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:
 Every
point
on a
line
can be paired with a
real number.
 The number associated with a point A on
the line is called the
coordinate
of A.
 Two
arbitrary
points can be paired with the numbers 0 and
1, defining the length of a unit.
 The
distance
between any two points A and
B is designated
AB.
 The distance between two points is taken to be positive. Note that a
directed distance
can be positive or negative.
 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.
References
 McAdams, David E.. All Math Words Dictionary, ruler postulate. 2nd Classroom edition 201501084799968. pg 159. Life is a Story Problem LLC. January 8, 2015. Buy the book
 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. https://www.allmathwords.org/en/r/rulerpostulate.html.
Image Credits
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.)