6.8: Topology, Tiling, and Non-Euclidean Geometry

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Topology

Topology is a branch of mathematics studying spaces, in which “connectiveness” of objects is a main focus. Robert Bruner has written a more detailed description: “What is Topology?”

For this course, we will determine whether two objects are topologically equivalent by comparing their genus, or number of holes. Please read and work through the lesson starting from page 1. Be sure to click the link at the bottom right hand corner of each page to get to the next page in the sequence (there are five pages in total). On the last page, you’ll find topics that can be used in the Application of Geometry Discussion Board.

This is a link to a deformation, showing how a coffee mug can be transformed into a donut; thus they are topologically equivalent.

Tiling

Please read through the following three pages for a mini-lesson on tiling:

Mathematics for the Liberal Arts I. Provided by: Extended Learning Institute of Northern Virginia Community College. Located at: http://eli.nvcc.edu/. License: CC BY: Attribution