Wednesday, September 14, 2011

A Dialogue On Logarithms - Chris Valle

a dialogue on logarithms - chris valle
a dialogue on logarithms - chris valle

This book presents a fictional dialogue between Pythagoras and his precocious pupil named Bitsy. The topic of the day: Logarithms. The book is intended to help students who need to learn about logarithms in their math class, and attempts to do so in an engaging way.

Some of the most powerful ideas in mathematics have very humble beginnings. Every now and then an invention so profound comes along that those who overlooked it may cry out in disbelief over its sheer brilliance and simplicity. In 1614 a Scotsman named John Napier provided such an invention in the form of a list of numbers he called logarithms.

In order to understand these numbers it is best to first consider the historical context in which they arose. The early 1600’s saw the birth of the Scientific Revolution; In Italy Galileo was conducting his famous experiments regarding the behavior of falling bodies, while in Austria Kepler was poring over thousands of astronomical observations to uncover the laws of planetary motion, and in England William Gilbert published his monumental work arguing that the Earth itself was a great magnet, paving the way towards our modern understanding of electricity and magnetism.

Each of these endeavors and others like them demanded an enormous amount of laborious computations which in some cases consumed years of effort, inevitably distracting their poor victims from more important matters. In fact a growing consensus began to emerge among scientists that a new mathematical tool was desperately needed to aid them with their arithmetical calculations. Relief gratefully arrived via Napier and his table of logarithms.

The notion of a logarithm thus arose out of necessity; to simplify the tedious process of arithmetic. It should be noted that today the calculations presented in this book could be carried out on any pocket calculator in a fraction of a second, but our aim here is to illustrate the basic properties of these logarithms, as they have certainly outgrown their original purpose and are still quite useful today. Near the end we will show how logarithms may be used to solve some real world problems.

DOWNLOAD A DIALOGUE ON LOGARITHMS - CHRIS VALLE

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