""Euclid's 'Elements' Redux"" is an open textbook on mathematical logic and geometry for use in grades 7-12 and in undergraduate college courses on proof writing. It is a new edition of the most successful textbook of all time, ""The Elements,"" compiled by Euclid around 300 BC. It contains several hundred exercises as well as a partial answer key. Although it is a copyrighted work, it is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. Download it for free at: http: //starrhorse.com/euclid/

"The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

"The foundations of modern knowledge--philosophy, math, astronomy, geography--were laid by the Greeks, whose ideas were written on scrolls and stored in libraries across the Mediterranean and beyond. But as the vast Roman Empire disintegrated, so did appreciation of these precious texts. Christianity cast a shadow over so-called pagan thought, books were burned, and the library of Alexandria, the greatest repository of classical knowledge, was destroyed. Yet some texts did survive and The Map of Knowledge explores the role played by seven cities around the Mediterranean--rare centers of knowledge in a dark world, where scholars supported by enlightened heads of state collected, translated and shared manuscripts. In 8th century Baghdad, Arab discoveries augmented Greek learning. Exchange within the thriving Muslim world brought that knowledge to Cordoba, Spain. Toledo became a famous center of translation from Arabic into Latin, a portal through which Greek and Arab ideas reached Western Europe. Salerno, on the Italian coast, was the great center of medical studies, and Sicily, ancient colony of the Greeks, was one of the few places in the West to retain contact with Greek culture and language. Scholars in these cities helped classical ideas make their way to Venice in the 15th century, where printers thrived and the Renaissance took root. The Map of Knowledge follows three key texts--Euclid's Elements, Ptolemy's The Almagest, and Galen's writings on medicine--on a perilous journey driven by insatiable curiosity about the world"--Pages [2-3] of cover.