My article at Decoded Science explains the rules to calculate triangular numbers, and their unusual relationship to square numbers.
Of course, I also promote this article in "Triangular Numbers can Create Square Numbers" at DeHaan Services.
The DeHaan Blog of Writing 

My fifth article at Decoded Science is "How to Change Triangular Numbers into Square Numbers". "FourTen Triangle" by Mike DeHaan Although not many people could spout a definition of a triangular number, they are easy to spot. "Ten Pin Bowling" by DJDwayne Professional pinsetters, for example, easy spotted (or "placed") tenpin bowling pins in a triangular pattern. (There are ten pins in total, with 4 on each side. The fourth triangular number is 10).
My article at Decoded Science explains the rules to calculate triangular numbers, and their unusual relationship to square numbers. Of course, I also promote this article in "Triangular Numbers can Create Square Numbers" at DeHaan Services.
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