Equilateral into 13 Isosceles triangles

edp · June 25, 2019, 7:24pm

7 years ago William Somsky showed me how to divide an equilateral triangle into 13 strictly acute isosceles triangles.

When I noticed the image, I realized I could now solve it exactly. Seems to need roots of order 10 polynomials.

edp · June 26, 2019, 2:05am

How to solve something like this? Consider the problem of covering the largest possible equilateral triangle with two unit squares.

I make a sketch in Geometer’s Sketchpad first.

Then put the equations right into Mathematica. z0==z1==1.

Root[144 + 96 #1 + 16 #1^2 + 72 #1^3 - 168 #1^4 + 9 #1^6 &, 3]

About 1.322159389397273286325082341278424475

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