The Ben Paul Thurston Blog
Math, Movies, Science, Computers, and so on...
Wednesday, December 30, 2015
Parameterized Quadratic Conformal transformation
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Q(s,t) Note that the same formula applies first to the x coordinates, and then to the y coordinates and can work in any n...
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Tuesday, December 29, 2015
Interesting non-regular pentagon
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Questions for further study: Can you tile the plane with these? Are the angles inside the points of the star the same? Is the center penta...
Sunday, December 27, 2015
Tr(n)^2+Tr(n+1)^2=Tr((Tri(n) + Tri(n+1)) for triangular numbers
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I found this about the triangular numbers, also known as the number of distinct pairwise combinations of n items or the sum of the first n o...
Tuesday, December 22, 2015
MacLaurin Generating Function
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Exponential generating functions follow the form: I was considering a modification of this structure to read: Where f_n_(x) at x is ...
Factorial sum Maple doesn't know
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Considering the sum: But it's clear this sum should be equal to one, consider the first 7 terms: If we were to increase the last c...
Alternate numbering system
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Just considering this series, here are the first 9 terms: Where the next coefficient is chosen so the sum is as large as it can be not ex...
Thursday, December 17, 2015
Quadratic rule of eighths
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This follows simply by substituting 1/4 and 3/4 into the E_Bezier formula from last post...
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