Topology Essay -- Mathematics Geometry Essays

TopologyTopology is the study of those properties of geometric figures that argon unchanged when the shape of the figure is twisted, stretched, shrunk, or otherwise distorted without breaking. It is sometimes referred to as rubber sheet geometry (West 577). Topology is a basic and subjective part of any post school mathematics curriculum. Johann Benedict list introduced this subject, while Euler is regarded as the founder of topology. Mathematicians such as August Ferdinand Mbius, Felix Christian Klein, Camille Marie Ennemond Jordan and others have contributed to this field of mathematics. The Mbius band, Klein bottle, and Jordan curve ar totally examples of objects commonly studied. These and other topics prove to be intricate and fascinating numeric themes.Topologists are mathematicians who study qualitative questions about geometrical structures. They ask questions handle does the structure have any holes in it? Is it all connected, or cigaret it be separated into parts? Top ologists are not concerned with size, straightness, distance, angle, or other such properties. An often-cited example is the London Underground map. This will not reliably tell you how far it is from Kings Cross to Picadilly, or even the attain direction from one to the other. However, it will tell you how the lines connect between them, utilize topological rather than geometric information (What 1).Furthermore, if one figure can be distorted into another figure without breaking, then the two figures are expound as being topologically equivalent to each other. Two examples of topologically equivalent figures are a coffee cup and doughnut, and groups of the letters of the alphabet. First, an object shaped resembling a doughnut is a torus. A torus can... ...and. New YorkOxford University Press, 1993.Felix Christian Klein. useable Online.http//www-groups.dcs-and.ac.uk/history/Mathematicians/Klein.html. Accessed12/4/99.Flegg, Graham. From Geometry to Topology. New York Crane, Russa k, and Company, Inc.,1974.Jordan Curve Theorem and its Generalizations. Available Online.http//www.math.ohio-state.edu/fiedorow/math655/Jordan.html. Accessed 12/6/99.Marie Ennemond Camille (1838-1922). Available Online.http//ukdb.web.aol.com/hutchinson/encyclopedia/91/M0046091.htm. Accessed 12/6/99.What is Topology? Available Online. http//www.shef.ac.uk/pm1nps/Wurble.html.Accessed 12/4/99.West, Beverly Henderson, and others. Topology. The Prentice-Hall Encyclopedia ofMathematics. 1982. 21 577-585.Yaglom, I.M. Felix Klein and Sophus Lie. capital of Massachusetts Birkhauser Boston, 1988.