TopologyMathematics is such a large and diverse field that it is impossible to be an expert in everything. It is also a field that is constantly evolving and expanding outwards. The field of topology is one of the newest and most widely studied branches of mathematics. “A simple way to describe the topology is to describe it as a rubber sheet geometry” [2]. “Topology is an offshoot of geometry that originated in the 19th century and studies the properties that an object retains under deformation – particularly bending, stretching and compression, but not rupture or tearing” [1]. Under these conditions, we could say that a square is topologically equivalent to a circle because a square can be folded and stretched to form a circle [3]. However, a square is not topologically equivalent to a torus because a torus can only be formed if a hole is drilled in the middle or two pieces are put together. Topologists have obviously developed these simple concepts over time to create theorems even further from our ordinary experiences. Some of these shapes and objects exist in four-dimensional space or higher dimensions and cannot exist in our world. Theoretically, these shapes would be as common as a tree or a rock in a higher dimensional universe. However, in our universe, topologists turn to mathematics to understand these shapes [6]. The first mathematical problem that led to the origins of topology was the Königsberg bridge problem. The people of Königsberg wondered if they could walk around the city in such a way that they crossed each bridge exactly once. The plan of the city looked like this [2]: Euler determined that it was indeed impossible to accomplish this feat. He rationalized this problem...... middle of article...... end space. Works Cited [1] http://www.britannica.com/bcom/eb/article/2/0,5716,115452 +1.00.html EncyclopediaBritannica: Topology. Accessed December 6, 1999.[2] http://www.forum.swarthmore.edu/~isaac/problems/bridges1.html The 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 FélixChristian 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, IM Felix Klein and Sophus Lie. Birkhauser, Boston. 1988.