Posed by Dan Meyer - [url=http://blog.mrmeyer.com/2014/confab-circle-square/] Circle-square [/url]:
Where does point C cut the segment so that the areas of the resulting shapes are equal?
In Meyer's proposal, the shapes are a square and circle; here users can select the type of regular polygon, or include a circle.
Also see [url=http://www.geogebratube.org/student/m90339] davemath's [/url], [url=http://www.geogebratube.org/material/show/id/90172] John Golden's [/url], or [url=http://vimeo.com/87427065] Dan's [/url].