How to turn a circle inside out (Visual Calculus and the Tractrix)

The shape that a dog walks in when pulled by its owner shows up in more places than you might think. This video explores a curve called the tractrix and introduces visual calculus, a method for calculating integrals without any calculations.

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0:00 Dog on a leash, intro
1:23 Deriving the tractrix
3:17 Visual calculus
6:01 Area between bike tracks
8:04 Conclusion

Yo-yo on the ISS:    • International Toys in Space: Yo-Yo  
Proof of Tractrix Equation: https://proofwiki.org/wiki/Equation_o...
Mamikon's Visual Calculus: https://www.its.caltech.edu/~mamikon/...
Gaussian curvature of the pseudosphere: Manfredo P. do Carmo, "Differential Geometry of Curves and Surfaces", p.168-169
Great video on bike tracks:    • A Curious Track, or What Bikes Are Hi...