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The Gathering, also referred to as G4Gn (n denoting the number in the series), is a biennial conference that started with G4G1 in 1993. At each Gathering, there are lectures, performance art, puzzle and book displays, close-up and stage magic acts, and guided sculpture building. Traditionally, each conference has a Gift Exchange in which attendees swap puzzles, magic tricks, artwork, mathematical papers, novelty items, books, etc.The following items were exchange gifts from several different Gatherings.Pyrolytic Graphics Levitator by Anthony RizzoA puzzle: Orient the magnets to levitate the pyrolytic graphite. Demonstrates diamagnetism. Magnets are extremely strong and have safety precautions. The Twiddle Bolts from Tim Udall In “My Best Mathematical and Logic Puzzles,” Gardner presented the puzzle of “The Twiddle Bolts.” If you hold two bolts by their heads, engage their threads, as shown, then rotate the bolts around each other while maintaining contact, what happens? Do the bolt heads get closer together, farther apart or stay the same distance apart? Think it through before trying it out. Now, extending the puzzle: If you screw the bolts into the provided “double nut,” one from each side, and repeat the experiment, what happens? Do the bolt heads repeat their behavior from above? What happens to the double nut? Does it move or stay put? Make a prediction, then try it out.Benham’s Top from Kenneth Brecher Spin clockwise, then counterclockwise. Enjoy the colors. Spidron Magnets by Daniel ErdelyThere are magnets of a mathematical structure called the “Spidron.” This structure was discovered by Daniel Erdely of Hungary, a student of Dr. Rubik. He won a gold medal for the “Genius Europe” award in 2004. To learn more about Spidrons, visit www.spidron.hu.Hinge-a-Tron by George Hart It’s a variation on the classic rotating ring of tetrahedra (which goes back at least to W. W. Rouse Ball’s 1939 book Mathematical Recreations and Essays). Although it is made from solid plywood, the parts flex and it is fun to rotate it around and around into itself. This version is made of six laser-cut plywood pieces. The living hinge can easily bend back on itself as shown below, but be careful not to stretch or twist the pieces, as they will snap. see georgehart.com/hinge-a-tron.

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