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.

Nice Numbers

  • Filename: nice-numbers.
  • ISBN: 9783319468310
  • Release Date: 2016-12-25
  • Number of pages: 329
  • Author: John Barnes
  • Publisher: Birkhäuser



In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author informs and intrigues his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal's triangle, the Rubik cube, Mersenne's curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty style and requiring only basic school mathematical knowledge, this book will appeal to both young and mature readers fascinated by the curiosities of numbers.

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.

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: 0691150990
  • Release Date: 2014
  • Number of pages: 187
  • Author: Eli Maor
  • Publisher:



"Mathematicians always claim their subject is beautiful. Eli Maor and Eugen Jost prove it. This is geometry as you've never seen it before. A feast for the eyes."--Ian Stewart, author of Visions of Infinity "This book shows that math is more than theorems and proofs--it is full of history, philosophy, and glimpses of different cultures. I was immediately attracted by the book's intriguing and beautiful illustrations, and once I started reading the text, I could not stop following its fascinating stories about the origins of geometrical theorems."--Carlo H. Sequin, University of California, Berkeley "Reading Beautiful Geometry is like touring a personal art collection, except the masterpieces here are elegantly presented theorems and constructions by ancient and modern mathematicians. Eli Maor teaches the thought process of a geometry connoisseur as he highlights important details in each of these gems, and Eugen Jost illustrates these ideas with colorful and creative artworks. Readers who like to see real math in their math books will enjoy how Beautiful Geometry brings these enduring mathematical achievements to life."--George Hart, mathematical sculptor "Beautiful Geometry teaches and delights with its marriage of art and mathematics. The lovely illustrations range from conversation starters to dazzling Proofs Without Words--clever diagrams that explain why something is true. A feast for the eye and mind."--Frank Farris, Santa Clara University "A beautiful book that is as delightful to see as to read. Once you start you are compelled to read the next subject, and the next, and the next."--Zentralblatt MATH "

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.

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.

New Horizons in Geometry

  • Filename: new-horizons-in-geometry.
  • ISBN: 9780883853542
  • Release Date: 2012
  • Number of pages: 513
  • Author: Tom M. Apostol
  • Publisher: MAA



New Horizons in Geometry represents the fruits of 15 years of work in geometry by a remarkable team of prize-winning authors—Tom Apostol and Mamikon Mnatsakanian. It serves as a capstone to an amazing collaboration. Apostol and Mamikon provide fresh and powerful insights into geometry that requires only a modest background in mathematics. Using new and intuitively rich methods, they give beautifully illustrated proofs of results, the majority of which are new, and frequently develop extensions of familiar theorems that are often surprising and sometimes astounding. It is mathematical exposition of the highest order. The hundreds of full color illustrations by Mamikon are visually enticing and provide great motivation to read further and savor the wonderful results. Lengths, areas, and volumes of curves, surfaces, and solids are explored from a visually captivating perspective. It is an understatement to say that Apostol and Mamikon have breathed new life into geometry.

The VSEPR Model of Molecular Geometry

  • Filename: the-vsepr-model-of-molecular-geometry.
  • ISBN: 9780486486154
  • Release Date: 2012-01
  • Number of pages: 248
  • Author: Ronald J. Gillespie
  • Publisher: Courier Corporation



" Valence Shell Electron Pair Repulsion (VSEPR) theory is a simple technique for predicting the geometry of atomic centers in small molecules and molecular ions. This authoritative reference, written by the developer of VSEPR theory features extensive coverage of structural information as well as theory and applications. Helpful data on molecular geometries, bond lengths, and band angles appear in tables and other graphics. 1991 edition"--

Advanced Euclidean Geometry

  • Filename: advanced-euclidean-geometry.
  • ISBN: 9780486154985
  • Release Date: 2013-01-08
  • Number of pages: 336
  • Author: Roger A. Johnson
  • Publisher: Courier Corporation



This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.

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