SHARPEST APEX RIGHT TRIANGLES ON EVEN POLYGONS
Excel file with Horizontal bases: 8.H_SharpestRightTrianglesOnEvenPolygons
Excel file with Slanted bases: 8.S_SharpestRightTrianglesOnEvenPolygons
Partial Paper: SharpestAngleRightTriangles
The files here are modified versions of File 7 which looked at sharpest isosceles triangles on odd-polygons. This is a natural extension of the material discussed there and formulas developed there are quickly used to answer how many sharpest apex angle right triangles occur when n is even. Interestingly, two distinct images emerge for each value of n, one has horizontal bases with slanted hypotenuse and the other with slanted base and vertical hypotenuse.
Neither the files or the paper are in polished shape but they do show the images and provide a quick synopsis of what is going on here.