Mathematics Commons^™

What Is A Riemmian Manifold?, Frederick Griffin

Journal of the Arkansas Academy of Science

No abstract provided.

The Spieker Circle And Certain Related Configurations, Berthola Elmo Lumzy

Electronic Theses and Dissertations

This thesis, presented to the Department of Mathematics at Xavier University in partial fulfillment of requirements for the degree of Master of Arts in 1952, examines the Spieker circle, a circle inscribed in the median triangle of a given triangle, and extends its defining properties to related geometric configurations. Lumzy first establishes a series of analogies between the Spieker circle and the nine-point circle, demonstrating parallel relationships involving radius, center, harmonic conjugates, and homothetic centers relative to the incenter, median point, and Nagel point of a triangle.

The thesis then proves that the Spieker circle is inscribed in two congruent …

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 …

The Construction Of Triangles Having Given Three Elements, Mary Eugene Wolter

Bachelors’ Theses

It is with great pleasure and satisfaction that I dedicate these following pages to those who are especially interested in mathematics, to those who are more geometrically than algebraically inclined, and in particular to my students in mathematics. It is through my students of the past that I have been assisted in bringing forth this work, by applying such knowledge as I have acquired in my teaching experience. To the pupils who in the future will come under my guidance and direction I hope to impart the benefits and fruits that should be the outgrowth of the labor and study …

The Important Lines In A Triangle, Jane Bogiel

Bachelors’ Theses

Geometry, as one of the fields of Mathematics, has been the object of extensive studies in ancient, Greek times, as well as in modern times, times of revival of scientific interests and researches. Analytical, descriptive, and projective geometry has been introduced as means of symplifying the study of the relations of different geometrical elements. Consequently, pure geometrical methods have been almost altogether abandonned, and, it is only in introducing basic geometrical concepts that they are now used. --This, however, seems to be the only reasonable course as long as the new methods do not change the basic structure of the …

A Study Of The Groups Of The Regular Solids, Lawrence J. Stanton

Bachelors’ Theses

Groups of movements are special groups in general group theory. Particular groups of movements are those obtained by rotating the regular solids. Before we take up the study of these groups of the regular solids, we shall first discuss subjects related to this work, namely, inversion in a sphere, stereographic projection, and rotations in a sphere.

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?

Modern Geometry Of The Triangle, Irene Nolan

Bachelors’ Theses

It has been the object of t he writer to present in this thesis theorems and proofs of modern geometry which seemed most useful and most interesting to her. Concepts of modern geometry have been presented and developed with reference to the triangle.

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 …