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
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
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
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
Videos:
This is a whimsical video on Lobachevski (time 3:08)
This is a nice introduction to elliptical and hyperbolic geometry (time: 8:33)
Restful video of math in art (time: 3:16)
Interesting video on the proportions of the human face (time: … See the whole entry
The Golden Ratio is discussed at this site:
http://www.geom.uiuc.edu/~demo5337/s97b/art.htm
The Golden Section in Nature is discussed at this site:
https://www.goldennumber.net/nature/
There are many sites that discuss the relationship between math and art (that is between perspective and projective geometry). You … See the whole entry
A discussion some of the historical proofs of the Pythagorean theorem are listed.
http://www.cut-the-knot.org/pythagoras/index.shtml
These sites provide some information about the Great Pyramid.
http://discoveringegypt.com/pyramids-temples-of-egypt/pyramids-of-giza/