The Number 1 is called a triangular number because it is the first number in the series of triangular numbers given by the forumula T(n) = n(n+1)/2:

1 = 1 = 1 x (1 + 1)/2

3 = 1 + 2 = 2 x (2 + 1)/2

6 = 1 + 2 + 3 = 3 x (3 + 1)/ 2

etc.

Likewise, 1 is the first square number because it is the first in the series generated by n^2 = n x n

1 = 1 x 1

4 = 2 x 2

9 = 3 x 3

etc.

In my book, its just a convention. You can choose to talk about Trinagular numbers starting at 1 or 3. All that matters is that you are clear in your definitions.

Richard

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