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Dominique Laurain
Dominique Laurain is a collaborator on projects that contain the following public CoCalc documents:
PathDescriptionLast Edited
EllipseDoubling.png
PythagoreanOrbit.png
EllipsesDoubleUnfolding.png
TXM-Delta.png
ParabolasProperty2.png
ParabolasProperty.png
DecagonalOrbit.pngDecagonal orbit for the circle with vertices Vi and Wi
Tangential.pngPentagon 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
PentagonalOrbit.pngElliptic 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"
EllipticBilliard.pngTo Dan
CosineCircle.pngTo Dan
Triangular orbits in elliptic billiards - Triangle geometry.sagewsTo Dan
PerfectTriangleModelDissection.pdfDraft paper in pdf for forum geometricorum
SquareCeviansProperty.pngMaking harmonic orthodiagonal quadrilateral
2015-12-30-150601.sagewstest save version
Last Bracket in comment.sagewsPost at google groups sage-support
Inellipse of convex quadrilateral.sagews
CheckMd.sagews
Planar plot.sagews
Inellipse of convex quadrilateral.sagews.html
Check-Markdown.sagews
Soddyian_Curve.png
Help_Asksage_array.texasksagemath array issue
Sagecloud handling of out and infile for sagetex.tex