Imagine Magazine - Johns Hopkins - March/April 2011 - (Page 20)

by Amy Dusto When you think of science fairs, projects in biology, chemistry, or physics might come to mind. But top prizes at prestigious national and international science fairs often go to math projects, which explore topics ranging from theoretical to applied mathematics. Following are snapshots of ﬁve research projects that focused on mathematical topics or used innovative mathematical analyses—and earned accolades at competitions including the Intel Science Talent Search and the Siemens Competition in Math, Science, and Technology. Whether they studied stars or spheres, cells or games, the student researchers behind these projects all discovered the capacity of mathematics to shed new light on scientiﬁc topics. “High Dimensional Sphere Packing” KATHERINE RUDOLPH , NAPERVILLE , IL rAtION INtEL COrPO Anyone who’s packed a cooler realizes that organizing soda cans in tight rows and columns is the most eﬃcient way to fit them in. Similarly, packing spheres in two dimensions (where they are just circles) or in three dimensions also works best when they are highly organized. But in other high dimensions, scientists have encountered a puzzle: sometimes a random packing of spheres is tighter than any organized lattice. Kate Rudolph worked on this problem at the Research Science Institute, where the paper she produced was named one of the top five out of more than seventy. Why does it matter how spheres pack in high dimensions? Even though we live in a 3D world, says Rudolph, it is only in some higher dimensions that problems such as glass-making can be explained. Glass makers usually begin by melting silica, otherwise known as beach sand, into a liquid state. When the liquid silica cools into glass, it has the strong molecular bonds of a solid but the randomly ordered molecules of a liquid, which is what makes it transparent. “If you think of molecules as tiny little spheres, the glass transition is just their moving from an ordered packing to a random packing,” Rudolph explains. Her project also has applications in information security: computer scientists use the concept of eﬃcient sphere packing to detect and correct errors in codes used to store and compress information. Determining the most eﬃcient way to space data signals without overlapping them turns out to be a geometry problem analogous to sphere packing. So when mathematicians find good solutions to sphere-packing problems, computer scientists can use them too—and vice versa. A finalist in the 2010 Intel Science Talent Search, Rudolph ultimately came in 8th place, winning $20,000. She says the coolest thing about her project is that it’s so accessible. During her public presentation at the Intel Science Talent Search, she explained the sphere packing problem to everyone “from math professors to seven-yearolds,” letting spectators try their hand at packing a bowl of brightly colored spheres in two and three dimensions. Rudolph now attends MIT, where she is majoring in mathematics. Mar/Apr 2011

Table of Contents for the Digital Edition of Imagine Magazine - Johns Hopkins - March/April 2011

Imagine Magazine - Johns Hopkins - March/April 2011
Contents
Big Picture
In My Own Words
Problem Solving
Orange County Math Circle
Number Theory
Count Me In
National Mathematics Competitions
Math at the Science Fair
Just My Speed
MathPath
When Origami Meets Rocket Science
Selected Opportunities & Resources
Making a Difference
High School Options for Gifted Students
Off the Shelf
Word Wise
Exploring Career Options
One Step Ahead
Planning Ahead for College
Students Review
Mark Your Calendar
Knossos Games

Imagine Magazine - Johns Hopkins - March/April 2011