TRM intern Alvaro Gonzalez Hernandez and his dog Txoki explain the maths behind involutes - the curve formed when a dog unwraps its lead from around a tree trunk.

Involutes have been studied throughout history, most notably by Christian Huygens when trying to construct an accurate clock using a pendulum. They are also found in gear systems where the shape of the gears follows that of a circular involute to reduce friction and increase torque.

Calculation of the parametric form of the circular involute by Dr Tom Crawford.

Produced by TRM intern Alvaro Gonzalez Hernandez with assistance from Dr Tom Crawford. Alvaro is a fourth year mathematics undergraduate at the University of Oxford.

Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: https://www.conted.ox.ac.uk/

For more maths content check out Tom's website https://tomrocksmaths.com/

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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With thanks to
Alvaro Gonzalez Hernandez
Txoki
Oxford University Micro-Internship Scheme
Science Museum London
Vysotsky (Wikipedia)
Rob Koopman
Ag2gaeh (Wikipedia)
Sam Derbyshire
Stephan Heiss