Math Forum Internet News

Volume 3, Number 41

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12 October 1998                                   Vol. 3, No. 41

                 THE MATH FORUM INTERNET NEWS

Famous Math Problems - Reed | Perfect Number Journey | AskA+ Locator


  FAMOUS PROBLEMS IN THE HISTORY OF MATHEMATICS - Isaac Reed

      http://mathforum.org/~isaac/mathhist.html

An investigation of some of the great problems that have 
inspired mathematicians throughout the ages. Included are 
problems suitable for middle and high school math students, 
with links to solutions, biographies, references, and other 
math history sites. Problems include:

- The Bridges of Königsberg
    a problem that inspired the great Swiss mathematician 
    Leonard Euler to create graph theory, which led to the
    development of topology

- The Value of Pi
    discovering the value of and different expressions
    for the ratio of the circumference of a circle to its 
    diameter

- Puzzling Primes
    understanding the properties of the prime numbers
    and the difficulty of finding primes

- Famous Paradoxes
    Zeno's Paradox and Cantor's Infinities

- The Problem of Points
    an age-old gambling problem that led to the development 
    of probability by French mathematicians Pascal and Fermat 

- A Proof of the Pythagorean Theorem
    a proof that relies on Euclidean algebraic geometry,
    and is thus beautifully simple

- A Proof that e is irrational
    a proof by contradiction that relies on the expression 
    of e as a power series

See also Isaac's Bibliographic Guide to Math History Books:

    http://mathforum.org/~isaac/problems/bib1.html


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            THE PERFECT NUMBER JOURNEY - Heng O.K.
            
    http://home1.pacific.net.sg/~novelway/MEW2/lesson1.html

 "Mathematicians and non-mathematicians have been fascinated 
  for centuries by the properties and patterns of numbers. 
  They have noticed that some numbers are equal to the sum 
  of all of their factors (not including the number itself).
  The smallest such example is 6, since 6 = 1 + 2 + 3. Such 
  numbers are called perfect numbers." 

This journey through number patterns and properties of
numbers offers math facts and exercises that address:

 - How to find perfect numbers?
 - What are Mersenne numbers?
 - How are Mersenne primes related to perfect numbers? 
 - How to find Mersenne primes? 
 - How were the larger perfect numbers found?
 - Are there any odd perfect numbers?
 - Some properties of perfect numbers
 - How are perfect numbers and triangular numbers related? 
 - Are all perfect numbers hexagonal?
 - What is the largest known prime?

From the same author comes The Maths Room, a "Virtual 
Mathematics Resource Room," offering selected sites in a 
variety of mathematical categories:

           http://sunflower.singnet.com.sg/~okheng/


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                         ASKA+ LOCATOR

                  http://www.vrd.org/locator/ 

A database of "AskA" services designed to link students, 
teachers, parents, and other K-12 community members with 
experts available via the Internet. 

Profiles of each AskA service include identification 
information (e.g. publisher, e-mail address, contact person, 
links to service home page), scope, target audience, and a 
general description of the service. Some of the Web sites 
provide additional resources such as on-line references, 
archives of previously asked questions, and links to 
related sites. 

You can browse by subject or search for services in the 
Locator by keyword, subject, grade, etc.


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