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This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks-a sort of potato-stamp method-Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics.Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own.Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.

Symmetry (Mathematics) --- Symmetry (Art) --- Abstract algebra. --- Addition. --- Algorithm. --- Antisymmetry. --- Arc length. --- Boundary value problem. --- Cartesian coordinate system. --- Circular motion. --- Circumference. --- Coefficient. --- Complex analysis. --- Complex multiplication. --- Complex number. --- Complex plane. --- Computation. --- Coordinate system. --- Coset. --- Cyclic group. --- Derivative. --- Diagonal. --- Diagram (category theory). --- Dihedral group. --- Division by zero. --- Domain coloring. --- Dot product. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Eisenstein integer. --- Epicycloid. --- Equation. --- Euler's formula. --- Even and odd functions. --- Exponential function. --- Fourier series. --- Frieze group. --- Function (mathematics). --- Function composition. --- Function space. --- Gaussian integer. --- Geometry. --- Glide reflection. --- Group (mathematics). --- Group theory. --- Homomorphism. --- Horocycle. --- Hyperbolic geometry. --- Ideal point. --- Integer. --- Lattice (group). --- Linear interpolation. --- Local symmetry. --- M. C. Escher. --- Main diagonal. --- Mathematical proof. --- Mathematical structure. --- Mathematics. --- Mirror symmetry (string theory). --- Mirror symmetry. --- Morphing. --- Natural number. --- Normal subgroup. --- Notation. --- Ordinary differential equation. --- Parallelogram. --- Parametric equation. --- Parametrization. --- Periodic function. --- Plane symmetry. --- Plane wave. --- Point group. --- Polynomial. --- Power series. --- Projection (linear algebra). --- Pythagorean triple. --- Quantity. --- Quotient group. --- Real number. --- Reciprocal lattice. --- Rectangle. --- Reflection symmetry. --- Right angle. --- Ring of integers. --- Rotational symmetry. --- Scientific notation. --- Special case. --- Square lattice. --- Subgroup. --- Summation. --- Symmetry group. --- Symmetry. --- Tetrahedron. --- Theorem. --- Translational symmetry. --- Trigonometric functions. --- Unique factorization domain. --- Unit circle. --- Variable (mathematics). --- Vector space. --- Wallpaper group. --- Wave packet. --- Abstract algebra. --- Addition. --- Algorithm. --- Antisymmetry. --- Arc length. --- Boundary value problem. --- Cartesian coordinate system. --- Circular motion. --- Circumference. --- Coefficient. --- Complex analysis. --- Complex multiplication. --- Complex number. --- Complex plane. --- Computation. --- Coordinate system. --- Coset. --- Cyclic group. --- Derivative. --- Diagonal. --- Diagram (category theory). --- Dihedral group. --- Division by zero. --- Domain coloring. --- Dot product. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Eisenstein integer. --- Epicycloid. --- Equation. --- Euler's formula. --- Even and odd functions. --- Exponential function. --- Fourier series. --- Frieze group. --- Function (mathematics). --- Function composition. --- Function space. --- Gaussian integer. --- Geometry. --- Glide reflection. --- Group (mathematics). --- Group theory. --- Homomorphism. --- Horocycle. --- Hyperbolic geometry. --- Ideal point. --- Integer. --- Lattice (group). --- Linear interpolation. --- Local symmetry. --- M. C. Escher. --- Main diagonal. --- Mathematical proof. --- Mathematical structure. --- Mathematics. --- Mirror symmetry (string theory). --- Mirror symmetry. --- Morphing. --- Natural number. --- Normal subgroup. --- Notation. --- Ordinary differential equation. --- Parallelogram. --- Parametric equation. --- Parametrization. --- Periodic function. --- Plane symmetry. --- Plane wave. --- Point group. --- Polynomial. --- Power series. --- Projection (linear algebra). --- Pythagorean triple. --- Quantity. --- Quotient group. --- Real number. --- Reciprocal lattice. --- Rectangle. --- Reflection symmetry. --- Right angle. --- Ring of integers. --- Rotational symmetry. --- Scientific notation. --- Special case. --- Square lattice. --- Subgroup. --- Summation. --- Symmetry group. --- Symmetry. --- Tetrahedron. --- Theorem. --- Translational symmetry. --- Trigonometric functions. --- Unique factorization domain. --- Unit circle. --- Variable (mathematics). --- Vector space. --- Wallpaper group. --- Wave packet.