{"id":96,"date":"2021-04-04T14:34:13","date_gmt":"2021-04-04T14:34:13","guid":{"rendered":"http:\/\/blogs.dickinson.edu\/playing-with-polygons\/?page_id=96"},"modified":"2024-10-23T15:57:58","modified_gmt":"2024-10-23T15:57:58","slug":"file-7","status":"publish","type":"page","link":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/file-7\/","title":{"rendered":"7. Sharpest Triangles"},"content":{"rendered":"

SHARPEST TRIANGLES<\/strong><\/p>\n

Excel file with Horizontal<\/span> bases: 7.H_SharpestRightTrianglesOnEvenPolygons<\/a><\/p>\n

Excel file with Slanted<\/em> bases:\u00a0\u00a0 \u00a0 \u00a0\u00a0\u00a0\u00a0 7.S_SharpestRightTrianglesOnEvenPolygons<\/a><\/p>\n

Partial Paper: SharpestAngleRightTriangles<\/a><\/p>\n

Challenge Question: CQ Sharpest Right Triangles with 4 sets of lines<\/a><\/p>\n

The files here are modified versions of File 6 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 angle right triangles occur when n<\/em><\/strong> is even. Interestingly, two distinct images emerge for each value of n<\/em><\/strong>, one has horizontal bases with slanted hypotenuse and the other with slanted base and vertical hypotenuse. Neither the files or the paper above are in polished shape but they do show the images and provide a quick synopsis of what is going on here.<\/p>\n

The explainers below are more polished and they go beyond the sharpest right triangles on even polygons case which starts off this chapter. The rest of the chapter uses the general Excel<\/em> file from File 9 to create images rather than relying on individual files like was done for isosceles triangles on odd polygons or right triangles on even polygons.<\/p>\n

P4. Sharpest Triangles<\/strong><\/p>\n