Edward Teller - Discovering an interest in projective geometry (8/147)

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Hungarian-American physicist, Edward Teller (1908-2003), helped to develop the atomic bomb and provided the theoretical framework for the hydrogen bomb. He remained a staunch advocate of nuclear power, calling for the development of advanced thermonuclear weapons. [Listener: John H. Nuckolls]

TRANSCRIPT: Now, Klug was a mathematician and he did two things for me. One is that he told me about his specialist- about his specialty which was projective geometry. What is that? In geometry, at least a part in which we discussed at that time, we talk about drawings, about figu- figures, a circle, a triangle, in a plane. Now, what happened if this plane was transparent with the figures drawn upon it and then light in- illuminating it and projecting it onto another plane behind? What are the properties of geometrical figures that remain invariant, that is, do not change in that operation? This is projective geometry, the part of geometry which remains valid when you pro- perform a projection. From Professor Klug I got problems which I usually could not solve. I remember one that I liked very much, I could not solve it, I could not prove it, but I'll tell you what it is. In projective geometry, four figures, four kinds of figures, are declared to be the same. A circle, an ellipse, a parabola and a hyperbola. If you take any of the four in one plane and project it onto another plane, you will not get the same thing but you will get one of the four. Projecting a circle can give a parabola. Now, here is a theorem in projective geometry. Take one of these four - in the simplest case, a circle - and inscribe into it a hexagon, so that the corners, all the corners, all the six corners, lie on the circle. Now, the six sides of the hexagon, select three pairs, each pair has the opposite two lines of the hexagon. Each of these pairs will intersect at one point. Out of the three points you get three intersections. Nothing interest- interesting so far. Now comes the theorem. The three points so constructed lie on a straight line. True for a circle and once you have proved it for the circle, you have proved it for the ellipse, for the parabola, for the hyperbola because that happens to the circle and straight lines remain straight lines; and the statement of three points lying on a straight line is again a sur- statement, invariant, not changing, on the projection. This was a group of new ideas wit- which I found very attractive.

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