Some time ago now, Wouter (an old friend of mine), Tom (another friend of mine) and I were having a drink when Wouter came up with this seemingly little math problem. A circle, as you know, is the collection of all points with a certain distance to a focus point A. An ellipse has the same definition, but then with two focus points. What would the name and shape be of the object that’s defined the same way as circles and ellipses, but with three focus points?
We couldn’t really think of what the shape would look like, except the symmetric aspect, and that it kinda nears to a circle as you make it bigger. But it must be very simple, I thought, and it must be very easy to come by some nice pictures and descriptions of such objects on the internet. But astonishingly, I couldn’t find anything at all!
So we set out to draw this apparently stubborn shape ourselves. As the distance of (x,y) to the three focus points A, B and C it is defined as:



