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About Varied / Hobbyist Joshua CooperMale/United States Recent Activity
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Throwing by joshuancooper
Throwing
A projectile is thrown, idealized (no resistance, constant gravity, etc).  What angle sends it the "farthest"?  If "farthest" means that it lands as far away as possible, the answer is a simple Calculus exercise: 45 degrees.  But if "farthest" means the total arc length traveled, the answer oddly enough is the solution x to csc(x) = coth(csc(x)), about 0.9855 radians or 56.47 degrees.  Joint work with Anton Strizhov.
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Binomial Pairs by joshuancooper
Binomial Pairs
A certain matrix can be used to bound values of the Product Ramsey Theorem "output" for small parameters.  See paper "Monochromatic Boxes in Colored Grids", by Cooper-Fenner-Purewal.  Its rows and columns are indexed by subsets of {1,...,n}; its (S,T) entry is binomial(|S intersect T|,2) + binomial(|S complement intersect T complement|,2).  This is a spectral-colormap visualization of the ninth-order instance of this matrix using matplotlib in Python.
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joshuancooper
Joshua Cooper
Artist | Hobbyist | Varied
United States
I am a professor of mathematics, and aesthetically interesting pictures arise from time to time in my research. I thought I'd share.
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:iconhektor41:
hektor41 Featured By Owner Feb 18, 2014
thanks for the favorites! Nice gallery btw
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