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Researchers, Mathematicians and Enthusiasts. Download "Billiards Covers" to see the most current list of periodic paths in triangles. Download "Billiards Everything" to discover new periodic billiard paths, an unresolved problem from 1775! Follow "The Great Periodic Path Hunt" at gwtokarsky.github.io for the latest news. Email tokarsky@ualberta.ca for feedback.

The ObjectVolume program calculates the volume, surface area and centroid of a closed triangular mesh represented in an object file (.obj). The process goes through the list of triangles that make up the surface and, for each triangle, forms a tetrahedron with an external point. The program uses the origin (0,0,0). The volume of the tetrahedron is then calculated. Tetrahedrons with back facing triangles are added and those with forward facing triangles are subtracted yielding the object volume...

Not working yet. To deal with the Halting Problem, computing and data are navigated using debugger ops: linearForward and treeForward, which navigate an astronomically large bit string where 1 is ( and 0 is ). All pairs are derived from (). For example, true is represented as ((()())()), and false is (()(()())). It appears related to the church encoding of lambda where T chooses first parameter and F chooses second, of a pair. Continuations are nearly finished code and are represented as a pair...