Number of words: 256

Geometrical curves, their beauty and their forms, held fascination for the Greeks; they are enshrined in their sculptures and their architecture. The straight line and the circle dominate Euclid; and the perfection of the circle was sacrosanct: it underlies Aristotle’s conception of celestial bodies and it provides the basis for Greek astronomy from Eudoxus to Ptolemy. But the Greeks did not confine their studies to straight lines and circles only. They sought curves that would encompass the geometrical properties of straight lines and circles in a more beautiful and harmonious synthesis; and they discovered this harmony in the curves obtained as sections in a cone: the ellipse and the hyperbola. Their curiosity with respect to these curves was not motivated by any physical fact they discerned. And yet, in the second half of the third century BC, Apollonius of Perga wrote eight monumental volumes devoted to these curves. Apollonius is eloquent about their geometrical properties; he describes them as miraculous. But it did not occur to him, or to the other Greek mathematicians, that the curves, which they studied so earnestly for their intrinsic beauty, had any relevance to the real physical world.

Yet some eighteen centuries later, when Kepler was analysing the orbits of the planets on the Copernican system, he discovered that the very curves that the Greek mathematicians had studied for their intrinsic mathematical beauty were exactly those needed to represent the orbits of the planets (Fig. 1)

Excerpted from page 33  of  S. Chandrasekhar ‘Man of Science ’ by A.P.J. Abdul Kalam