Can Dogs Do Math?

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: www.conted.ox.ac.uk/
For more maths content check out Tom's website tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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Get your Tom Rocks Maths merchandise here:
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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

[@TomRocksMaths]

The dogs name is Txoki :)

[@JalebJay]

I thought you were going to mention the mathematician Timothy Pennings who has done talks about his dog finding the fastest route to try and collect his ball when thrown into beach water given 0 resistance while on land, and a slower pace when jumping into water. The idea of calculus through trial and error was a fun thing to hear talks about.

[@isobar5857]

I've read or heard a similar scenario where by a dog on a beach will retrieve a stick thrown into the water by doing it in a way that 'minimises' energy, not the by the fastest time. Strange, if it's true, that the dog is aware of the 'calculus of variations,'

[@easondu9236]

Tom I’ve applied to study undergraduate maths at Oxford! Won’t apply without ur vid

[@Qermaq]

Cats can do math, but they can't be bothered to.

[@hansduran9462]

New look?

[@david.hilbert1234]

I think...🤔 Everything we see around us is governed by one single mathematical equation

[@user-cs8ei5ph1o]

Lonely eagle 14

[@user-vx7rt8rq4g]

Fast boy 72

[@fulla1]

You're doing a video about dogs and curves and leave out "pursuit curves" (which at least in German are called "dog curves")?! One variation is described as follows: You stand at (0,0) and your dog (on a leash of length 1) is positioned at a tree at (0,1). You are moving along the x-axis and pull on the leash as the dog is not willing to follow. The dog will describe a curve called "tractrix" (= the "dog curve").