Beyond Measure: A Guided Tour Through Nature, Myth And Number A Guided Tour Through Nature, Myth, and Number

This book consists of essays that stand on their own but are also loosely connected. Part I documents how numbers and geometry arise in several cultural contexts and in nature: the ancient musical scale, proportion in architecture, ancient geometry, megalithic stone circles, the hidden pavements of the Laurentian library, the shapes of the Hebrew letters, and the shapes of biological forms. The focus is on how certain numbers, such as the golden and silver means, present themselves within these systems. Part II shows how many of the same numbers and number sequences are related to the modern mathematical study of numbers, dynamical systems, chaos, and fractals. Contents: Essays in Geometry and Number as They Arise in Nature, Music, Architecture and Design: The Spiral in Nature and Myth; The Vortex of Life; Harmonic Law; The Projective Nature of the Musical Scale; The Music of the Spheres; Tangrams and Amish Quilts; Linking Proportions, Architecture, and Music; A Secret of Ancient Geometry; The Hyperbolic Brunes Star; The Hidden Pavements of the Laurentian Library; Measure in Megalithic Britain; The Flame-hand Letters of the Hebrew Alphabet; Concepts Described in Part I Reappear in the Context of Fractals, Chaos, Plant Growth and Other Dynamical Systems: Self-Referential Systems; Nature's Number System; Number: Gray Code and the Towers of Hanoi; Gray Code, Sets, and Logic; Chaos Theory: A Challenge to Predictability; Fractals; Chaos and Fractals; The Golden Mean; Generalizations of the Golden Mean - I; Generalizations of the Golden Mean - Il; Polygons and Chaos; Growth of Plants: A Study in Number; Dynamical Systems. Readership: Polytechnic or college students, designers, mathematicians and general readers A collection of essays that stand on their own but are also connected. Part I examines how numbers and geometry arise in nature and several cultural contexts. Part II shows how many of the same numbers and number sequences are related to the study of numbers, dynamical systems, chaos and fractals. Jay Kappraff. Includes Bibliographical References (p. 565-576) And Index.