Follow That Bike!

The direction a bicycle has traveled can be determined by examining its tracks and thinking about tangent lines, geometric constraints and the bike's steering mechanism
bike diagram

Simons Foundation Mathematical Impressions

From Simons Science News (find original story here).

A nice mathematical puzzle, with a solution anyone can understand, is to determine the direction a bicycle went when you come upon its tracks. The answer involves thinking about tangent lines, geometric constraints and the bicycle’s steering mechanism. Once you learn the trick, you’ll find yourself using it every time you happen upon a bike trail.

The question goes back to the early days of the bicycle age and a 1903 Sherlock Holmes story by Sir Arthur Conan Doyle called “The Adventure of the Priory School.” Surprisingly, Holmes did not analyze the tangents as we do in the video and his reasoning in the story was incorrect. A geometric approach to the question was included in a 1990s “Geometry and the Imagination” course that John Conway, Peter Doyle, Jane Gilman and William Thurston taught at Princeton and the Geometry Center at the University of Minnesota. Holmes’ error is discussed in the book “Which Way Did the Bicycle Go?” by Joseph D. E. Konhauser, Dan Velleman and Stan Wagon.



More videos from the Mathematical Impressions series.

Reprinted with permission from Simons Science News, an editorially-independent division of whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the computational, physical and life sciences.

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