Moebius pendant — intriguing mathematical jewelry
Designed and hand-assembled by Joe Marasco




The Moebius strip is named after August Ferdinand Moebius, a German mathematician and theoretical astronomer who discovered this geometric phenomenon in 1858. What is this strange construction? Here is the simplest demonstration of how a twist in a surface can create a three-dimensional object with only a two-dimensional surface:

The object above was made from a strip of paper and tape. Take the two ends of the strip and bring them together, giving one end a single twist, then tape them together like closing a belt that has a kink in it.

"If its full length were crawled by an ant, the ant would return to its starting point having traversed both sides of the paper without ever crossing an edge." — Wikipedia
Even stranger shapes result if this loop is cut in half lengthwise. See Joe Marasco's instructive leaflet of experiments you can try, starting with the Moebius figure above. The mathematics we can learn from it is almost like magic, or transformational art.

For many people, mathematics and art are inseparable. The difference is that mathematics requires notation, while art needs no artifice to reveal its beauty. The similarity is that once one's palate is attuned to either preference, sophistication follows from experience. This piece evokes the joy of seeing and feeling a human-scale physical manifestation of a purely mathematical object, taking the abstract into the real world. And embedded in a piece of jewelry, it is a joy to wear.

In the Moebius pendant, the colored beads ride in a track which is a Moebius surface. The track is continuous and in three dimensions, closing back upon itself. The beads can thus slide through the looped channel without end or beginning. Its holding fixture was made by 3D printing. Handle gently when playing with it. Instructions for use are included.

These pendants are offered exclusively by Kadon Enterprises, Inc., on this website and at art shows where we exhibit our puzzles and games. The chain is included. A Moebius pendant makes an exquisite gift as well, delivered in a velvet pouch. Recommended for careful teens to adults. $65

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