John Napier

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/