Mathematics Commons^™

Euler's Anticipations, Christopher Goff, Erik Tou

Euleriana

Welcome to Volume 3 of Euleriana. This issue highlights occasions where Euler's work anticipated future results from other others, sometimes by decades or even centuries!

Variety And Variation, Christopher Goff, Erik R. Tou

Euleriana

Welcome to Volume 2 of Issue 2 of Euleriana. While we occasionally discover themes that emerge from the articles and translations presented in a given issue, the wide range of Euler’s work more often results in a variety of topics for each issue. This is no less true for Issue 2.

Group Of Point Transformations Of Time Dependent Harmonic Oscillators, Jose Ricardo Bernal

University of the Pacific Theses and Dissertations

In general, a physical system has invariant quantities which are very often related to its symmetry and to the invariance of the equation that describe it. A detailed study of the invariance property of the differential equation will be helpful in understanding this relation.

The work is concerned with a preliminary investigation of the Lie-group which leaves invariant the Newtonian and Lagrangian equation of motion for a one-dimensional harmonic oscillator. A brief review of Ehrenfest's adiabatic principle and the later treatments on exact and adiabatic invariants will be presented.

A Dictionary Of Mathematical Terms For High School Students, Matilda O. Iverson

University of the Pacific Theses and Dissertations

In compiling and writing this dictionary the needs of the high school student and teacher interested in mathematics have been kept constantly in mind. The mathematics of the high school is perhaps the simplest of its kind and yet very few textbooks carefully define all technical terms as they are introduced. The thoughtful student may turn to an abridged or unabridged dictionary but will find in most cases that the definitions of the terms are vague, often misleading, and in some cases not given.

The words in the vocabulary have been arranged in alphabetical order so that the reference to …

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.