Edited by Richard Walker, Tuesday 23 September 2025 at 14:23
According to Wolfram MathWorld "Any triangle can be positioned such that its shadow under an orthogonal projection is equilateral. "
You can try this for yourself.
I cut a triangle out of printer paper and taped it to a cocktail stick. Then we put a sheet of paper under the kitchen light and a friend experimented with positioning the triangle until we got a shadow that was a pretty fair equilateral triangle. Here's the photo.
A is the paper triangle (the shadow behind is my friend's hand) and B is the triangle's shadow, which you can see is more or less equilateral. It took two or three minutes of trial and error to get the position right but we were pleased with the eventual result!
A Maths Experiment To Try At Home
According to Wolfram MathWorld "Any triangle can be positioned such that its shadow under an orthogonal projection is equilateral. "
You can try this for yourself.
I cut a triangle out of printer paper and taped it to a cocktail stick. Then we put a sheet of paper under the kitchen light and a friend experimented with positioning the triangle until we got a shadow that was a pretty fair equilateral triangle. Here's the photo.
A is the paper triangle (the shadow behind is my friend's hand) and B is the triangle's shadow, which you can see is more or less equilateral. It took two or three minutes of trial and error to get the position right but we were pleased with the eventual result!