Is The Golden Ratio Really All That? (Paperback) (ISBN-13: 9781687723253)

Note: This edition is printed in color. The golden ratio, φ = (1+√(5))/2, has been a subject of fascination from as far back as 300 BC. It has been treated as a singular and unique number in a category of its own, and has been given such descriptors as divine, precious, and intriguing. However, relatively recently, it has been proposed that φ is actually one of many golden ratios (plural!). Like φ, these ratios: (i) can be seen in architecture, art, and nature; (ii) can be described geometrically as line segments divided by golden points; (iii) are found in certain polygons, curves, fractals, and 3D objects; (iv) are the positive roots of certain types of polynomial equations; (v) can be expressed as infinite continued fractions and as infinite nested radicals; (vi) have powers that can be written as linear combinations of themselves and constants; and (vii) are the values to which the ratios of successive terms in certain sequences converge and are roots of the characteristic equations of the matrices representing these sequences.If you are willing to consider the shocking idea that φ is not all that extraordinary, then this book is for you! You are invited to follow mathematical investigations that will show you that φ has many siblings in various families of golden ratios.

Author: Marlena Herman
ISBN-10: 1687723257
ISBN-13: 9781687723253
Publisher: Independently Published
Language: English
Published: 08/21/2019
Pages: 252
Format: Paperback
Weight: 1.80lbs
Size: 11.00h x 8.50w x 0.65d