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The Fifth Postulate
The great discovery that no one wanted to make It's the dawn of the Industrial Revolution, and Euclidean geometry has been profoundly influential for centuries. One mystery remains, however: Euclid's fifth postulate has eluded for two thousand years all attempts to prove it. What happens when three nineteenth-century mathematicians realize that there is no way to prove the fifth postulate and that it ought to be discarded—along with everything they'd come to know about geometry? Jason Socrates Bardi shares the dramatic story of the moment when the tangible and easily understood world we live in gave way to the strange, mind-blowing world of relativity, curved space-time, and more. "Jason Socrates Bardi tells the story of the discovery of non-Euclidian geometry—one of the greatest intellectual advances of all time—with tremendous clarity and verve. I loved this book." —John Horgan, author, The End of Science and Rational Mysticism "An accessible and engrossing blend of micro-biography, history and mathematics, woven together to reveal a blockbuster discovery." —David Wolman, author of Righting the Mother Tongue and A Left-Hand Turn around the World
General Investigations of Curved Surfaces
This influential work defines the concept of surface curvature and presents the important theorem stating that the "Gauss curvature" is invariant under arbitrary isometric deformation of a curved surface. 1902 edition.
Gauss
Classic biography of Gauss, updated with new introduction, bibliography and new material.
In the Dark on the Sunny Side
A memoir that describes the groundbreaking life and career of blind mathematician Larry Baggett, interspersed with musings on mathematics.
The German Genius
From the end of the Baroque age and the death of Bach in 1750 to the rise of Hitler in 1933, Germany was transformed from a poor relation among western nations into a dominant intellectual and cultural force more influential than France, Britain, Italy, Holland, and the United States. In the early decades of the 20th century, German artists, writers, philosophers, scientists, and engineers were leading their freshly-unified country to new and undreamed of heights, and by 1933, they had won more Nobel prizes than anyone else and more than the British and Americans combined. But this genius was cut down in its prime with the rise and subsequent fall of Adolf Hitler and his fascist Third Reich-...
A New Approach to Differential Geometry using Clifford's Geometric Algebra
Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.
Calculus Gems: Brief Lives and Memorable Mathematics
Calculus Gems, a collection of essays written about mathematicians and mathematics, is a spin-off of two appendices ("Biographical Notes" and "Variety of Additional Topics") found in Simmons' 1985 calculus book. With many additions and some minor adjustments, the material will now be available in a separate softcover volume. The text is suitable as a supplement for a calculus course and/or a history of mathematics course, The overall aim is bound up in the question, "What is mathematics for?" and in Simmons' answer, "To delight the mind and help us understand the world". The essays are independent of one another, allowing the instructor to pick and choose among them. Part A, "Brief Lives", i...
Calculus and Its Origins
The story of how calculus came to be, accessible to anyone with a basic knowledge of geometry and algebra.
Aha! A Two Volume Collection
Previously published separately, the two books aha! Gotcha and aha! Insight are here combined as a single volume. The aha! books, as they are referred to by fans of Martin Gardner, contain 144 wonderful puzzles from the reigning king of recreational mathematics. In this combined volume, you will find puzzles ranging over geometry, logic, probability, statistics, number, time, combinatorics, and word play. Gardner calls these puzzles aha! problems, that 'seem difficult, and indeed are difficult if you go about trying to solve them in traditional ways. But if you can free your mind from standard problem solving techniques, you may be receptive to an aha! reaction that leads immediately to a solution. Don't be discouraged if, at first, you have difficulty with these problems. After a while you will begin to catch the spirit of offbeat, nonlinear thinking, and you may be surprised to find your aha! ability improving.'
Geometry and Symmetry
This new book for mathematics and mathematics education majors helps students gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The first is devoted to a rigorous introduction of Euclidean geometry, the second covers various noneuclidean geometries, and the last part delves into symmetry and polyhedra. Historical contexts accompany each topic. Exercises and activities are interwoven with the text to enable the students to explore geometry. Some of the activities take advantage of geometric software so students - in particular, future teachers - gain a better understanding of its capabilities. Others explore the construction of simple models or use manipulatives allowing students to experience the hands-on, creative side of mathematics. While this text contains a rigorous mathematical presentation, key design features and activities allow it to be used successfully in mathematics for teachers courses as well.
