John Barnes
Springer | 2012 - 2.ª edição | páginas | pdf | 5 Mb
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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.
Contents
1 The Golden Number 1
Pieces of paper, The golden ratio, Fibonacci’s rabbits, Continued fractions, Pentagons, Phyllotaxis, Further reading, Exercises.
2 Shapes and Solids 27
Flatland, Polygons, Tiling, Vision and projection, Five classical polyhedra, Duality, Kepler and Poinsot, The Archimedean figures, Non-convex polyhedra, Pentagonal tilings, Further reading, Exercises.
3 The Fourth Dimension 63
What is the fourth dimension? Honeycombs, The 4-simplex, The hypercube and the 16-cell, Other regular convex figures, Non-convex regular figures, Honeycombs, five dimensions and more, Nets, Further reading, Exercises.
4 Projective Geometry 89
Pappus’ theorem, Desargues’ theorem, Duality, Duality in three dimensions, Infinity and parallels, Quadrilaterals and quadrangles, Conics, Coordinates, Finite geometries, Configurations, Further reading, Exercises.
5 Topology 113
Hairy dogs, Colour problems, Colouring maps on the torus, The Möbius band, The Klein bottle, The projective plane, Round up, Further reading, Exercises.
6 Bubbles 137
Surface tension, Two bubbles, Three bubbles, Four bubbles, Foam, Films on frames, Films on cylinders, That well known theorem, Further reading, Exercises.
7 Harmony of the Spheres 157
Steiner’s porism, Inversion, Coaxial circles, Proof of Steiner’s porism, Soddy’s hexlet, Further reading, Exercises.
8 Chaos and Fractals 179
Shaken foundations, Fractals, Fractional dimensions, Cantor sets, Population growth, Double, double, boil and trouble, Chaos and peace, And so to dust, Newton’s method, Julia and Mandelbrot sets, Natural chaos, Further reading, Exercises.
9 Relativity 205
The special theory, Time changes, The Lorentz–Fitzgerald contraction, Distortion of bodies, Lorentz transformation, Time and relativity, Mass and energy, Coordinates, Curvature, Einstein’s equations, The Schwarzchild solution, Consequences of general relativity, Black holes, Properties of black holes, Further reading, Exercise.
10 Finale 231
Squares on a quadrilateral, The Argand plane, The quadrilateral revisited, Other complex problems, Trisection, Bends, Pedal triangles, Coordinates of points and lines, Further reading.
A The Bull and the Man 247
The problem, The proof.
B Stereo Images 251
Compound figures, Desargues’ theorem.
C More on Four 261
Archimedean figures in four dimensions, Prisms and hyperprisms.
D Schlegel Images 271
Schlegel diagrams, The hypercube, The 16-cell, The 24-cell, The 120-cell, 600-cell and tetroctahedric.
E Crystals 287
Packing of spheres, Crystals, Diamonds and graphite, Silica structures, Gems, Further reading.
F Stability 305
Stability of fixed points, The fixed points, The two cycle, Three cycles.
G Fanoland 319
Seven girls and seven boys, Plus six girls and six boys, Explanation.
Bibliography 321
Index 323
1.ª edição
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Idioma: Inglês
Editora: Berlin [u.a.] Springer 2009
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