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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
The Mathematics Of The Card Game Set, Paola Y. Reyes
The Mathematics Of The Card Game Set, Paola Y. Reyes
Honors Projects
SET is a card game of visual perception. The goal is to be the first to see a SET from the 12 cards laid face up on the table. Each card has four attributes, which can vary as follows: 1. Shape: oval, squiggle, or diamond 2. Color: red, green, or blue 3. Number: the number of copies of each symbol can be 1, 2, or 3 4. Filling: solid, unfilled, stripped Each card has a unique combination, for a total of 34 = 81 different cards in a deck. A SET consist of three cards for which each of the …
Convexity Properties Of The Diestel-Leader Group Γ_3(2), Peter J. Davids
Convexity Properties Of The Diestel-Leader Group Γ_3(2), Peter J. Davids
Honors Projects
The Diestel-Leader groups are a family of groups first introduced in 2001 by Diestel and Leader in [7]. In this paper, we demonstrate that the Diestel-Leader group Γ3(2) is not almost convex with respect to a particular generating set S. Almost convexity is a geometric property that has been shown by Cannon [3] to guarantee a solvable word problem (that is, in any almost convex group there is a finite-step algorithm to determine if two strings of generators, or “words”, represent the same group element). Our proof relies on the word length formula given by Stein and Taback …
Graph-Ene, James E. Torres
Graph-Ene, James E. Torres
Honors Projects
GRAPH-ENE is a rich internet application for building and manipulating undirected, simple graphs. It is intended for use as a classroom teaching aid, plus as a tool for students to interactively manipulate graphs for assignments. Being web based, it is portable—it can run anywhere a browser is available. Since it is interactive, it provides problem-solving capabilities that are not available using pencil and paper.
Geodesic Circulant Graphs Embedded On The Flat Torus, Cameron Richer
Geodesic Circulant Graphs Embedded On The Flat Torus, Cameron Richer
Honors Projects
In this paper, we will investigate graphs that arise from the intersections of geodesics embedded on the at torus. For any size collection of geodesics, the number of unique intersections is countable via their slopes. As well, any embedding of two geodesics gives rise to a circulant graph for which its chromatic number can be calculated from their respective slopes. Furthermore, the previously described circulant graphs embedded on the at torus are self-dual. This provides an effective face coloring of any graph arising from the embedding of two slopes on the torus.