Wolfram Demonstrations Project

A complete graph on

vertices has

edges. This number is also the sum of the first

integers, as shown here: the complete graphs are built up by adding one vertex at a time, and the colors show that the

vertex adds

edges, thus showing visually that

This Demonstration was suggested by the following article:

J. DeMaio and J. Tyson, "Proof without Words: A Graph Theoretic Summation of the First

Integers," The College Mathematics Journal, 38, 2007 p. 296.

After work by: J. DeMaio and J. Tyson (see citation above)

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Common Core State Standards for Mathematics

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A Graph Theory Interpretation of the Sum of the First n Integers