Einstein and MathDate: Sat, 4 Mar 1995 23:21:46 -0500 (EST) From: Dov Peretz Elkins Subject: Geometry Hello, My name is Jonathan Stadlin. I go to Princeton High school. I have to give a presentation to my class on Albert Einstein and I wondered if you could give me some information on how he related to math or geometry. A fellow student asked me if you could give him some information on a mathematician named Sonya Kovaleski. Thank you very much. Date: 4 Mar 1995 23:21:59 -0500 From: Dr. Ken Subject: Re: Geometry Hello there! Yeah, the ideas that Einstein used in his work on redefining the geometry of the universe are pretty neat. To understand them, you have to know a little bit about non-euclidean geometry. The geometry we all learn in high school is the geometry of a plane, where there is only one line through a given point that is parallel to another given line. But it turns out you can define two other perfectly good geometries: where given any line and a point not on that line, there is no line through the given point that's parallel to the given line; and where given any line and any point not on that line, there are infinitely many lines through that point parallel to the given line. The first kind of geometry is called projective geometry, and the second kind is hyperbolic geometry. While this stuff is really neat, the important stuff is this: if you study what's called the "curvature" of the surfaces that you use for each of these geometries (this is a concept that's pretty deep, and it can take up an entire college course), you find that projective geometries have positive curvature, euclidean geometry has zero curvature, and hyperbolic geometry has negative curvature. This, as I understand, is the main idea that Einstein latched onto when forming his theories. Except for one key difference: when we do geometry in two dimensions, well, we're in two dimensions. So you have to think about extending this concept of curving space to three dimensions. What Einstein said was that when an object sits in space, it curves it a little bit, the same way a person sitting in the middle of a trampoline curves the surface of the trampoline. This is how you can think of the attraction of gravity: two objects are attracted to each other because the space in between them is curved. For instance, if you're sitting in the middle of the trampoline and your sister throws a tennis ball onto the trampoline, it will settle down into the depressed region created by your weight. That's like an object being attracted to a big planet. Of course, I'm not really an expert on Einstein's theories. If you really want to know the ins and outs of his work, you could ask a Physics teacher at your high school, or better yet, go to college and take some physics classes. Neat stuff. About your second question: I really didn't find much mention of Kovalevsky in my math history book, but it did say that she did some good work in the theory of Differential Equations, and she won the Paris Academy's prize for "a work of 1888 on the integration of the equations of motion for a solid body rotation around a fixed point; in 1889 she became a professor of mathematics in Stockholm." This is from Morris Kline's book "Mathematical Thought from Ancient to Modern Times." Here are a couple of biographies I turned up on her, too. I hope they help some. AUTHOR Kovalevskaia, S. V. (Sofia Vasilevna), 1850-1891. TITLE Sonya Kovalevsky. PUBLISHER N. Y., Century, 1895. DESCRIPT p. 155-297. SUBJECT Kovalevskaia, S. V. (Sofia Vasilevna), 1850-1891. Autobiography. Kovalevskaia, S. V. (Sofia Vasilevna), 1850-1891. ALT. ENTRY Hapgood, Isabel Florence, tr. Cajanello, Anna Carlotta Leffler Edgren, duchessa di, 1849-1892. Wolffsohn, Lily. Bayley, A. M. Clive, tr. IN Kovalevskaia, Sof'ia Vasil'evna. Sonya Kovalevsky. 1895. p. 155-297. AUTHOR Cajanello, Anna Carlotta Leffler Edgren, duchessa di, 1849-1892. TITLE Sonya Kovalevsky : biography / by Anna Carlotta Leffler, Duchess of Cajanello ; and, Sisters Rajevsky : being an account of her [own] life / by Sonya Kovalevsky ; translated by A. de Furuhjelm and A.M. Clive Bayley ; with a biographical note by Lily Wolffsohn. EDITION Authorized ed. PUBLISHER London : T. Fisher Unwin, 1895. DESCRIPT x, 377 p., 1 leaf of plates : port. ; 24 cm. SUBJECT Kovalevskaia, S. V. (Sofia Vasilevna), 1850-1891. ALT. ENTRY Bayley, Anna M. Furuhjelm, A. de, tr. Kovalevskaia, S. V. (Sofia Vasilevna), 1850-1891. Sisters Rajevsky. ALT. TITLE The sisters Rajevsky. -Ken "Dr." Math |
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