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.
“This unusual book contains many interesting observations about the real world and relates these observations to one another by means of the 'higher artithmetic' of real numbers. The book is thus a carefully crafted combination of philosophy, history, biology, geography, philology, geology, and chemistry engagingly woven together by the quadrivium of music, astronomy, geometry and number.”
H S M Coxeter
University of Toronto
“Broad in scope, ‘Beyond Measure’ is filled with fascinating and valuable information — not only for curious students and lay people — but also for the seasoned researcher. From ancient myths, to music, to fractals and consiousness itself, Jay Kappraff ranges far and wide in an exhilarating, challenging, and innovative book sure to stimulate reader's sense of wonder at the incredible vastness of our mathematical universe.”
Clifford A Pickover
T J Watson Research Centre, IBM
“Jay Kappraff has a rare ability to convey discoveries and ideas of fellow mathematicians and scientists to the interested general public. In his latest book, ‘Beyond Measure’, he presents the unity of numbers and culture and helps the reader make his and her own discoveries in the world around us.”
Istvan Hargittai
Budapest Technical University
“Beyond Measure is bound to increase your appreciation of the role of matheamtics in our world.”
Library of Science
“… the topics are interesting … it is very well written and contains much of interest.”
Mathematical Reviews
“This pleasant book should be in the hands of many non-mathematicians and is of interest also for mathematicians.”
Zentralblatt MATH
The author is an Associate Professor at NJIT since 1974. Professor Jay Kapraff is also the author of the book — Connections: The Geometric Bridge between Art and Science, which was chosen by the National Association of Publishers (USA) as the best book in “ Mathematics, Chemistry and Astronomy — Professional and Reference” in 1991. He is selected for Who's Who in Science and Technology in 1983 and Who's Who in American Education in 1993. He has also received the CAPE award from Cable TV of NJ for best Distance Learning Course of 1996.
