Individual Research Project Section 8.1
Project 8.1
Suppose you drive you car in a roundabout traffic circle that is 100 ft in diameter. Assume your tires are on the circumference of the circle, and also assume that your car is six feet wide.
- If you
Individual Research Projects
Individual Research Projects 7-7
Individual Research Project 7.9
Write a paper on perspective. How are three-dimensional objects represented in two dimensions?
References:
Mathematics and Perspective
http://mathforum.org/sum95/math_and/perspective/perspect.html
Morris Kline, Mathematics, a Cultural Approach (Reading, MA: Addison-Wesley, 1962), Chapters 10-11.
C. Stanley Ogilvy, Excursions in Geometry… See the whole entry
Individual Research Projects Section 7.6
Project 7.6
Do some research on the length-to-width ratios of the packaging of common household items. Form some conclusions. Find some examples of the golden ratio in art. Do some research on dynamic symmetry.
References:
Philip J. Davis and Reuben … See the whole entry
Individual Research Projects Section 7.5
Project 7.5
Historical Quest
The Historical Note in Section 7.5 asks the question, Why did the Egyptians build the pyramids using a slant height angle of about 44° or 52°? Write a paper answering this question.
References:
Arthur F. Smith… See the whole entry
Individual Research Projects Section 7.1
Project 7.1
What are optical illusions?
What are the following optical illusions:
Find some unusual optical illusions and illustrate with charts, models, advertisements, pictures, or
illusions.
References:
Martin Gardner, “Mathematical Games,” Scientific American, May 1970.
Richard Gregory, “Visual Illusions,” Scientific … See the whole entry
Individual Research Projects Section 6.4
Project 6.2
Write out a derivation of the quadratic formula.
References:
You can check almost any high school algebra book.
Project 6.3
Find any replacements for x, y, and z such that xn + yn = zn, … See the whole entry
Individual Research Projects Section 6.2
Project 6.1
Write a paper on the relationship between geometric areas and algebraic expressions.
References:
Albert B. Bennett, Jr., “Visual Thinking and Number Relationships,” The Mathematics Teacher, April, 1988.
Robert L. Kimball, “Sharing Teaching Ideas: Using Pattern … See the whole entry
Individual Research Project Section 5.8
Project 5.13
Prepare an exhibit on cryptography. Include devices or charts for writing and deciphering codes, coded messages, and illustrations of famous codes from history. For example, codes are found in literature in Before the Curtain Falls, by J. Rives … See the whole entry
Individual Research Project Section 5.7
Project 5.12
What is a Diophantine equation?
Reference
Warren J. Himmelberger, “Puzzle Problems and Diophantine Equations,” The Mathematics Teacher, February 1973, 136-138, or a more complete reference, see any number theory textbook.… See the whole entry
Individual Research Project Section 5.6
Project 5.11
Symmetries of a Cube
Consider a cube labeled as shown below:
List all the possible symmetries of this cube. See Problem 60, Problem Set 5.6 to help you get started… See the whole entry