Honors College Thesis
 

Orienting the Cube in Minkowski Space and Orienting Myself in Mathematics

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https://ir.library.oregonstate.edu/concern/honors_college_theses/fn1076212

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  • This is a two-part thesis. The first part is a generalization of vector calculus tools to Minkowski Space, a non-Euclidean 3-dimensional geometry that has a distance function that is not positive definite. We orient a cube in Minkowski Space using the generalized Stokes' Theorem to relate a divergence integral to a flux integral, generalized to the language of differential forms, in Minkowski Space. Furthermore, we compute the curvature of the hyperboloid in Minkowski Space, and of the Poincare disk model for hyperbolic geometry intrinsically using differential forms. This computation suggests an immediate application for our orientation of the cube to compute the curvature extrinsically using the shape operator. The second part of this thesis discusses traditional approaches to philosophy of mathematics, the emerging-in-popularity project of humanist mathematics, and finally how feminist theory and in particular feminist philosophy of science might inform a new philosophy of mathematics or critically expand the humanist project.
  • Key Words: Minkowski Space, Hyperbolic Geometry, Philosophy of Mathematics
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