Much of this issue is about the center of mass, including Julia Zimmerman’s cover drawing which features a mobile fantasy. In Math In Your World, we cover the basics involved in ensuring that a mobile will balance properly. You could use this knowledge to get your pet hamster to lift your car. In Center of Mass, we explain the “piecemeal” property of the center of mass: that you can compute the center of mass part by part. This property forms the basis of the problem solving technique known as “mass points.”
To understand the center of mass and torque, it helps to learn about vectors. So Robert Donley, a.k.a. Math Doctor Bob, introduces vectors in his second installment of Learn by Doing. If you work through the problems in his column, you’ll learn about vector addition, scalar multiplication, and the dot and cross products. Because Bob wanted to lay the groundwork for understanding physical vectors such as force and torque, he confined himself to discussing vectors over the real numbers.
In our interview, meet University of Michigan Professor of Mathematics Karen Smith. Prof. Smith discusses a wide range of topics, including math that interests her, how she goes about solving math problems, and how she got into math. Her route to math is rather exceptional in that after graduating from Princeton with a Bachelor’s degree, she taught in the school system before going to math graduate school. She is a recent Clay Scholar and she contributed an autobiographical essay to the book Complexities: Women In Mathematics, edited by Bettye Anne Case & Anne M. Leggett. In this interview, she even describes an unsolved problem which middle school students could begin to explore.
“You” helps 3/7 find a nifty solution to a curious dilemma in Coach Barb’s Corner…involving fractions, of course!
Finally, if you like dissection problems, see if you can find a nice way to tile a regular hexagon into pieces that can be rearranged to form an equilateral triangle. Henri, a student at the Buckingham, Browne, and Nichols middle school in Cambridge, was presented with just this challenge, and we exhibit his beautiful solution inside. This problem is an instance of the Wallace-Bolyai-Gerwien theorem which says that any polygon can be dissected into parts that can be rearranged to form any other polygon of the same area. Even though there is a general construction to create such tilings, there’s still the challenge of finding nice ones, and Henri’s is quite elegant.
We hope you enjoy it!
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