Gems of Geometry

  • Filename: gems-of-geometry.
  • ISBN: 9783642309649
  • Release Date: 2012-08-17
  • Number of pages: 325
  • Author: John Barnes
  • Publisher: Springer Science & Business Media

Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein's Theories of Relativity. Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes' book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment. In this second edition, stimulated by recent lectures at Oxford, further material and extra illustrations have been added on many topics including Coloured Cubes, Chaos and Crystals.

Six gems of geometry

  • Filename: six-gems-of-geometry.
  • ISBN: 9781935638025
  • Release Date: 2010-05-26
  • Number of pages: 137
  • Author: Thomas Reale
  • Publisher: PSIpress

Six gems of geometry is an introductory geometry textbook for general audiences. The book focuses mainly on the teachings of Euclid. It contains a story inspired by William Blake's painting, Newton the Measurer, where an encounter is imagined between Euclid and Newton, suggesting a deep influence the former may have had on the latter.

Geometry by Its History

  • Filename: geometry-by-its-history.
  • ISBN: 9783642291630
  • Release Date: 2012-04-10
  • Number of pages: 440
  • Author: Alexander Ostermann
  • Publisher: Springer Science & Business Media

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.

Introduction to Geometry

  • Filename: introduction-to-geometry.
  • ISBN: 0471504580
  • Release Date: 1989-03-09
  • Number of pages: 496
  • Author: H. S. M. Coxeter
  • Publisher: Wiley

This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises.

Professor Stewart s Cabinet of Mathematical Curiosities

  • Filename: professor-stewart-s-cabinet-of-mathematical-curiosities.
  • ISBN: 9781847651280
  • Release Date: 2010-09-03
  • Number of pages: 320
  • Author: Ian Stewart
  • Publisher: Profile Books

School maths is not the interesting part. The real fun is elsewhere. Like a magpie, Ian Stewart has collected the most enlightening, entertaining and vexing 'curiosities' of maths over the years... Now, the private collection is displayed in his cabinet. There are some hidden gems of logic, geometry and probability -- like how to extract a cherry from a cocktail glass (harder than you think), a pop up dodecahedron, the real reason why you can't divide anything by zero and some tips for making money by proving the obvious. Scattered among these are keys to unlocking the mysteries of Fermat's last theorem, the Poincaré Conjecture, chaos theory, and the P/NP problem for which a million dollar prize is on offer. There are beguiling secrets about familiar names like Pythagoras or prime numbers, as well as anecdotes about great mathematicians. Pull out the drawers of the Professor's cabinet and who knows what could happen...

Beautiful Geometry

  • Filename: beautiful-geometry.
  • ISBN: 9781400848331
  • Release Date: 2014-01-19
  • Number of pages: 208
  • Author: Eli Maor
  • Publisher: Princeton University Press

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important and beautiful branches of mathematics.

Architecture After Geometry

  • Filename: architecture-after-geometry.
  • ISBN: STANFORD:36105020308412
  • Release Date: 1997
  • Number of pages: 96
  • Author: Maggie Toy
  • Publisher: Academy Press

This issue features and explores architectural and urban design projects which derive from non-Euclidean geometries.

The Geometry of Physics

  • Filename: the-geometry-of-physics.
  • ISBN: 9781139505611
  • Release Date: 2011-11-03
  • Number of pages:
  • Author: Theodore Frankel
  • Publisher: Cambridge University Press

This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.

Euclidean Geometry in Mathematical Olympiads

  • Filename: euclidean-geometry-in-mathematical-olympiads.
  • ISBN: 9780883858394
  • Release Date: 2016-05-02
  • Number of pages: 311
  • Author: Evan Chen
  • Publisher: The Mathematical Association of America

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.

Euler s Gem

  • Filename: euler-s-gem.
  • ISBN: 0691126771
  • Release Date: 2008
  • Number of pages: 317
  • Author: David S. Richeson
  • Publisher: Princeton University Press

Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to giant all-carbon molecules. "Euler's Gem" tells the illuminating story of this indispensable mathematical idea. Line drawings and tables throughout.

Pi A Source Book

  • Filename: pi-a-source-book.
  • ISBN: 0387205713
  • Release Date: 2004-06-17
  • Number of pages: 797
  • Author: J.L. Berggren
  • Publisher: Springer Science & Business Media

This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein fall into various classes. First and foremost there is a selection from the mathematical and computational literature of four millennia. There is also a variety of historical studies on the cultural significance of the number. Additionally, there is a selection of pieces that are anecdotal, fanciful, or simply amusing. For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, and new translations of works by Viete and Huygen.

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