Friday, October 10, 2003; Noon-1pm Sc N207
Speaker:
John de Pillis, Professor of Mathematics, University of California, Riverside
How Graphics Illuminate Deep Ideas of Mathematics
Illustrations can be ornamental (e.g., the occasional cartoon panel in a calculus text) or they can be essential to the understanding of an idea. We will show how illustrations and graphics illuminate ideas of:
- SPECIAL RELATIVITY: specifically, the following three paradoxes will be discussed:.
(a) The twin paradox: Time travel into the future.
(b) The Train-in-the-Tunnel paradox: What happened to simultaneity?
(c) The pea-shooter paradox: why velocities do not add "correctly."
- AXIOM of CHOICE (AC):
It has been said (e.g., in a review by Lester Dubins in the MAA Monthly in the 1950's) that Alfred
Tarski thought the Axiom of Choice was rubbish. He therefore developed the Banach-Tarski paradox to
prove that ridiculous results can arise using this "rubbish." We present a weak form of B-T where a full
proof is accessible.
- MONTY HALL PROBLEM
There is a long history of the best strategy to use on "Let's Make a Deal." A contestant must choose one
of three doors, one of which hides a valuable prize. The odds of winning are1 in 3. Now Monty Hall, the
MC, opens an empty remaining door. (The odds of winning are 1 in 2!) Should the contestant switch
to the remaining door? Does it matter? Hear Monty Hall's response to a mathematician who, in the
1970's, showed that if you always switch, your odds of winning grow to 2 out of 3!
- WAVE PROPAGATION
How can a graphic show why the speed of a propagated wave in a rope does not change its when you
add more energy to the rope (increase the wave's frequency)?
Please join us beforehand for pizza.