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You are not logged in. #1 20070507 09:41:05
FigurometryGood afternoon. A member of my forum that I host referred us to you lovely site. We are looking for formulas that help generate and extracts roots of figurate numbers. It is an interesting but often neglected field of study. You could be the ones who help us make great discoveries. You are welcomed to share info with us: http://forums.delphiforums.com/figurate/start #2 20070510 12:41:10
Re: FigurometryPlease consider visiting our forum. Please let me know if their is any way I can contribute to yours. Say, as you may well be aware, just as one can generate square numbers (n x n), one can also generate triangle numbers. Where any of you aware that just as there is a square root, there is also a triangle root? I'm not kidding. #3 20070603 01:36:06
Re: FigurometryIf you meant cube root, most of us are aware that there exist cube roots. Regarding extracting cube roots, I think of prime factorization as the only possible method. Logarithms help, but they are an approximation. For higher roots also, prime fasctorization is the ideal method. Character is who you are when no one is looking. #4 20070603 09:15:14
Re: FigurometryYes, we know about the cube root. How about the tetrahedron root, octahedron root, etc;? The extracting of 3D figurate numbers is what has me stumped. I'm glad you like my forum. #5 20070603 09:20:54
Re: FigurometryRoots aren't given in shapes with different number of sides. They are all cubes of different dimensions. A 2dimensional cube is called a square, and so we say a number is squared. A 3dimensional cube is simply called a cube, so we say the number is cubed. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #6 20070606 10:05:36
Re: FigurometryActually, they can! Soon, I will be posting a chart at my forum that shows the triangle root, pentagonal root, etc; we simply have the square and cube in their simplest form. After all, Pascal's triangle does not have squares and cubes. It has triangle and tetrahedron numbers. #7 20070702 09:13:58
Re: FigurometryI just posted charts that give proof that you CAN INDEED have roots of other polygonal numbers besides squares. Just look under "Triangle Root" and "Pascal Genesis" for the most recent postings and you see that the door to yet another world is opened to you. Enjoy! #8 20070702 09:43:51
Re: FigurometryPerhaps you can define things such as "triangle" roots, and the like, because I (nor Google) haven't the slightest idea what you mean by such. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #9 20070705 13:01:18
Re: FigurometryOK. Let us take a trip to the bowling alley, shall we? Now how many pins are set up? Usually 10! That's right. How many rows are there? Four. We know that 1+2+3+4=10. Ten is a triangle number. What is its triangle root? 4! Did you know that 666 is a triangle number? Yikes! Its triangle root is 36. Why? Because if you add the numbers from 1 to 36, you will get the sum of 666. Last edited by R3hall (20070705 13:02:22) #10 20070831 12:18:53
Re: FigurometryI hope the last entry answered your question. At my Figurometry forum, I just posted an application to the Twelve days of Christmas that should also clear the waters for you. 