Well, thanks to having a two year old kid, I now have the solution: The entire shower is a whiteboard!
Crayola Bathtub Crayons (and this is not a paid advertising post), and you can use them to write on the walls of the shower:
These are fantastic! Now, whenever I have a great idea in the shower I can just scrawl it on the wall, dry off at my leisure, then transpose it to a paper/electronic copy. And the stuff washes (mostly) off! Now, if only I could figure out a way to find the volumes of irregular objects, I'd be set!