The Garden of Archimedes
 The Garden of Archimedes
 A Museum for Mathematics

Objects of the exhibition
Beyond the compasses




     




The ellipse has two particular points, called focuses, which are on the longer diameter. The focuses have the following property:
The sum of the distances of any point of the curve from the focuses is constant.

Another property of the focuses is that the perpendicular to the ellipse at any of its points halves the angle formed by the segments joining this point to the two focuses. Consequently, a ray of light, starting from one of the two focuses and reflected on the ellipse, passes through the other focus. The same goes for sound waves. If somebody speaks, or even whispers, standing in one of the focuses of an elliptic vault room, the sound waves will be reflected on the vault and will gather together again in the other focus, where they can be heard by whoever is standing there.

 

The Garden of Archimedes
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