convert any sketch into a single mathematical equation (using ellipses)
unfortunately, the equation isn't multiplied out (it would look a lot cooler but it would also be a lot longer)
How It Works
Being the bored student I am in math class, I was staring at a few equations until I realized this neat trick.
As you know, equations for circles are usually something like
x^2+y^2=1--let's convert this to
x^2+y^2-1=0. The neat thing about this form of a circle equation is that if you multiply it by another circle in that form(e.g.,
x^2/4+y^2/4-1=0), you'll actually be able to graph both of the individual equations at the same time.
What you'll have is a classic case of concentric circles, graphed in one single equation.
This is the essence of the trick here, except it can be used for any number of circles. All I did was make the circles into extremely slim ellipses to disguise them as lines. From there, I can just treat them as line segments. Multiply all your equations, and you'll have your equation!!
In the actual demo, the equations are graphed seperately because Desmos cannot handle such big equations. If you can find a powerful grapher than can take LaTeX as an input, please let me know.