Explore the beauty of mathematics in this short book on triangular numbers and their higher-order generalisations.

Triangle Numbers

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Triangle Numbers

Page 5: Pyramid of 35 spheres animation Uploaded to Wikimedia Commons 1 August 2005 by User: Blotwell CC BY-SA 3.0 Page 6: Pascal triangle simplex numbers Uploaded to Wikimedia Commons 12 April 2014 by User: Cmglee CC BY-SA 4.0

The triangle numbers are the sums of the first n natural numbers.

The natural numbers are given by 1, 2, 3, 4, 5, 6, ... etc.

The triangle numbers Tn are the sums of the first n natural numbers.

They are so named because they form a triangle of size n.

The tetrahedral numbers are the sums of the first n triangle numbers.

Name

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