Some N-Dimensional analytic geometry : angles and more
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
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Taylor, Michael D.
Bachelor of Science (B.S.)
College of Arts and Sciences
Arts and Sciences -- Dissertations, Academic;Dissertations, Academic -- Arts and Sciences
Length of Campus-only Access
Honors in the Major Thesis
Khosravi, Mehrdad, "Some N-Dimensional analytic geometry : angles and more" (2002). HIM 1990-2015. 306.