Instructor: Bob Connelly (email@example.com) 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
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
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
4. Show that the Pascal's Theorem implies Desargues' Theorem in any
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
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".