Math Chat: Shifting River Beds And Earthquakes

Old challenge (Robert Kimble)

Can you name three US states that all meet at three different points?

Answer

Mike Bevan proves that this cannot happen unless one of the states is disconnected. Mike Tupper writes, "I figured the Mississippi River had to be involved in such a ridiculous thing occurring. And sure enough, that's where I found it. The [north-south] border between Tennessee and Kentucky [follows] a straight line," with Missouri to the west on the other side of the river. James Fahs continues, "The Mississippi takes a sharp turn, called the New Madrid Bend," crossing the Tennessee-Kentucky border three times. Tupper adds, "A little piece of Kentucky gets completely separated from the rest, causing there to be three distinct points shared by these three states."

John Connolly reports that the river's path was changed by the New Madrid earthquakes in 1811 and 1812, which were among the most violent ever to hit the US. According to a description of "On Shaky Ground," by Norma Hayes Bagnall, on the University of Missouri Press home page (www.system.missouri.edu/upress), "Vibrations were felt from the Rocky Mountains to the Atlantic coast and from Mexico to Canada.... Five towns in three states disappeared, [new lakes appeared], and the river flowed backward for a brief period."

(Correct answers also by Joe Conrad, Neil Gleickman, Bill Hasek, Don Holcomb, Michael Jackson, and Jeff Sander.)

Wallpaper patterns

Wallpaper patterns are featured in a popular geometry course for the mathematically timid at Tufts University, in Medford, Mass. Prof. Martin Guterman, who teaches the course, thinks that society sends out a false message that math is too hard for most of us.

There are 17 mathematical types of wallpaper patterns! Such patterns or symmetries turn up in important ways throughout mathematics and physics. For example, the latest physical theories analyze structures such as black holes via small-scale supersymmetries in an 11-dimensional model of the universe, in which the extra dimensions occur on a scale too small for us to observe.

New space station challenge

The new space station will be only about 6 percent farther from the center of the earth than the earth's surface. Therefore gravity should be just about 12 percent less than on the earth's surface (by Newton's inverse square law of gravity, if you like). Then why will the astronauts appear weightless?

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