SHARPEST ISOSCELES TRIANGLES

The top material has been left in as it shows how my thoughts have evolved. Beneath the initial material is the 5th chapter of PwP which backs into Sharpest Isosceles Triangles on Even Polygons.

Excel file: 8.SharpestIsocelesTriangles

Chakerian and Erfle October, 2020 paper: 8._SharpestTrianglesPaper

This is a more general and expansive paper than provided for Files 6 and 7. Indeed, the paper for File 6 used the simplest results from this paper in order to create a version accessible to very young students.

This was the first paper I wrote with my mentor, Don Chakerian. This is an early draft of what became the September 2023 College Mathematics Journal piece mentioned in File 6. The original impetus for the paper came from some images based on n = 4k+2 polygons that I shared with Don. I had obtained these images using the second double jump aestheometry File 4.2. (Specifically, you can obtain rotated versions of some the images in File 8 using File 4.2  for n = 4k+2 polygons by setting S = Jump 1 = 1 and P = n-1 with last n jumps counted counterclockwise clicked on in cell H2.) Don was intrigued enough that we started working together.

As we worked jointly on this paper, Don pointed out to me that there were actually two distinct sets of isosceles triangle images when n is even … my aestheometry files only captured one of them for n = 4k+2, and I pointed out to him that when n is odd, the solution is even easier (but it was also not achievable using my existing aestheometry files).

This led me to create File 8, but it also led me to create File 9 which allows users to examine all possible triangular images created using the vertices on a polygonal frame.

P5. The sections below move beyond isosceles triangles and consider second sharpest triangles in a more general context.