- Research Experiences for Undergraduates (REU)
For over four decades, the Department of Mathematics at Indiana University has offered experiences in mathematics research to students from all over the country. During the summer, a select group of undergraduates participates in research projects with individual faculty mentors on a wide variety of topics. The National Science Foundation has supported our program most years through Research Experiences for Undergraduates (REU) grants.
For information about our program see: IU Math REU
- Mathematics Alumni NewsletterThe Department of Mathematics publishes an annual newsletter about the goings on in the department for alumni and friends of the department. See: Alumni Newsletter
- American Mathematics Competition ExamsThe Department of Mathematics hosts the American Competition Exams (AMC). The AMC 8 takes place in November and is typically taken by children in grades 6-8. The AMC 10/12 takes place in February. There are two exams: the AMC 10 for high school students in grades 10 and below and the AMC 12 for students in grades 11 and 12. The reward if you do well is the invitation to take another exam, the AIME!
- Bloomington Math CircleThe Department of Mathematics runs the Bloomington Math Circle for area school children who enjoy mathematics. The program covers fun mathematics topics not typically taught in elementary and middle schools. The Circle runs one day a week for about an hour for 9 weeks each semester. Sample topics from the past include symbolic logic, modular arithmetic, regular polyhedra, inequalities, the fourth dimension, approximating square roots, and different sizes of infinity.
- Science Fest
The Department of Mathematics participates in ScienceFest, the annual day of hands-on educational science fun at Indiana University Bloomington. For more information, see:
- Departmental T-Shirts
To purchase a shirt, stop by Rawles Hall 115 or download and print the order form: Purchasing a shirt
INFORMATION ABOUT THE DESIGN
Four Dragon Curves Cover the Plane
The four colored dragon curves begin in the middle and represent paths between integer points on the plane. Here is an explanation of how the red figure works. The first 2 steps are east, north (EN). To get the first 4 steps, we take EN, write it backwards to get NE, and then rotate counterclockwise to get WN. We put WN after the first two steps (EN) to get ENWN, and this is the first 4 steps on the red dragon. Similarly, the first 8 steps will be
The other colors work the same way, but with different starting directions. What you see are the first 512 steps for each color, with all corners rounded a bit.
The four dragon curves never cross themselves or each other. Evern more surprising: when extended forever, the dragon curves would pass through every integer segment in the plane exactly once.
The infinite sequences of directions are examples of automatic sequences; the name “automatic” comes from “automaton”, a computational device with finitely many states but no memory. The nth term in the each dragon sequence is the output of an automaton whose input is the binary expansion of n. Automatic sequences have connections to continued fractions, number theory, formal language theory, and physics.
Most sources credit the discovery of the dragon curve to John Heighway, a physicist at NASA.
The paper that proves its properties is Chandler Davis and Donald Knuth, ”Number representations and dragon curves”, J. Recreational Math 3 (1970) 61–81 and 133-149.
It was popularized in one of Martin Gardner’s columns from Scientific American and reproduced in his book Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, 1978.
Finally, the main reference on automatic sequences is the book with that name by Jean-Paul Allouche and Jeffrey Shallit, published by Cambridge University Press in 2003.- Larry Moss