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1. Beautiful geometry [2014]

Book
x, 187 pages : illlustrations (some color) ; 25 cm
  • Prefaces ix 1. Thales of Miletus 1 2. Triangles of Equal Area 3 3. Quadrilaterals 6 4. Perfect Numbers and Triangular Numbers 9 5. The Pythagorean Theorem I 13 6. The Pythagorean Theorem II 16 7. Pythagorean Triples 20 8. The Square Root of 2 23 9. A Repertoire of Means 26 10. More about Means 29 11. Two Theorems from Euclid 32 12. Different, yet the Same 36 13. One Theorem, Three Proofs 39 14. The Prime Numbers 42 15. Two Prime Mysteries 45 16. 0.999... = ? 49 17. Eleven 53 18. Euclidean Constructions 56 19. Hexagons 59 20. Fibonacci Numbers 62 21. The Golden Ratio 66 22. The Pentagon 70 23. The 17-Sided Regular Polygon 73 24. Fifty 77 25. Doubling the Cube 81 26. Squaring the Circle 84 27. Archimedes Measures the Circle 88 28. The Digit Hunters 91 29. Conics 94 30. 3/4 = 4/4 99 31. The Harmonic Series 102 32. Ceva's Theorem 105 33. e 108 34. Spira Mirabilis 112 35. The Cycloid 116 36. Epicycloids and Hypocycloids 119 37. The Euler Line 123 38. Inversion 126 39. Steiner's Porism 130 40. Line Designs 134 41. The French Connection 138 42. The Audible Made Visible 141 43. Lissajous Figures 143 44. Symmetry I 146 45. Symmetry II 149 46. The Reuleaux Triangle 154 47. Pick's Theorem 157 48. Morley's Theorem 160 49. The Snowflake Curve 164 50. Sierpinski's Triangle 167 51. Beyond Infinity 170 APPENDIX: Proofs of Selected Theorems Mentioned in This Book 175 Quadrilaterals 175 Pythagorean Triples 176 A Proof That 2 Is Irrational 176 Euclid's Proof of the Infinitude of the Primes 176 The Sum of a Geometric Progression 177 The Sum of the First n Fibonacci Numbers 177 Construction of a Regular Pentagon 177 Ceva's Theorem 179 Some Properties of Inversion 180 Bibliography 183 Index 185.
  • (source: Nielsen Book Data)9780691150994 20160612
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.
(source: Nielsen Book Data)9780691150994 20160612
Green Library, eReserve
ME 13AX
Book
1 online resource (366 p.) : digital, PDF file(s).
  • Introduction John Tyler Bonner-- 1. Introductory-- 2. On magnitude-- 3. The forms of cells-- 4. The forms of tissues, of cell-aggregates-- 5. On spicules and spicular skeletons-- 6. The equiangular spiral-- 7. The shapes of horns and of teeth or tusks-- 8. On form and mechanical efficiency-- 9. On the theory of transformations, or the comparison of related forms-- 10. Epilogue-- Index.
  • (source: Nielsen Book Data)9781107672567 20160613
Why do living things and physical phenomena take the form they do? D'Arcy Thompson's classic On Growth and Form looks at the way things grow and the shapes they take. Analysing biological processes in their mathematical and physical aspects, this historic work, first published in 1917, has also become renowned for the sheer poetry of its descriptions. A great scientist sensitive to the fascinations and beauty of the natural world tells of jumping fleas and slipper limpets; of buds and seeds; of bees' cells and rain drops; of the potter's thumb and the spider's web; of a film of soap and a bubble of oil; of a splash of a pebble in a pond.
(source: Nielsen Book Data)9781107672567 20160613
eReserve
ME 13AX
Book
xxvii, 486 p. : ill. ; 23 cm.
  • Proportion in architecture-- similarity-- the golden mean-- graphs-- tilings with polygons-- two-dimensional networks and lattices-- polyhedra - platonic solids-- transformation of the platonic solids I-- transformation of the platonic solids II-- polyhedra - space filling-- isometries and mirrors-- symmetry of the plane.
  • (source: Nielsen Book Data)9789810245856 20160528
A comprehensive reference in design science, bringing together material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition, there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition.
(source: Nielsen Book Data)9789810245856 20160528
Art & Architecture Library (Bowes), eReserve
ME 13AX