Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 161 for “"triangles"”.
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Pell's Equation and nearly equilateral triangles
In this paper, we seek a family of triangles that have integer sides and integer area. We focus mainly on scalene triangles since it is impossible to have such triangles that are equilateral and isoceles triangles with these properties are fairly simple to construct. We restrict the scalene …
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Surgery Exact Triangles in Instanton Theory
The introduction of instanton Floer theory and Donaldson polynomial invariants in the 1980s revolutionised the study of low dimensional topology. Since then, many Floer theories have been introduced with different structural properties and qualitative features. One of these Floer theories, Heegaard …
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Random obtuse triangles and convex quadrilaterals
… We then introduce the concept of Random Walk in Triangles and show that the probability that a triangle formed during the process is obtuse is itself random. We also propose the idea of Differential Equation in Triangle Space and study the variation of angles during this dynamic process. We then …
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On triangles and quadrilaterals of groups
… a pair of algebraic and geometric structures on triangles of groups and on quadrilaterals of groups. These structures are an automatic and biautomatic structure. In addition, this paper also discusses the growth function for the quadrilaterals. We show that these groups have these desired …
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The Mattila-Sjölin Problem for Triangles
… dimension then the set of congruence classes of triangles formed by triples of points of $E$ has nonempty interior. These types of results on point configurations with nonempty interior can be categorized as extensions and refinements of the statement in the well known Falconer distance problem …
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Optimal Point Sets With Few Distinct Triangles
… in $mathbb{R}^d$ which form exactly $t$ distinct triangles, which we denote by $F_d(t)$. We determine the values of $F_d(1)$ for all $dgeq3$, as well as determining $F_3(2)$. It was known from the work of Epstein et al. cite{Epstein} that $F_2(1) = 4$. Here we show somewhat surprisingly that …
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Illuminating triangles, quadrilaterals and convex polygons with vertex floodlights.
This work presents the solution to three problems in Computational Geometry. First we introduce a theorem to illuminate every triangle with three p6 vertex-floodlights and we provide three proofs. Secondly we show that three p4 vertex-floodlights suffice to illuminate every quadrilateral. Finally …
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Spectral problems on triangles and disks: Extremizers and ground states
… part of the thesis, we prove that among all triangles of given diameter, the equilateral triangle minimizes the sum of the first n eigenvalues of the Neumann Laplacian, when n is greater than or equal to 3. The result fails for n = 2, because the second eigenvalue is known to be minimal for …
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Parallel Mining and Analysis of Triangles and Communities in Big Networks
… are often characterized by an abundance of triangles and the existence of well-structured communities. Thus, counting triangles and detecting communities in networks have become important algorithmic problems in network mining and analysis. In the era of big data, the network data emerged …
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Music of the triangles: How students come to understand trigonometric identities and transformations
<p>Trigonometry is an essential part of mathematics education (NCTM, 2000; NGA, 2010). Trigonometry is prevalent in studies of pure mathematics as well as physical applications. Trigonometric identities and transformations are particularly important. However, students and even teachers have …
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Unit organization of the topics similar triangles and logarithms in college-preparatory mathematics
Thesis (Ed.M.)--Boston University This item was digitized by the Internet Archive.
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Filters, Neighbors, and Triangles: A Behaviorally and Electrophysiologically Informed Perspective on Visual Word Recognition
Two Event-Related Potential (ERP) studies and one behavioral study are presented in service of a single goal: to evaluate current prevalent computational models of visual word recognition. Specifically, the functionally homogenous cooperative division of labor model (Triangle) and the full family …
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An Almost Threesome: Erotic Love Triangles and Authorial Choice in Malory’s Le Morte D’ Arthur
… Furthermore, critical discussion on the love triangles in Malory’s work often focuses not on the notion of the relationships being triangular, but rather focuses more on the act of adultery itself. Thus, only two characters are truly involved in the romance, with the third (King Arthur and …
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An Algorithm for Triangulating 3D Polygons
… or the total dihedral angles between adjacent triangles. Our algorithm generalizes a classical method for optimally triangulating a single polygon. The key novelty is a mechanism for avoiding non-manifold outputs for two and more input polygons without compromising opti- mality. For better …
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Optimal Two-Dimensional Triangulations
… It is thus a plane graph whose bounded faces are triangles. For a fixed set of vertices, there are, in general, exponentially many ways to form a triangulation. Various criteria related to the geometry of triangles are used to define what one could mean by a triangulation that is optimal over all …
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Counting with convolutional neural networks
… and white images with variable numbers of white triangles on a black background, oriented right-side up, down, left or right. We train a network to count the right-side up triangles; specifically, we see this as a closed-set classification problem where the class is the number of right-side up …
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A recursively defined computer network
… This structured definition allows to analyze triangles of a practical size and to compute their reliability. A comparison is made between triangles and various ring networks in order to show the meritt of the proposed topology. The research also leads to the definition of 'connectivity …
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Generating Random Graphs with Tunable Clustering Coefficient
… degree sequence (representing the number of triangles/corners at a node) and single-edge degree sequence (representing the number of single-edges/stubs at a node) as input and generate a random graph with a tunable clustering coefficient. We analyze them theoretically and empirically for the …
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On the Existence of Knots and Links in the Complete Directed Graph on Six Vertices
… vertices contains at least one pair of disjoint triangles that forms a nontrivial link. The complete directed graph on six vertices is defined to be the graph consisting of six vertices such that each pair of distinct vertices is connected by exactly one pair of edges with the property that this …
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High-order adaptive methods for computing invariant manifolds of maps
… from geometric modeling. He uses Bezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of Bezier curves/triangles. The author develops and tests the methods for an ordinary …
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