Tag Archives: Geometry

The proof of the Morley miracle: an example to learn from on how to do maths

450px-Morley_triangle.svg

In the picture above, the purple triangle is always equilateral if the two inside lines at each corner of the outside triangle trisect the angle at that corner (i.e. divide it into three equal bits). This result is called “Morley’s Miracle”. Lola Behanzin, Taija Williams, and Serene Williams proved it, given nine “thin” triangles with angles (α, β+60, γ+60), (β, γ+60, α+60), (γ, α+60, β+60); their short sides (the sides connecting the “+60” angles) all equal; and 3α+3β+3γ=180. Continue reading