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Essay Instructions: Report on mathematical components used in digital photography technologies. The goal of report is to learn how to integrate, apply and extend knowledge and skills previous acquired in mathematics and science. Use of mathematical/scientific concepts in the report must be very specific in the detailed level (e.g., with some examples, equations, formulas, theories, proof, historical background, pros & cons, …)

Essay Instructions: I will fax the article "Mathematics As A Creative Art", Paul Halmos, American Scientist, April 1968 vol. 56, no. 4 over for your review.

I am requesting a reation essay is be word prosesses and must identify a. The name of the article: "Mathematics As A Creative Art" b. My name: "Carol Procopio" and c. the due date: "September 20, 2006.

A little about me:

I have a BA in Math from Augsburg in 1990 and I live in northern Minnesota. I teach jr. high math. I have 3 children and I wonderful husband of 18 years.


When I read the article I agree that Mathology is a art, but math and science go hand in hand in the real world.

My husband is a car artist of sorts, he paint cars and does sum great custom paint work, I see him "the painter" and I "the math chick" think the same way, thus is article hit home for me.

Being a teacher Mathematics of today is very important to me and making sure that children understand the important of doing math because math is all around us and math is what will make childrens future bright.


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Essay Instructions: Teacher's actions encourage students to think, question, solve problems, and discuss their ideas, strategies, and solutions.

TASK STATEMENT: Write an essay of 1000 words describing a variety (at least 5 methods) of specific questions and strategies that encourage students to discuss their ideas, procedures, rules and definitions that they used to solve a problem. Discuss ways (at least 4) in which justification of solutions improves students' relational understanding of mathematics. Include references in APA format.



Note: No more than a combined total of 30% of a submission can be directly quoted or closely paraphrased from outside sources, even if cited correctly.

Essay Instructions: Write a five paragraph essay on the aesthetic appeal of Mathematics

Question: How are patterns and mathematics related? Be specific

. Focus in particular on the ideas of "symmetry", "patterns", "order out of chaos". A primary focus of your essay will be the illustration of the aesthetic appeal of Mathematics, based on your reading of the text and outside references. Try to teach your reader some Mathematics in the course of explaining its aesthetic appeal. Be creative!!!

NEED:
 WORKS CITED LIST.
 CITATIONS.
 TWO OUTSIDE REFERENCES

Some hint to help:
1. What are two principle functions of the use of symbols in Mathematics?
2. What is the different between abstraction as idealization and abstraction as extraction? Give examples of each.
3. Name one benefit of the process of generalization in Mathematics?
4. Based on your reading of The Stretched String (Davis et al. pages 174-178) name a quality that describe what constitutes the ?straightness? of a straight line, which Euclid neglected to mention.
5. How are the ideas of order, chaos, and pattern related, both in general terms, and in mathematical terms?
6. A major theme regarding patterns and Mathematics is the fact that patterns often "create Mathematics" and Mathematics often creates patterns. Try to give examples of each of these two ideas, different from the ones in your text and already given in this assignment.
7. With respect to order and chaos, how does the goal of Mathematics compare to the goal of practitioners of your field?
8. What is the difference between a proof and a conjecture?
9. What is Goldbach?s conjecture? Can you give an example different from the one in the book to illustrate this conjecture for the even number 16?

 SUGGESTED RESOURCES

To illustrate the aesthetic appeal of Mathematics, you can investigate some interesting mathematical ?objects? . These investigations should give you some good ideas for your final paper.

1. Illustrations of how Mathematics is used to describe patterns abound. For example, special patterns, called frieze patterns, are ones that you see in wallpaper designs and on fabrics. In general, a frieze pattern consists of repeated copies of a single motif.
In geometry, a frieze pattern is any of a number of "tilings" that repeat an object through a horizontal translation (which is a certain type of transformation). Mathematicians classify frieze patterns by what they contain It turns out that there are only 7 possible types! This is astonishing

Abas, S. J. and A S Salman: Symmetries of Islamic Geometrical Patterns. World Scientific. ISBN 981-02-1704-8. 1993.

Appleton, Le Roy H. American Indian Design and Decoration. New York: Dover, 1971.

Boles, Martha and Rochelle Newman. Art, Mathematics and Nature in the Interdisciplinary Classroom. Leonardo: Volume 21, Number 2, 1988. Pages: 182-186

Brahier, Daniel J. Patterns at your fingertips. Teaching Children Mathematics May2003, Vol. 9 Issue 9, p521. Available on-line.

Cross, K. and A. Haworth. Images of balance and order: patterns in Islamic art as geometric teaching aid. Times Educational Supplement 0040-7887 May 19, 2000 i4377, pS12(2). Available on-line.

Deck, K. Spirograph Math. Humanistic Mathematics Journal March 1999, Vol.19, p13-17. Available on-line. http://web.stcloudstate.edu/szkeith/index11.html (Click on archives)



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