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About Triangular Square Numbers
Member rating: No Rating | Words: | Submitted: Thu Aug 14 2003
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About Triangular Square Numbers By August Pieres January 18th, 2003 I believe I have discovered an algorithm which generates an infinity of triangular squares. "Triangular squares" are triangular numbers which are also perfect squares. These are triangular numbers: 1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,... Notice that 120=5! (and 6=3!) and that 1,3,21, and 55 are also Fibonacci numbers; one might call them "Fibonacci triangles." Are there any more Fibonacci triangles? These are the perfect squares: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,... The only triangular squares listed so far are 1 and 36. Earlier today I thought that these were the only existing triangular squares, but I found out that there are more and quite possibly an infinity of them. I made a program on my programmable Texas Instruments TI-86 calculator. Here it is: PROGRAM:TRISQUAR 1-->N Lbl A N*(N+1)/2-->M If ?M==iPart?M Then Disp M End 1+N-->N Goto A I ran the simple program above and it found the following additional triangular squares: 1225, 41616, 1413721. Then I "played" with these new numbers -- with the help...
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