Topology Essay -- Mathematics Essays Mathematical Math

analysis situs Mathematics is a knowledge domain so vast and diverse that it is unachievable to be an expert in all areas. It is also a field that is constantly evolving and branching outward. The field of topology is one of the newest intensively canvas branches of math. A simple way to describe topology is as hawkshaw sheet geometry 2. Topology is an offshoot of geometry that originated during the 19th century and that studies those properties an object retains chthonian deformation - specifically, bending, stretching and squeezing, but not breaking or separate 1. Under these conditions, one could say that a square is topologically equivalent to a circle because a square can be bent and stretched into a circle 3. However, a square is not topologically equivalent to a tore because a torus cannot be formed unless a hole is blase through the medium, or two pieces are joined together. Topologists obviously let expanded upon these simple concepts over time to create the orems further removed from our ordinary experiences. Some of these shapes and objects exist in four dimensional length or higher dimensions and cannot exist in our world. Theoretically these shapes would be as commonplace as a tree or rock in a higher dimensional universe. However, in our universe topologists turn to mathematics to understand these shapes 6. The first mathematical problem, which led to the origins of topology, was the Konigsberg bridges problem. The people of Konigsberg wondered if they could head around the city in a way that they would also embroil every bridge exactly once. The city map looked something like this 2 Euler inflexible that it was indeed impossible to accomplish this feat. He rationalized this problem... ...nal space. Works Cited 1 http//www.britannica.com/bcom/eb/article/2/0,5716,115452+1,00.html Encyclopedia Britannica Topology. Accessed declination 6, 1999.2 http//www.forum.swarthmore.edu/isaac/problems/bridges1.html T he Beginnings of Topology. Accessed December 6, 1999.3 http//www.geom.umn.edu/docs/doyle/mpls/handouts/node13.html Topology. Accessed December 6, 1999.4 http//www-groups.dcs.st-and.ac.uk/history/HistTopics/topology_in_mathematics.htmlTopology Enters Mathematics. Accessed December 6, 1999.5 http//www-groups.dcs.st-and.ac.uk/history/Mathematicians/Klein.html FelixChristian Klein. Accessed December 7, 1999.6 http//www.pepperdine.edu/seaver/natsci/faculty/kiga/topology.htm What is Topology. Accessed December 7, 1999.7 Yaglom, I. M. Felix Klein and Sophus Lie. Birkhauser, Boston. 1988.