Mathematics Commons^™

The Fermat Point And The Steiner Problem, J. N. Boyd, P. N. Raychowdhury

Virginia Journal of Science

We revisit the convex coordinates of the Fermat point of a triangle. We have already computed these convex coordinates in a general setting. In this note, we obtain the coordinates in the context of the Steiner problem. Thereafter, we pursue calculations suggested by the problem.

Studies On Finite Linear Cellular Automata., Palash Sarkar Dr.

Doctoral Theses

Cellular Automata were originally proposed by John von Neumann as formal models of self reproducing organisms. The structure studied was mostly an ane and two dimensional infinite grida, though higher dimensions were also considered. Computation universality and other computation theoretic questions were considered important. See Burks [24] for a collection of essays on important problems on cellular automata during this period. Later physicists and biologists began to study cellular automsta for the purpose of modelling in their respective domains. In the present era, cellalar automata is being atudied from many widely different angles, and the relationship of these structurea to …

Affine Varieties, Groebner Basis, And Applications, Eui Won James Byun

Theses Digitization Project

No abstract provided.

Investigation Of The Effectiveness Of Interface Constraints In The Solution Of Hyperbolic Second-Order Differential Equations, Paul Jerome Silva

Theses Digitization Project

Solutions to differential equations describing the behavior of physical quantities (e.g., displacement, temperature, electric field strength) often only have finite range of validity over a subdomain. Interest beyond the subdomain often arises. As a result, the problem of making the solution compatible across the connecting subdomain interfaces must be dealt with. Four different compatibility methods are examined here for hyperbolic (time varying) second-order differential equations. These methods are used to match two different solutions, one in each subdomain along the connecting interface. The entire domain that is examined here is a unit square in the Cartesian plane. The four compatibility …

Constructible Circles On The Unit Sphere, Blaga Slavcheva Pauley

Theses Digitization Project

In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry.

Definitions, Solved And Unsolved Problems, Conjectures, And Theorems In Number Theory And Geometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason why the present book appears. Here, of course, there are problems from various types. Solving these problems is addictive like eating pumpkin seed: having once started, one cannot help doing it over and over again.

Muyltivariate And Regression Analysis Based On The Geometry Of Data Clouds., Biman Chakraborty Dr.

Doctoral Theses

Median is a natural estimate of location of a data set, and there are several versions of inultivariate median studied in the literature, each of which is an interesting descriptive statistic for multivariate data and provides some nice geometric insights into the data cloud. One would expect that multidimensional median will be a natural estimate for the center of symmetry of a multivariate distribution. However, there is no unique concept of symmetry in multivariate problems. The center of symmetry can be defined in several ways there. For example, the d-dimensional random variable X is spherically symmetric about e €Rd if …

A Lower Bound For The Cyclic Cutwidth Of The N-Cube, James Shigeo Namekata

Theses Digitization Project

No abstract provided.

On The Geometrisability Of Some Strongly Regular Graphs Related To Polar Spaces., Pratima Panigraphi Dr.

Doctoral Theses

GraphsA graph G = (VE) consists of a finite set V and a subset E of ). (Here () denotes the set of all 2-subsets of V.) Elements of Vare called the vertices and the elements of E are called the edges of the graph. So Vis the vertex set and E is the edge set of the graph G. Two vertices a, y are said to be adjacent if the pair {a, y} is an edge; otherwise they are non-adjacent. If two vertices are adjacent then each is called a neighbour of the other vertex.Sometimes the edges of a …

A Study In Geometric Construction, Nichola Sue Mcclain

Theses Digitization Project

No abstract provided.

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Branch Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră şi …

Cyclic Cutwidth Of Three Dimensional Cubes, Ray N. Gregory

Theses Digitization Project

No abstract provided.

Controlling Curvature In The Minkowski Plane, Mostafa Ghandehari

Mathematics Technical Papers - Archive

Pontryagin's maximum principle is used to find the curve of shortest length with bounded Minkowskian curvature passing through two points with given initial and terminal tangents.

On Texture Image Analysis Using Fractal Geometry Based Features., Nirupam Sarkar Dr.

Doctoral Theses

Visual textureTexture is a property to characterize a region of a scene. A set of natural texture images is shown in Fig. 1.1. A specific texture may be generated due to certain organization of several objects in a region, or due to the reflectance pattern caused by color variation or unevenness of an object surface. Since texture provides a lot of information of a region, texture analysis and synthesis are important components of digital image processing.It is difficult to provide a formal definition of texture although we perceive and recognize texture rather easily. According to Sklansky [152) "A region in …

Analysis On A Hyperplane Of The Quaternions, Pamela Jean Whelchel

Theses Digitization Project

No abstract provided.

Audio Magazine: Proposed Series Chapter 09 - Geometry, Richard C. Heyser

Unpublished Writings

Richard C. Heyser prepared this chapter as part of a series originally intended for AUDIO magazine in an effort to find an objective way of dealing with the subjective perception of sound. Through the implementation of the time delay spectrometry (TDS) method, Heyser was able to explore the mathematical analysis of audio and the philosophical principles of audio measurement. Chapter 9 discusses the geometric measuring of sound and the existence of a sound image.

Transformational Geometry Unit, Elizabeth Ann O'Neill

All Graduate Projects

The study included the development and writing of a unit on transformational geometry which involved a holistic approach including the cognitive, psychomotor, and affective domains. This unit was taught to the eighth grade class in the Oakville School District in Oakville, Washington. The results showed support that the teaching of this unit was effective.

Fifty Years Of Uncertainty, Richard C. Heyser

Unpublished Writings

Richard C. Heyser frequently explores ways to find a "mathematical basis for perception" in his writings. In this article, Heyser discusses implementing geometry elements to quantum physics.

Linear Geometry, Phyllis L. Thomas

Masters Theses

"This paper contains material suitable for a one semester course in linear geometry where the student has had a one semester course in linear algebra previously. It compiles information in the areas of affine sets, affine geometry, convex sets, and a few applications. Also included are Caratheodory's theorem and the well-known theorem by Helly as proved by Radon"--Abstract, page ii.

The Fundamental Groups Of The Complements Of Some Solid Horned Spheres, Norman William Riebe

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the methods used for the construction of the classical Alexander horned sphere leads naturally to generalization to horned spheres of higher order. Let M₂, denote the Alexander horned sphere. This is a 2-horned sphere of order 2. Denote by M₃ and M₄, two 2-horned spheres of orders 3 and 4, respectively, constructed by such a generalization.

The fundamental groups of the complements of M₂, M₃, and M₄ are derived, and representations of these groups onto the Alternating Group, A₅, are found. The form of the presentations …

Solutions Of Some Balanced Doubly Balanced And Partially Balanced Statistical Designs., Chilakamarri Ramanujacharyulu Dr.

Doctoral Theses

The theory and methods of con struction of statistical designs have connections with Modern algebraic systems, theory of numbers, arithmetic theory of quadratic forms, information theory and construction of codes. The properties of finite linear spaces have been used for the construction of (i) complete set of mutually orthogonal latin squares (Bose and Nair, 1941) (ii) balanced incomplete block designs (Bose 1939) (iii) partially balanced incomplete block designs (Bose and Nair 1939) (iv) designs where some effects of treatments are confounded (Bose, 1947). Primrose (1951) studied quadric surfaces and used them in the construction of balanced incomplete block designs. Roychoudhuri …

A Study Of Certain Substitution Groups, Merle Mitchell

Mathematics & Statistics ETDs

This thesis purposes to study a certain group of movements which can be expressed as substitutions. The groups of movements which send a square into itself is to be studied as a group of eight substitutions on the vertices for the purpose of leading up to the real problem of this paper. From the octic group, it is natural to proceed to a study of the movements which send a cube into itself. In particular, it is the aim of this thesis to discover the group of the cube and to analyze some of its properties. There are twenty-eight rotations …

A Comparison Of I.Q. And Achievement In Plane Geometry Among Students In The Senior High School At Joplin, Missouri, Vivian L. Hummer

Electronic Theses & Dissertations

No Abstract

Development Of Geometry And Its Assistance In Promoting Society, Nelson Jean

Electronic Theses and Dissertations

Geometry, the science of space and its relations which exist between its various elements, linear, superficial and solid, develops and helps society.

History Of Applied Geometry, Evelyn Jackson

Electronic Theses and Dissertations

Mathematics: Just what does the word mean to us? After a moment of thought many different meanings may present themselves to our minds. At first we are inclined to say that the word mathematics covers a vast field. We are justified in so thinking because mathematics embraces a wide scope of study. Were we to say that it is a science we should place it in its proper genius, for it is truly a science of numbers and space. However, could not the science be the art of calculation or the art of computation?

History Of Applied Geometry, Evelyn Jackson

Electronic Theses and Dissertations

No abstract provided.

Experimental And Observational Geometry, Albert D. Field

University of the Pacific Theses and Dissertations

Geometry has the distinction of being one of the oldest subjects given in the high-school.

Its subject-matter was formulated and organized by the Greeks into a fine system of thought before the time of Christ. Since leaving the hands of the Greeks, geometry has received only a few minor changes, and these largely in recent years.

Heretofore, the study of geometry has been made almost entirely dependent upon memory and reasoning. Geometricians have been slow in adopting the laboratory and observational methods.

This thesis has been written to encourage the student in his work of observing geometrical forms, and in …

Institutionum Calculi Differentialis Sectio Iii, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Problematis Ex Theoria Maximorum Et Minimorum Solutio, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Solutio Trium Problematum Difficiliorum Ad Methodum Tangentium Inversam Pertinentium, Leonhard Euler

All Works by Eneström Number

No abstract provided.