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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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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/ -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problem of the Week http://mathforum.org/geopow/ Internet Resources http://mathforum.org/~steve/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \ |

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