Math puzzle: Bicycle, string and a rubber ducky

In this day of slickly science and math videos from the likes of John and Hank Green, it’s kind of refreshing to see an old school math demonstration that gets the facts across.

Bicycle string puzzle

Today, the Simons Foundation Mathematical Impressions blog features a mental puzzle involving a bicycle and a piece of string. If you pull backwards on a bicycle pedal with a string, will the Cannondale Super V 900 mountain bike roll forward? Or backward?

The answer turns on the behavior of the trochoid formed by the motion of the pedal as it moves forward in space with the bike. You can read the discussion, look up the references and view the original video here. I swiped the mp4 and uploaded to YouTube for better streaming, also, if that’s your preference.

James Harris Simons founded the Paul Simons Foundation to advance math and science research and education in the United States. Jim Simons is a genius research mathematician who left academia and entered the business world in 1978 to become a zillionaire by managing other people’s money in financial markets. The Foundation is named for his late son Paul, who lost his life at age 34 while riding his bicycle after he was hit by a car.

One Comment

  1. Does this bike not have a freewheel? On the great side, however, it explains the shape I got when I taped sparklers on my bike wheel and photographed my riding with in the dark with a 30 second exposure. It looked just like the middle example. Still confused about how the bike goes backwards.I think my cranks would turn and the bike wouldn’t move.

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