## 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 GeometrySee 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. SmithSee 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

Videos:
Math in Nature – Fibonacci (time: 3:44)

A short history of Fibonacci, Fibonacci numbers and the golden ratio (time: 10:00)

Phi and the Golden Ratio (time: 4:08)
See the whole entry

Videos:
This is a video discussing polygons (time: 6:35)

Low key introduction to angles (time: 9:55)

Here is a video on angles and parallel lines (time: 6:03)
See the whole entry