Generalizing Morley’s and other theorems with automated realization

A new approach is shown that mechanically proves various theorems in plane geometry by recasting them in terms of constraint satisfaction. A Python 3 implementation called GEOPAR affords transparent proofs of well-known theorems as well as new ones, including a generalization of Morley’s Theorem

Why Didn\u27t Euclid Think of That?: The History and Development of Geometry in the Western World

The subject of geometry has been in existence around the world for thousands of years and is a topic that continues to be taught in high school classrooms around the world today. When one thinks about geometry, the name Euclid and concepts such as proving triangles are congruent and examining properties of parallel lines usually come to mind. In fact, most of what is taught in the education system today can be found in Euclid\u27s Elements, a compilation of what was known about geometry up until around 300 B.C.E. But what has become of geometry in the Western world cultures that lasted for hundreds of years? This project investigates the origins of geometry in the Western world and its significance throughout history. In particular, it examines several important theorems and their proofs are based on ideas found in the Elements. This paper not only shows how geometry has developed up until this present time but also gives the reader a brief account of how geometry is expanding today and where it is heading in the future

Hilbert's thesis : some considerations about formalizations of mathematics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1982.MICROFICHE COPY AVAILABLE IN ARCHIVES AND HUMANITIESBibliography: leaves 175-176.by Lon A. Berk.Ph.D

Morley´s miracle – part II

In Part I of this article we had narrated the history of this theorem and discussed a beautiful ‘pure geometry’ proof found by M. T. Naraniengar over a century back. Readers will recall the curious logic used: the proof starts with an equilateral triangle and then constructs a co

Quaternions: A History of Complex Noncommutative Rotation Groups in Theoretical Physics

The purpose of this dissertation is to clarify the emergence of quaternions in order to make the history of quaternions less opaque to teachers and students in mathematics and physics. ‘Quaternion type Rotation Groups’ are important in modern physics. They are usually encountered by students in the form of: Pauli matrices, and SU(2) & SO(4) rotation groups. These objects did not originally appear in the neat form presented to students in modern mathematics or physics courses. What is presented to students by instructors is usually polished and complete due to many years of reworking. Often neither students of physics, mathematics or their instructors have an understanding about how these objects came into existence, or became incorporated into their respected subject in the first place. This study was done to bridge the gaps between the history of quaternions and their associated rotation groups, and the subject matter that students encounter in their course work

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques