Today, I present to you Bayes theorem like you have never seen it before.

Take a moment to think: how would you calculate a Bayesian update using only basic geometry? I.e., you are given (as line segments) a prior P(H), and also P(E | H) and P(E | ~H) (or their ratio). How do you get P(H | E) only by drawing straight lines on paper?

Can you think of a way that would be possible to implement using a simple mechanical instrument?

It just so happens that today I noticed a very neat way to do this.

Have fun with this GeoGebra worksheet.

And here's a static image version if the live demo doesn't work for you:

Your math homework is to find a proof that this is indeed correct.

Hint: Vg'f cbffvoyr gb qb guvf ryrtnagyl naq jvgubhg nal pnyphyngvbaf, whfg ol ybbxvat ng engvbf bs nernf bs inevbhf gevnatyrf.

Please post answers in rot13, so that you don't spoil the fun for others who want to try.

Edit: For reference, here's a pictograph version of the diagram that came up later as a follow-up to this comment.