Theorem of the Owl's Eyes

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No matter which way the owl turns its beak, the eyes remain the same size. The interpretation as a picture of an owl is just for fun, but it is a real result, also known as Archimedes' Twins. The diameters of the two dark orange semicircles lie on the diameter of the larger, lighter semicircle. The line between the eyes is perpendicular to the diameters of the three semicircles. The two blue circles are inscribed in the curvilinear triangles so formed. The theorem states that the two blue circles are the same size. The ears have nothing to do with the theorem, but the hope is that they make the picture look more like an owl.

Contributed by: Greg Markowsky and Catherine Wolfram (March 2011)
Open content licensed under CC BY-NC-SA


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