Browsing by Author "Bezdek, Andras"

Now showing items 1-13 of 13

The Application of Complex Numbers and Quaternions in Navigation

Lakhani, Alason (2020-11-30)

Complex numbers and quaternions have a wide array of applications. This paper beginsby briefly going over the history of complex numbers and quaternions, bringing up little knownfacts on main discoverers. Then, we ...

Applications of Stationary Sets in Set Theoretic Topology

Clontz, Steven, Jr. (2010-11-10)

The notion of a stationary subset of a regular cardinal, a set which intersects any closed unbounded subset of that cardinal, is a useful tool in investigating certain properties of topological spaces. In this paper we ...

Evading Triangles without a map

Carrigan, Braxton (2010-01-06)

We divise a heuristic which enables a traveler to traverse the plane from a start point S to a target point T while evading unknown obstacles. The obstacles are assumed to be equilateral triangles which are all translates ...

Isoperimetric Properties of the Circle

Holman, Kimberly (2022-05-03)

Jakob Steiner and Karl Weierstrass provided formal proofs of the isoperimetric property of the circle in the late 1830s. New mathematical tools, proof language, and concepts were needed to prove this rather obvious fact, ...

Iterative processes generating dense point sets

Ambrus, Gergely (2006-05-15)

The central problem of the thesis is the question of denseness of certain sets of points in the plane. All of the following results are joint with A. Bezdek. We consider point sets P, not a subset of a line, having the ...

Mathematics Behind Planimeters

Yardimci, Osman (2013-06-18)

Original master thesis project: By studying the literature, collect and write a survey paper on the mathematics of the planimeters. Planimeter is a somewhat forgotten ingenious device which was invented in 1814 to satisfy ...

On The Number of Cylinders Touching a Sphere

Yardimci, Osman (2019-06-14)

The kissing number problem is a packing problem in geometry where one has to fi nd the maximum number of congruent non-overlapping copies of a given body so that they can be arranged each touching a common copy. The ...

On the role of 1-LC and semi 1-LC properties in determining the fundamental group of a one point union of spaces

Moore, Emilia (2006-05-15)

Concerning the fundamental group of spaces written as a union of two topological spaces, the result by Seifert and van Kampen is well known and frequently used. Over the years there have been various theorems published ...

On Translative Packing Densities in $E^2$ and $E^3$

He, Yangyang (2023-12-01) ETD File Embargoed

The theory of packing and covering is an essential part of discrete geometry. In this dissertation we focus on and contribute to the knowledge on the densities of translative and lattice packings in $E^{2}$ and ...

Path Curvature on a Convex Roof

Ford, Robert (2007-12-15)

Given a set of rectangles, R1 through Rk, where Ri and Ri+1 share a common edge and these common edges are congruent and parallel to each other. The resulting ”roof” is part of the surface of a convex body. We’ll consider ...

Phenomenal Three-Dimensional Objects

Wade, Brennan (2011-03-29)

Original thesis project: By studying the literature, collect and write a survey paper on special three-dimensional polyhedra and bodies. Read and understand the results, to which these polyhedra and bodies are related. Although ...

Triangle Centers and Kiepert's Hyperbola

Baker, Charla (2006-12-15)

In this paper, we discuss the proofs of the primary classical triangle centers and Kiepert's Hyperbola as a solution to Lemoine's Problem. The definitions of terms which will be used throughout the paper are presented. ...

Triangulations and Simplex Tilings of Polyhedra

Carrigan, Braxton (2012-07-09)

This dissertation summarizes my research in the area of Discrete Geometry. The particular problems of Discrete Geometry discussed in this dissertation are concerned with partitioning three dimensional polyhedra into ...