The idea of lines and angles in the two dimensional space is a fairly simple and intuitive idea. However, as we move to N-dimensions, this idea may not be as intuitive. In this project, we are going to take the intuitive ideas in a plane and move to a higher dimensional space. We will introduce some machinery, such as the wedge product and the Hodge star operator, which will assist us to investigate these concepts in N-dimensions. We will then look at what we mean by oriented volume of an object in N-dimensions. This will lead us to interesting generalizations of two well-known ideas: the Pythagorean theorem and the law of cosines
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:honorstheses1990-2015-1305 |
| Date | 01 January 2002 |
| Creators | Khosravi, Mehrdad |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | HIM 1990-2015 |
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