### Volume 3, Number 41

 ``` 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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/ -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problems of the Week http://mathforum.org/pow/ Internet Resources http://mathforum.org/~steve/ Teacher2Teacher http://mathforum.org/t2t/ Discussion Groups http://mathforum.org/discussions/ 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\ / \ / \ / | / \ / \ ```