler, an english ruler or even a clock. As long as a number can be assigned to a point on a dimension, this postulate applies.


  1. McAdams, David E.. All Math Words Dictionary, ruler postulate. 2nd Classroom edition 20150108-4799968. pg 159. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Richard S. Millman, George D. Parker. Geometry: A Metric Approach with Models. 2nd edition. pg 30. Springer. December 17, 1990. Buy the book

Cite this article as:

McAdams, David E. Ruler Postulate. 5/2/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

5/2/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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