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Topic: Newsletter: Math Forum Internet News 2.37 (Sept. 15)
Replies: 0

 Sarah Seastone Posts: 1,240 Registered: 12/3/04
Newsletter: Math Forum Internet News 2.37 (Sept. 15)
Posted: Sep 13, 1997 10:54 AM

15 September 1997 Vol.2, No.37

THE MATH FORUM INTERNET NEWS

CIRCLES OF LIGHT: THE MATHEMATICS OF RAINBOWS

http://www.geom.umn.edu/education/calc-init/rainbow/

How are rainbows formed? Why do they only occur when the sun
is behind the observer? If the sun is low on the horizon, at
what angle in the sky should we expect to see a rainbow?

This lab helps to answer these and other questions by
examining a mathematical model of light passing through a
water droplet. The contents include:

- How does light travel?
- Reflection
- Refraction
- Rainbows: Exploration
- Rainbows: Analysis
- Conclusion

Objectives of the lab:

- to examine the use of Fermat's Principle of least-time to
derive the Law of Reflection and the Law of Refraction

- to experimentally determine the angle at which rainbows
appear in the sky

- to understand geometric properties of rainbows by
analyzing the passage of light through a raindrop

- to apply a knowledge of derivatives to a problem in
the physical sciences

- to better understand the relation between the geometric,
symbolic, and numerical representation of derivatives

This lab from the Curriculum Initiative Project at the
University of Minnesota is based on a module that was
developed by Steven Janke and published in "Modules in
Undergraduate Mathematics and its Applications" in 1992.

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NEW LARGEST KNOWN PRIME NUMBER!

http://www.mersenne.org/prime.htm

On August 24th, Gordon Spence, using a program written by
George Woltman, discovered what is now the largest known
prime number. The prime number, 2^(2976221)-1, is one of a
special class of prime numbers called Mersenne primes;
it is 895,932 digits long.

An introduction to prime numbers can be found in the
Dr. Math FAQ:

http://forum.swarthmore.edu/dr.math/faq/faq.prime.num.html

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MATH FORUM MIDDLE SCHOOL PROBLEM OF THE WEEK

http://forum.swarthmore.edu/midpow/

A project designed to challenge middle school students with
non-routine problems, and to encourage them to verbalize their
will be returned; incorrect solutions will be sent back with
an explanation of the error and students will be urged to
try again.

The problems are intended for students in grades 6-9 (ages
11-14), but may also be appropriate for students in other
grades. A variety of problem-solving techniques are encouraged,
including:

- guess and check
- make a list
- draw a picture
- make a table
- act it out
- logical thinking
- algebraic equations

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http://forum.swarthmore.edu/epigone/math-teach/frehkherdwimp

motivation and interest, the need for grades for college
of absolute truth, the effects of praise in the classroom,
GPA, SAT and IQ tests, and the effects of testing.

of grade inflation by Michael Paul Goldenberg, during a
discussion of "At-risk Algebra Students":

http://forum.swarthmore.edu/epigone/math-teach/khunclerverm

The archives of the Math-Teach mailing list are hosted by
the Math Forum:

http://forum.swarthmore.edu/epigone/math-teach/

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CHECK OUT OUR WEB SITE:

The Math Forum http://forum.swarthmore.edu/
Problem of the Week http://forum.swarthmore.edu/geopow/
Internet Resources http://forum.swarthmore.edu/~steve/
Join the Math Forum http://forum.swarthmore.edu/join.forum.html

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The Math Forum ** 15 September 1997

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