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### John Napier

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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

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.

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/
```
Associated Topics:
High School History/Biography
High School Logs
Middle School History/Biography
Middle School Logarithms

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