Topology Essay -- Math Mathmatics

Topology The two main figures of Topology, the spheroid and the torus. Shown together like this, they create the symbol for the sun in ancient times (2, 1). The field of mathematics encompasses many different sub-fields which have been studied and researched for a very long time. One of the most intriguing divisions of mathematics is topology. Topology, the mathematical study of the properties of objects which are preserved through deformations, twistings, and stretchings (4, 1), is rooted far back in time; so far back that it outdates all recorded history (2, 1). Modern topological mathematics was introduced in the late 19th century by a mathematician named Henri Poincare` (2, 2). Poincare` Pictures Henri Poincare` was born in Nancy, France in 1854. He received his education at The Ecole Polytechnique and the Ecole Superieur des Mines in Paris (8, 1). Poincare` then spent from 1879 to 1896 lecturing and teaching an array of fields ranging from physical and mathematical mechanics to celestial mechanics at both the University of Caen and the University of Paris. Although Poincare` was considered a physicist, his greatest accomplishments came in the fields of topology, differential equations, and probability, all mathematical fields (8,1). Poincare`’s greatest exposure to the public came in 1887, when King Oscar of Sweden announced that he would award 2,500 crowns to any man who could prove the stability of the orbital dynamics of our solar system. This was a great problem for the mathematicians of the day, and a very significant problem for every being on our Earth (2, 2). If the stability of the orbits could not be proven, one could not rule out the possibility of Earth be ing hurtled into space by the influence of the other p... ...logy and its functions. Works Cited Fauvel, John. MÃ ¶bius and his Band, Oxford University Press, New York, 1993. Gilmore, Tom. Mathematics of Topology, http://www.tomgilmore.com/z_top.htm, 4 pp., 12/5/99. Klein, http://history.math.csusb.edu/Mathematicians/Klein.html, 2 pp., 12/9/99. MÃ ¶bius Strip, http://www.treasure-troves.com/math/MoebiusStrip.html, 4 pp., 12/9/99. Paper Strip, http://cut-the-knot.com/do_you_know/paper_strip.html, 5 pp., 12/14/99. Poincare, http://euler.ciens.ucv.ve/English/mathematics/poincare.html, 2 pp., 12/9/99. 7. Poincare, Henri, http://www.treasure-troves.com/bios/Poincare.html, 1 p, 12/9/99. 8. Poincare, Jules Henri, Microsoft Encarta 1999 ed., Microsoft Inc. 9. Tarot FAQ Version 2, http://lonestar.texas.net/~r3winter/tarotfaq.html, 12/10/99. Topology, http://www.treasure-troves.com/math/Topology.html, 3 pp., 12/9/99.