5 January 1998 Vol. 3, No. 1
THE MATH FORUM INTERNET NEWS
Chaos, Fractals, Dimension | Int. Math Olympiad |
Triangle Centers
CHAOS, FRACTALS, DIMENSION - GLENN ELERT
Mathematics in the Age of the Computer
http://www.columbia.edu/~gae4/chaos/
An illustrated investigation of chaos, fractals, and
non-linear dynamics, progressing from the function y = f(x)
to the concept of fractal dimensions. Requiring moderate
mathematical knowledge and featuring many images on bite-sized
pages for quick loading, this site offers chapters on:
- Mathematical Experiments
Iteration and Orbits
Orbit and Bifurcation Diagrams
Universality
- Strange and Complex
Strange Attractors
Julia Sets
Mandelbrot Sets
- What is Dimension?
General Dimension
Topological Dimension
Fractal Dimension
- Measuring Chaos
Harmonic Oscillator
Logistic Equation
Lyapunov Exponent
Lyapunov Space
- Appendices
Printed Resources
Software Resources
Internet Resources
A directory of software available online for Mac computers
and an extensive list of external links are also included.
"Chaos, Fractals, Dimension" is a part of E-World,
maintained by Glenn Elert.
http://www.columbia.edu/~gae4/
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INTERNATIONAL MATHEMATICAL OLYMPIAD (IMO)
OLYMPIADE INTERNATIONALE DE MATHEMATIQUES (OIM)
http://www.camel.math.ca/IMO/
This world championship mathematics competition for high
school takes place each year in a different country. Its
membership, which is by invitation only, has gradually
expanded to over 70 countries from 5 continents.
This site, in English and French, includes the latest
competition results, results of prior competitions, problems
from previous examinations, related sites, countries with
Olympiad sites, and year by year competitions.
IMO 1997 was held in Mar de Plata, Argentina.
Results are available in English and Spanish:
http://www.oma.org.ar/imo/
IMO 1998, the 39th International Mathematical Olympiad,
is scheduled for July 10-21 in Taipei, Taiwan:
http://imo.math.ntnu.edu.tw
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TRIANGLE CENTERS AND THE EULER LINE
What's an Euler line? What are the incenter, orthocenter,
circumcenter, and centroid of a triangle? For explanations,
diagrams, and links to newsgroup discussions and relevant
Web sites, search the Dr. Math archives. You might look for
a word like orthocenter to find:
Incenter, Orthocenter, Circumcenter, Centroid:
http://mathforum.org/dr.math/problems/beck1.5.97.html
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On the Web, see Prof. Clark Kimberling's Triangle Centers:
http://www.evansville.edu/~ck6/tcenters/index.html
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For discussions of these and many other math questions,
search and browse the Dr. Math archives' more than
3150 entries in 91 categories:
http://mathforum.org/dr.math/
For more detailed explanations of some frequently asked
questions, see the Dr. Math FAQ:
http://mathforum.org/dr.math/faq/
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