| Description |
xiv, 215 pages : color illustrations ; 25 cm |
| Contents |
Contents note continued: Solid objects which are "essentially two-dimensional" -- The classification theorem for bounded objects -- Chirality -- Proper versus full symmetry groups -- Exercises -- 8.The Five Platonic Solids -- Counting their parts -- Duality -- Euler's formula -- The Euler characteristic -- An algebraic proof that there are only five Platonic solids -- The Platonic solids through the ages -- Exercises -- 9.Symmetry and Optimization -- Minimal surfaces -- The circle wins -- Exercises -- 10.What is a Number? -- Natural numbers -- Rational numbers -- Real numbers -- Which real numbers are rational? -- How many primes are there? -- Exercises -- 11.Cantor's Infinity -- The modern meaning of "same size" -- Are the rational numbers countable? -- Cantor's Theorem -- Exercises -- 12.Euclidean Space -- The Pythagoran Theorem and distance formula -- Naming the points on the unit circle -- The dot product and perpendicularity -- |
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Contents note continued: Using the dot product to find a lover or a song -- What is a rigid motion? -- Two exotic examples -- Exercises -- 13.Symmetry and Matrices -- Matrix computations -- Representing rigid motions as matrices -- Orthogonal matrices -- You finished the book. Now what? -- Exercises |
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Machine generated contents note: 1.Introduction to Symmetry -- A precise definition of "symmetry" -- Types of symmetries and types of objects -- The classification of plane rigid motions -- Exercises -- 2.The Algebra of Symmetry -- Cayley tables -- Symmetry groups -- The power of inverses -- An improved classification of plane rigid motions -- Exercises -- 3.Isomorphism -- What is an isomorphism? -- Isomorphism examples -- Rigid Equivalence -- A better notation for the cyclic groups -- Exercises -- 4.The Classification Theorems -- Bounded objects -- Border patterns -- Wallpaper Patterns -- Summary -- Exercises -- 5.Subgroups and Product Groups -- Subgroups -- Generating subgroups -- Product groups -- Exercises -- 6.Permutations -- Permutation groups -- Even and odd permutations -- Exercises -- 7.Symmetries of Solid Objects -- Rigid motions of space -- The symmetry group a tetrahedron -- The proper symmetry group a cube -- The proper symmetry group a dodecahedron -- |
| Summary |
"This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler's formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us."--Publisher's description |
| Analysis |
Geometry |
|
Mathematics |
|
Mathematics in Art and Architecture |
|
Mathematics in the Humanities and Social Sciences |
|
Mathematics, general |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Symmetry (Mathematics)
|
|
Mathematical Concepts.
|
|
Mathematics.
|
| LC no. |
2011940690 |
| ISBN |
1461402980 |
|
9781461402985 |
|
