**Puzzle:**show the total area of the two semicircles is half the area of the large circle.

If you get stuck, go to +Alexander Bogomolny's wonderful website:

http://www.cut-the-knot.org/proofs/Semicircles.shtml

On top you'll get an applet that lets you slide the point where the semicircles touch - no matter where it is, the semicircles have the same total area! Click "hint" and you'll get a hint. If you're still stuck, scroll down and see a proof.

This puzzle is a lot harder than my other recent area puzzles. Indeed, it seems this fact was proved only in 2011!

• Andrew K. Jobbings, Two semicircles fill half a circle,

*The Mathematical Gazette*

**95**(Nov. 2011), 538-540.

I find that amazing, since people have been thinking about this stuff for millennia! However, Andrew Jobbings is a genius when it comes to 'recreational mathematics' - by which I mean math that's not considered 'serious', which people do just because it's fun. (This is a curious concept, now that I think about it.)

Check out more of his stuff here:

http://www.arbelos.co.uk/papers.html

#geometry

View 39 previous comments

- Unfortunately I can't watch the Java demonstration on the linked page, and I don't have access to the Andrew Jobbings paper either. Could someone who does have access perhaps post a screenshot (or a re-construction) of the relevant diagram so we can see how our own solutions compare?Dec 31, 2013
- +Stuart Presnell +Michel Plungjan I too refuse to install Java to look at whatever it is, so I created my own in javascript: http://jsfiddle.net/eu6Aw/1/Dec 31, 2013
- +Joe Frambach very good!Dec 31, 2013
- +Joe Frambach - Very nice! Esthetically speaking, that horizontal gray bar looks a bit fat. I guess that's to make it easy to notice it and put the cursor on it? (If I could program worth a darn I'd just fiddle around and try something else.)Jan 4, 2014
- Jan 4, 2014
- Nice - thanks!!!Jan 4, 2014

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