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Triangle Numbersby YuckFoo (Abbot) 
on Apr 24, 2002 at 17:31 UTC ( #161681=CUFP: print w/ replies, xml )  Need Help?? 
I read about triangle numbers in book by
Clifford Pickover, I forget
which one.
Triangle numbers are numbers of the form 0+1+2+3...n, or .5*n*(n+1). The first few tnums are 0, 1, 3, 6, 10, 15, 21. These are numbers of items that can be arranged in a triangle, like bowling pins. There are many interesting features of tnums. Adding any two consectutive tnums is a square number (6+10, 10+15), which makes sense when you think about it. A notable tnum is the 36th tnum, 666. Of course 36 (6*6) is itself a tnum. What I found most fascinating was the claim that any whole number can be written as the sum of three tnums. I'm still trying to figure out why. In the meantime I wrote this program to check it out. The program is a bit brutish. I keep an array of tnums that I add to as needed. To find the three addends, I binary search for the largest tnum less or equal to the target. I initialize the three numbers to this value and iterate through all possibilities to find the answer. Any suggestions to optimize the search method? YuckFoo
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