Math Forum Internet News

Volume 2, Number 49

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8 December 1997                                   Vol. 2, No. 49

                  THE MATH FORUM INTERNET NEWS

Math Lessons - MSTE | Art of Algebra - Parshall | Large Numbers


          MATHEMATICS LESSONS DATABASE - UIUC/MSTE

       http://www.mste.uiuc.edu/mathed/queryform.html

A searchable database of Internet-based lessons in 
mathematics and programs related to teaching mathematics,
from the Office of Mathematics, Science, and Technology 
at the University of Illinois at Urbana-Champaign.

Search for lessons by keyword, content area, and level: 

   - algebra                - elementary
   - analytic geometry      - middle
   - calculus               - secondary
   - cross-content          - post-secondary
   - general mathematics
   - geometry
   - probability
   - statistics
   - trigonometry

or browse the complete list of titles:

      http://www.mste.uiuc.edu/mathed/lessontitles.html
      

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       THE ART OF ALGEBRA FROM AL-KHWARIZMI TO VIETE: 
         A STUDY IN THE NATURAL SELECTION OF IDEAS

                 by Karen Hunger Parshall

  http://www.lib.virginia.edu/science/parshall/algebra.html

A paper that describes some of the history of algebra from 
a not-so-linear perspective.

 "Suppose that at any given time and place, we define
  the mathematical environment as the known body of
  mathematical facts, techniques, theories, and ideas 
  together with the mathematicians who deal with them. 
  Within this context, every idea which presents itself, 
  whether new or newly rediscovered, effects a change in 
  the environment. Thus, the individual mathematician, 
  by generating new ideas, by remaining ignorant of an 
  idea, or by failing to absorb an idea, shapes the 
  particular niche within which his or her own theories 
  develop.The development of algebra from al-Khwarizmi 
  to Viete provides a good test case for this model of 
  the natural selection of ideas."

This document appeared as an article in the June 1988 
issue of History of Science, Vol.  26, No.  72, pp.129-164.


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                  LARGE NUMBERS AND INFINITY

http://mathforum.org/dr.math/faq/faq.large.numbers.html

- What's the largest number? 

  There is no largest number! Why? Well, 1,000,000,000 
  (1 billion) can't be the largest number because 1 billion 
  + 1 is bigger - but that is true for any number you pick.
  You can choose any big number and I can make a bigger one 
  just by adding 1 to it. 

- What's a googol?

  A googol is a 1 with a hundred zeroes behind it. We can 
  write a googol using exponents by saying a googol is 
  10^100.

  The biggest named number that we know is googolplex, 
  ten to the googol power, or (10)^(10^100). That's written 
  as a one followed by googol zeroes. 

How do we name large numbers? What is scientific notation?
What is infinity? Is one infinity larger than another?
Who invented the modern notation for infinity? Answers to
these questions and others, with links to discussions in
the Dr. Math archives and on the Web, can be found in the 
Dr. Math FAQ.

          http://mathforum.org/dr.math/faq/


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