Ebook: A History of Numerical Analysis from the 16th through the 19th Century

In this book I have attempted to trace the development of numerical analysis during the period in which the foundations of the modern theory were being laid. To do this I have had to exercise a certain amount of selectivity in choosing and in rejecting both authors and papers. I have rather arbitrarily chosen, in the main, the most famous mathematicians of the period in question and have concentrated on their major works in numerical analysis at the expense, perhaps, of other lesser known but capable analysts. This selectivity results from the need to choose from a large body of literature, and from my feeling that almost by definition the great masters of mathematics were the ones responsible for the most significant accomplishments. In any event I must accept full responsibility for the choices. I would particularly like to acknowledge my thanks to Professor Otto Neugebauer for his help and inspiration in the preparation of this book. This consisted of many friendly discussions that I will always value. I should also like to express my deep appreciation to the International Business Machines Corporation of which I have the honor of being a Fellow and in particular to Dr. Ralph E. Gomory, its Vice-President for Research, for permitting me to undertake the writing of this book and for helping make it possible by his continuing encouragement and support.

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The beaver's tooth and the tiger's claw. Sunflowers and seashells. Fractals, Fibonacci sequences, logarithmic spirals. These diverse forms of nature and mathematics are united by a common factor: all involve self-repeating shapes, or gnomons. Almost 2000 years ago, Hero of Alexandria defined the gnomon as that form which, when added to some form, results in a new form, similar to the original. In a spiral seashell, for example, we see that each new section of growth (the gnomon) resembles its predecessor and maintains the shell's overall shape. Inspired by Hero, Midhat Gazale - a fellow native of Alexandria - explains the properties of gnomons, traces their long and colourful history in human thought, and explores the mathematical and geometrical marvels they make possible. The text should appeal to anyone interested in the wonders of geometry and mathematics, as well as to enthusiasts of mathematical puzzles and recreations