Collaborative Calculation and Data Science

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Circumbilliard area of tangential triangle

Elliptic billiard, 3-orbit, circle through foci

Decagonal orbit for the circle with vertices Vi and Wi

Pentagon V1V2V3V4V5 made of vertices intersection of tangential pentagon T1T2T3T4T5 edges and its image  U1U2U3U4U5 edges is cyclic with radius 4*s/((9 - h^2)*sqrt(n))  where s is half perimeter, h = sqrt(1-2*k), k = r/R and lambda = (1 - h^2)*s^2*n/(9 - h^2). Number n is root of a sextic equation  h^6 n^6 - (h^2 + h - 3)(h^2 - h - 3)(h^2 - 3)h^2 n^5 - (7 h^4 - 41 h^2 + 63)h^2 n^4 - 18 (h^2 - 3) h^2 n^3 + (h^2 + 5 h + 3)(h^2 - 5 h + 3)n^2 + 5(h^2 - 3)n + 5 = 0

Elliptic billiard - Here is construction of a 5-orbit using D S Reznik observation about locus of tangent caustics and 2018 Dragovic  and Radnovic's paper "Caustics of Poncelet polygons and classical extremal polynomials"

Draft paper in pdf for forum geometricorum

Making harmonic orthodiagonal quadrilateral

Project: Pinwheel Geometry and Number Theory

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