Archimedes first glimpsed the infinite in the polish of his war mirrors. For centuries the Greeks had been fascinated with conic sections. Take a cone and cut it up; you get circles, ellipses, parabolas, and hyperbolas, depending on how you slice it. The parabola has a special property: it takes the rays of light from the sun, or any distant source, and focuses them to a point, concentrating all the light’s energy on a very small area. Any mirror that could set ships afire must be in the shape of a parabola. Archimedes studied the properties of the parabola, and it is here that he first
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