## The Golden Relationship: Universal patternsIn the series, The Golden Relationship: Art, Math & Nature, the common denominator is space. "Nature is relationships...,geometry describes relationships...,art creates relationships in space." Geometry, beyond theorems & proofs, is a powerful tool for approaching design problems, while art allows for the physical realization of geometric ideas. With their union, mathematics is given a forum for displaying its beauty & art for expressing its logic. For readers with limited experience with mathematics & art, the authors write to demystify the disciplines while showing nature as the source of both. The texts are elegantly & accurately illustrated with equal emphasis on visual & written information. Chapters contain problems to reinforce mathematical concepts, & project suggestions offer experiences for structuring artworks. Diagrams augment the glossary & appendices provide extended content. Book 1, UNIVERSAL PATTERNS, examines certain triangles, rectangles, spirals, & number sequences that relate to recurring patterns in nature. Book 2, THE SURFACEPLANE, plays out these patterns on the two dimensional surface, focusing on grids, symmetry, circles, tilings, fractals, & pliability. In both volumes, the concept of the Golden Ratio is the spatial thread that weaves the ideas into a unified fabric. |

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### Contents

Basic Constructions | 1 |

Congruent Line Segments | 5 |

Congruent Angles | 6 |

Copyright | |

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### Common terms and phrases

arc that intersects Archimedean spiral artist Bisect bisector changing the compass changing the setting Chapter 2 Project circle compass and straightedge Construct create Cubit curve cut an arc cut arcs diagonals drawn in Step Dynamic Rectangles endpoints equilateral triangle Fibonacci numbers Fibonacci Sequence figure geometric gnomon Golden Ratio Golden Rec Golden Rectangle Golden Section Golden Spiral Golden Triangle Greek Harmonic Triangle hypotenuse Label the point length line segment logarithmic spiral Lute of Pythagoras mathematical mathematical induction measure ment metal tip midpoint Open the compass pair parallel Parthenon pattern pencil tip pentagram perpendicular phyllotaxis Place the metal plane point of intersec points of inter polygon properties Put the metal pyramid Pythagorean radius vector reciprocal regular pentagon relationship right angle Right Triangle shape sides space Student subdivision symbol tangle tion F Triangle of Price unit V5 Rectangle vertex vertices whole number width York