57005 or alive

Project Euler visualizations - problem 431

Dec 9, 2013 math Mathematica neat Project Euler

I recently solved Project Euler problem 431, which (through a bizarre and unnecessarily confusing back-story) requires one to calculate the volume trapped above a cone, inside a cylinder.  The point of the cone is taken to be level with the top of the cylinder, but the cone angle and its horizontal offset compared to the cylinder are variable.

I solved this one with Mathematica, and along the way I cobbled together a little visualization that allows one to easily see the curve of intersection where the cone and the cylinder join together.  Why not take this opportunity to share the visualization via an embedded CDF?  I’ve been wanting to try this for a while.

Note: To see the full interactive visualization, you need to download the CDF player plugin.  At the time of writing this, IE 11 does not work with CDF unless you put the page in “compatibility mode,” so you might want to view this in Chrome.

It would appear that the diagram provided with the problem definition is inaccurate - the intersection curve does not cup downward, it cups upward.  Of course, Project Euler does not assert that their diagrams are to-scale or otherwise accurate, but it seems odd that they flipped this one upside-down.