Ancient Science · Part 13 · Alexandria · B2
Apollonius and the Conic Sections: Ellipse, Parabola, Hyperbola
Part 13 of Ancient Science: Apollonius, the Great Geometer, showed that the circle, the ellipse, the parabola and the hyperbola are all slices of one cone, and gave them their names. Sophia shows how his books survived, half of them only in Arabic, and how his curves came to describe burning mirrors, thrown stones and the paths of the planets. The steeper the cut, the longer the ellipse, with Philo, Sophia, Marcos and Demetria.
Tonight we cut a cone. Take this clay cone, Marcos, and slice it straight across.
Now tilt the knife a little. And a little more. And now cut it at the same slope as the side of the cone.
An oval, then a curve that never closes. The steeper the cut, the stranger the shape!
Those curves belong to Apollonius, the Great Geometer. Two thousand years from now, they will describe the paths of the planets. Let me show you.
Apollonius was born in Perga, in what is now southern Turkey, and studied in Alexandria with the followers of Euclid. Later writers called him the Great Geometer.
His great work is the Conics, in eight books. It studies the curves you get when you cut a cone with a flat plane: the circle, the ellipse, the parabola and the hyperbola. Earlier mathematicians had studied these curves, but Apollonius showed that all of them can be cut from a single cone, simply by changing the angle of the cut.
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