Ideas for a Math 4520 Project
Spring 2010
Tuesday, Thursday in Malott 224
2:55 to 4:10 PM

Instructor: Bob Connelly (connelly@math.cornell.edu)
Office: 433 Malott
Office hours: Tuesday, Thursday 10 - 11 AM in 433 Malott.

Last updated:   February 4
, 2010

There are a lot of materials that are available in the Math Library in Malott Hall, and you can look through them to get ideas.   You can see the list here if you put in the course number, etc.   Please come to see me before you start to work.

1.   Copy and scan some of the drawings in some of the art books, or others you can find, paste it into a drawing program such as Geometer's Sketchpad and use the algorithms in this course to calculate the viewing distance, center of vision, etc.  How tall was the artist?  

2. Read the book by David Hockney that claims that many of the great artists in the past used mechanical devises to enhance their drawings.  Do some calculations, as in Item 1, here, to see if you agree or disagree with his thesis.

3.  Take a picture of the cables of the suspension bridge over Fall Creek and use the method described in class to show that the nodes lie on a parabola.

4.  Show that the Pascal's Theorem implies Desargues' Theorem in any projective plane.

5.  Show that Desargues' property for any projective plane implies that there is a field (or a skew field) that can be used for coordinates.

6.  Make your best guess of a model of Brunelleschi's device that he used to convince people of the principles of perspective drawing.

7. Show how any Euclidean construction with compass and straightedge can be done with a compass alone.  

8.  Show how any Euclidean construction with compass and straightedge can be done with an arc of a circle in the plane, where the center of the circle is given, but it cannot be done if the center is not given.

9.  Prove Descarte's Theorem that shows the relation between four mutually tangent circles in the plane, show how this can be used to construct Appolonean circle packings.

10. Analyse and discuss the "impossible pictures" of the Penroses and Escher, in particular with respect to perspective.

11.  Make your own drawing in the spirit of Hogarth's satire of mistakes in perspective.  See how many mistakes you can put in one drawing.

12. Discuss Grunbaum's criticism of the inaccuracies of the Math Accosication's dodecahedron logo. It is available here.

13.  Do some historical sluthing to find evidence for or against Decartes being influenced or inspired by artists' techniques of using grids to make perspective drawings.  In particular, did Decartes see Durer's painting in perspective of an artist using a grid to paint in perspective?

14.  Explain the connection of the indefinite metric on 3-space and hyperbolic space and their connection to special relativity.

15.  Discuss and explain the Peaucellier mechanism and how it relates to inversion, how it relates to Watt's mechanism and give an account of the history with respect to Phillip Davis's book "The Thread".