Euclid s Elements of Geometry

Euclid ' S Geometry

Euclid ’ s Algorithm Andrzej

The main goal of the paper is to prove the correctness of the Euclid’s algorithm for SCM. We define the Euclid’s algorithm and describe the natural semantics of it. Eventually we prove that the Euclid’s algorithm computes the Euclid’s function. Let us observe that the Euclid’s function is defined as a function mapping finite partial states to finite partial states of SCM rather than pairs of in...

A Review of Euclid ’ s Window : The Story of Geometry from Parallel Lines to Hyperspace Reviewed

554 NOTICES OF THE AMS VOLUME 49, NUMBER 5 This is a shallow book on deep matters, about which the author knows next to nothing. The concept of the book is appealing: a popular review of geometrical notions from Euclid to Einstein as background to contemporary string theory with comments on the related intellectual history and portraits of some principal figures: Descartes, Gauss, Riemann and E...

Translating Euclid: Liberating the Cognitive Potential of Collaborative Dynamic Geometry

How should one translate the classic-education approach of Euclid’s geometry into the contemporary vernacular of computer visualization, social networking and discourse-centered pedagogy? The birth of geometry in ancient Greece and its systematization by Euclid played an important role in the development of deductive reasoning and science. As it was translated and refined over the centuries, ho...

Teaching Geometry According to Euclid, Volume 47, Number 4

460 NOTICES OF THE AMS VOLUME 47, NUMBER 4 I n the fall semester of 1988, I taught an undergraduate course on Euclidean and nonEuclidean geometry. I had previously taught courses in projective geometry and algebraic geometry, but this was my first time teaching Euclidean geometry and my first exposure to non-Euclidean geometry. I used the delightful book by Greenberg [8], which I believe my stu...