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The History Of The Parallel Postulate And Non-Euclidean Geometry, Clare Switalski May 1932

The History Of The Parallel Postulate And Non-Euclidean Geometry, Clare Switalski

Bachelors’ Theses

After approximately two thousand years mathematicians have ventured to dispute the geometry of Euclid. Euclid's axioms were regarded as indisputable laws of space, the sole source from which his theorems were deduced. One needs only to survey the history of the controversies concerning his parallel postulate to be convinced that his assumptions are only metaphysical, since these assumptions can be changed when a space different from Euclid's is considered.

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Thomas William Robertson, The Mid-Victorian Dramatist, James A. Fitzpatrick May 1932

Thomas William Robertson, The Mid-Victorian Dramatist, James A. Fitzpatrick

Bachelors’ Theses

It is the purpose of this thesis to determine the position of Thomas William Robertson in the dramatic history of the nineteenth century, and to discover what contributions, if any, he made to the drama of this period. In addition to making a careful analysis of Robertson's more important dramas, I have read all the outstanding dramatic histories of the middle of the last century and some of its popular dramatic works. In my investigation of this problem I have explained the dramatic conditions of the early and mid-nineteenth century, revealed the characteristic tendencies of its popular plays, set forth …

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Hyperbolic Functions, Dolores Fitzgerald May 1932

Hyperbolic Functions, Dolores Fitzgerald

Bachelors’ Theses

No abstract provided.

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Development Of Geometry And Its Assistance In Promoting Society, Nelson Jean May 1932

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.

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Development Of Geometry And Its Assistance In Promoting Society, Nelson Jean May 1932

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

Electronic Theses and Dissertations

No abstract provided.

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The Practical Evaluation Of Resultants, T. A. Pierce Mar 1932

The Practical Evaluation Of Resultants, T. A. Pierce

Department of Mathematics: Faculty Publications

The purpose of the present note is to give a practical method of evaluating the resultant of two equations. The method is particularly effective when the degree of one of the equations is high while that of the other is low. Use will be made of certain results in the theory of matrices.

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General Steps In The Evolution Of The Calculus From The Time Of The Ancients To The Present, Sister Mary Virginia Ssf Jul 1931

General Steps In The Evolution Of The Calculus From The Time Of The Ancients To The Present, Sister Mary Virginia Ssf

Electronic Theses and Dissertations

This thesis, submitted to Xavier University in partial fulfillment of requirements for a Bachelor of Science degree in 1931, traces the historical development of the calculus from ancient Greek mathematics through the early twentieth century. The study is organized chronologically across eight sections. The introduction defines key mathematical terms including calculus, variable, and limit, and situates the calculus as the most powerful instrument of mathematical investigation. The thesis then examines the Method of Exhaustion developed by Greek mathematicians including Antiphon (430 B.C.), Eudoxus (370 B.C.), and Archimedes (225 B.C.), whose summation of infinite series represents the nearest ancient approach to …

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The Theory Of Exponents, Olive Marie Lass Jun 1931

The Theory Of Exponents, Olive Marie Lass

Bachelors’ Theses

When one speaks of Algebra, with its laws and operations, one asks the question - Is it an ancient subject, and how old is it? In answer to this question I find it is necessary to go back to the years before Christ.

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The Fundamental Theorem Of Algebra, John D. Fitzpatrick Jun 1931

The Fundamental Theorem Of Algebra, John D. Fitzpatrick

Bachelors’ Theses

Algebra is indeed an interesting and intriguing field of knowledge. Many people fear and dread it, and­ yet what do they fear? Is not algebra a logical se­quence of simple facts based perhaps on a few self-evident truths? If people saw the value of algebra, they would strive more enthusiastically to understand its principles. John Locke has a fitting commentary on those who are unfamiliar with algebra.

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Probability, The Historical Development Of The Theory And Its Application To Games Of Chance, Rose M. Brandt May 1931

Probability, The Historical Development Of The Theory And Its Application To Games Of Chance, Rose M. Brandt

Bachelors’ Theses

The theory of probability had its origin in isolated mathematical problems taken from games of chance. The beginnings of many of our modern theories and concepts can be traced back to Chinese origin. So too can the theory of probability. With the exception of the Chinese problem, dating from the beginning of the Christian era, no reference seems to have again been made to the theory prior to the latter part of the fifteenth century. In 1494 an Italian monk, Pacioli, was one of the first to introduce the "Problem of Points" into a treatise on mathematics. By the solution …

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Remedial Work In Subtraction, Multiplication And Division, Margaret A. Fleming May 1931

Remedial Work In Subtraction, Multiplication And Division, Margaret A. Fleming

Bachelors’ Theses

The subject matter of this thesis is Remedial Work in Subtraction, Multiplication and Division of Whole Numbers. A class or 39 pupils, 15 girls and 24 boys were given the Compass Diagnostic Tests in Arithmetic in each or these three fundamentals.

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Oval Curves, Leona G. Harner May 1931

Oval Curves, Leona G. Harner

Bachelors’ Theses

It has been the aim of the writer to present in this thesis a discussion of the most commonly known oval curves and their chief properties.

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Continued Fractions, Alma Holmgren May 1931

Continued Fractions, Alma Holmgren

Bachelors’ Theses

The aim of this thesis is to give the reader a general idea of the two types of continued fractions -- the simple continued fractions and the general continued fractions. Some properties of each type are also included.

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A Certain Multiple-Parameter Expansion, H. P. Doole Jan 1931

A Certain Multiple-Parameter Expansion, H. P. Doole

Department of Mathematics: Faculty Publications

C. C. Camp has shown the convergence of the expansion of an arbitrary function in terms of the solutions of the systems of equations
X1’ (λa1 - Σi=2nμi)X1 = 0,
X1’ (λai + μi)Xi = 0, (j = 2, 3, …, n),
where the ai’s are functions of x, with the boundary conditions
Xi(-π) = Xi(π), (j = 1, 2, …, n).
In this paper it is intended to use a …

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Parametric Solutions Of Certain Diophantine Equations, T. A. Pierce Jan 1931

Parametric Solutions Of Certain Diophantine Equations, T. A. Pierce

Department of Mathematics: Faculty Publications

In this note parametric solutions of certain diophantine equations are given. The method of obtaining the solutions is derived from an equation involving the determinants of certain matrices. It will be recognized that the method is a generalization of the method of Euler and Lagrange which depends on forms which repeat under multiplication. The matrices used in this paper must be such that their forms are retained under matric multiplication and addition. When integer values are assigned to the parameters of our solutions we obtain integer solutions of the particular equation under consideration; however not all integer solutions are necessarily …

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The Spinning Top, Aaron Jefferson Miles Jan 1931

The Spinning Top, Aaron Jefferson Miles

Masters Theses

"Several mathematicians have solved the problems of motion of the top and gyroscope most completely, but none of them have considered in their solutions the effects of the supporting gimbal rings upon the motion or the effects of a variable rotor speed. It is the purpose of this paper to investigate the top equations by two well known methods; namely, by the method of Lagrange and by the method of Jacobi; considering in both the dynamics of the gimbal rings and varying rotor speed"--Introduction, page 3.

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On The Trigonometric Expansion Of Elliptic Functions, M. A. Basoco Jan 1931

On The Trigonometric Expansion Of Elliptic Functions, M. A. Basoco

Department of Mathematics: Faculty Publications

The problem of expressing an elliptic function in terms of infinite sums of trigonometric functions has been treated by Hermite, Briot and Bouquet, A. C. Dixon and others. In the present paper we treat the same problem from the point of view of Cauchy's residue theorem in function theory, which is also Briot and Bouquet's starting point, but we differ from these authors in that the integrand we use leads to an expansion for an elliptic function which is valid in an arbitrarily wide, but finite, strip of the complex plane, and which contains certain classical results as special cases. …

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The Construction Of Conic Sections By Means Of Pascal's And Brianchon's Theorems, Benjamin Lee Welker Jr. Jan 1931

The Construction Of Conic Sections By Means Of Pascal's And Brianchon's Theorems, Benjamin Lee Welker Jr.

University of the Pacific Theses and Dissertations

The discovery of conic sections was made by Menaechmus (375-325 B.C.) an associate of Plato and a pupil of Eudoxus. This discovery, in the course of only a century, raised geometry to the loftiest height which it was destined to reach during antiquity.

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A Determination Of The Solubility Curves Of Several Liquid Ternary Systems And The Effect Of Change Of Temperature On These Curves, Samuel Klieger May 1930

A Determination Of The Solubility Curves Of Several Liquid Ternary Systems And The Effect Of Change Of Temperature On These Curves, Samuel Klieger

Bachelors’ Theses

The following paper treats of the solubility relations found in ternary systems. The components of the system are, the lower alcohols, Benzene or toluene and water. The work consists of a determination of the solubility curve of the three components in various proportions. The influence of temperature on the solubility is so studied.

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Symmetric Functions, Mildred L. Roth Apr 1930

Symmetric Functions, Mildred L. Roth

Bachelors’ Theses

If function of two or more quantities is not altered when any two of the quantities are interchanged, it is called a symmetric function. For example, the trinomial a2+ b2+ c2 is a symmetric function of a, b, c, because if any two quantities, say a and b are interchanged, the expression is unaltered in value.

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On Polynomial Solutions Of A Class Of Linear Differential Equations Of The Second Order, W. C. Brenke Jan 1930

On Polynomial Solutions Of A Class Of Linear Differential Equations Of The Second Order, W. C. Brenke

Department of Mathematics: Faculty Publications

Certain well known polynomials have a number of common properties. They arise as coefficients of tn in the expansion of a generating function ; they may be obtained by means of orthogonalization of a set of functions xⁿg(x) when the function ρ(x) = g2(x) and the interval are properly chosen ; they may be regarded as polynomials which become orthogonal when multiplied by a proper factor g(x) ; they satisfy a certain type of difference equation ; they satisfy a certain type of differential equation. The results …

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Matrices Whose Characteristic Equations Are Cyclic, T. A. Pierce Jan 1930

Matrices Whose Characteristic Equations Are Cyclic, T. A. Pierce

Department of Mathematics: Faculty Publications

One of Sylvester's theorems f on matrices states that if the characteristic equation
(1) | M - λI| = f(λ) = 0
of a square matrix M has the roots λ1, λ2, … , λn, then the characteristic equation
(2) | φM - ρI| = = g(ρ) = 0
of any integral function of M, namely, φM, has the roots ρi = φ (λi), i = 1, 2, … , n. In this note an isomorphism is shown to exist between …

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History Of Applied Geometry, Evelyn Jackson Jan 1930

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?

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History Of Applied Geometry, Evelyn Jackson Jan 1930

History Of Applied Geometry, Evelyn Jackson

Electronic Theses and Dissertations

No abstract provided.

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The Utility Of Mathematics, Jack R. Dunn Jan 1930

The Utility Of Mathematics, Jack R. Dunn

Electronic Theses and Dissertations

No abstract provided.

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A Syllabus Of Line Geometry, Alice Willmarth Jan 1930

A Syllabus Of Line Geometry, Alice Willmarth

University of the Pacific Theses and Dissertations

In the study of advanced geometry, we shall deal with a certain important relation between pairs of figures in space, and also between their properties. There are two distinct parts to analytic geometry, the analytic work and the geometric interpretation. Two systems of geometry, depending upon different elements with the same number of coordinates, will have the same analytic expressions and will differ only in the interpretation of the analysis. In such a case it is often sufficient to know the meaning of the coordination and the interpretation of a few fundamental relations in each system in order to find …

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The Cycloid, Some Related Curves And Their Derivation, Ann Downer Jun 1929

The Cycloid, Some Related Curves And Their Derivation, Ann Downer

Bachelors’ Theses

In studying the history of the cycloid and the related curves, it is interesting to note that the earliest notations and explanations were given not by a mathematician but by an artist. The description and instrumental construction of the epicycloid curve was presented in about 1525 by Albrecht Durer (1471-1528) a celebrated sculptor and painter of Nurnberg in his book "Underweysund der Messung mit dem Zyrkenund Rychtsceyd." The original idea, however, goes as far back as the time of Hipparchus, an astronomer, who used it in his astronomical theory of epicycles. This curve was now neglected until G. Desargues and …

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The Study Of The Curves Of The Equations Having The Type Form X^N + Y^N = A^N, Lena S. Reif Jun 1929

The Study Of The Curves Of The Equations Having The Type Form X^N + Y^N = A^N, Lena S. Reif

Bachelors’ Theses

The object of this thesis is to determine the general properties of the family of curves, x^n + y^n = a^n from some of the specific curves in that family. The first curve to be considered is the one in which a = 4 and n =1. x+y = 4

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Curve Tracing In Polar Coordinates, Virginia Higgins Jun 1929

Curve Tracing In Polar Coordinates, Virginia Higgins

Bachelors’ Theses

No abstract provided.

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The Cubic Equation In One Variable, Ella M. Horst Jun 1929

The Cubic Equation In One Variable, Ella M. Horst

Bachelors’ Theses

No abstract provided.

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