Date: 06/17/98 at 10:28:23 From: Anonymous Subject: John Napier Dear Dr. Math, I want to know why John Napier's discovery of logarithms was such a great contribution to the field of mathematics. I need practical examples of what man can do today because of his discovery. I am looking for applications of his discovery not only to math-minded types but to the average person. I teach seventh grade math in and would appreciate your help. I've already researched Napier and your previous answers to related questions. I just found your website and think it's very helpful. Thanks for maintaining it and answering so many questions.
Date: 06/19/98 at 14:38:30 From: Doctor Mateo Subject: Re: John Napier Hello, John Napier's discovery of logarithms has had an enormous impact on the development of mathematics as well as other scientific endeavors. His discovery was a result of a more global endeavor and a direct result of simplifying computations associated with astronomy. Napier endeavored to simplify some of the tedious computations and work associated with complicated trigonometric tables used in astronomical studies. The invention of logarithms was essentially the result of two decades of trying to simplify the arithmetic involved in astronomical computations. What was the impact of this invention? An immediate result of Napier's discovery was the simplification of multiplication and division to addition and subtraction. Since astronomers dealt with large numbers this reduced the enormous amount of time spent doing tedious multiplication and division algorithms. A natural consequence of Napier's discovery of common logarithms was the introduction of decimal numeration - that certainly has some impact on seventh grade mathematics even today. Needless to say, Napier's invention of logarithms was also the catalyst for calculating machines, which were the catalyst for arithmetic machines and certainly the catalyst for the computer you are probably accessing at this moment. Some common applications involving "common logarithms (base 10 logs)" that would be relevant to a seventh grader might be the study of sound waves and in particular the intensity of a sound (measured in decibels) or perhaps applying litmus paper to determine the pH of soil for gardening potatoes, sea water, rain water, fruit juices, saline solutions, etc. There are numerous uses for natural logarithms in chemistry and in the sciences in particular. Another application might be examining the amplitude of seismic waves and energy released by earthquakes: the Richter scale. These are just a few ideas that might be grade level appropriate especially if you work in conjunction with the science teacher. Thank you for asking such an excellent question. Your students will no doubt benefit as a result of your effort to make mathematics useful and relevant to their everyday lives. -Doctor Mateo, The Math Forum http://mathforum.org/dr.math/
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