Euclid's masterpiece textbook, The Elements, was written twenty-three hundred years ago. It is primarily about geometry and contains dozens of figures. Five of these are constructed using a line that "is cut in extreme and mean ratio." Today this is called the golden ratio and is often referred to by the symbol Φ.
Many myths have grown up around this ratio. This book was written to learn about them. They arise from the pyramids, the Pythagorean Brotherhood, the platonic solids, the Fibonacci numbers, sea shells, and others. There is a common thread among these myths. Φ is an irrational number (a number whose digits after the decimal point go on forever and never form a repeating pattern). Φ can be used to draw pleasing figures. But its numerical value cannot be written down using integers and fractions, which were the only numbers used in Euclid's time.
Mathematicians before Euclid knew that irrational numbers existed. But to many people, a number that can't be written down was absurd. For centuries, many scientists and engineers believed that Φ was godlike.
This book discusses the myths from an engineering viewpoint. The last chapter of the book shows how Euclid handled irrational numbers; how Euclid did algebra using geometry; and a simple visual proof of why there are only five platonic solids.
About the Author: Francis D. Hauser earned his PhD in electrical engineering from the University of Denver in 1972.
He is a dynamic systems analyst in the motions and control of launch and reentry vehicles, multibody spacecraft, fixed and rotor-wing aircraft, large high-speed ocean-going watercraft, landcraft, and wind-driven turbines.
He is a university and college lecturer in graduate, undergraduate, and continuing-education courses on general optimization theory, Newtonian mechanics (statics and dynamics), linear algebra, Fourier analysis, and conventional, modern, and space-vehicle control.
The figures in this book were drawn using methods in Dr. Hauser's other book: Excel with VBA for Engineers and Mathematicians, CreateSpace Independent Publishing, 2015.
