Leon P Smith on Nostr: nprofile1q…targs nprofile1q…lxf95 The Stern-Brocot tree is suprisingly simple! ...
nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqzdp33shl69xr0uq3x8n5gsjykq9upycwh6nqm02c3f6x0frrn0dqftargs (nprofile…args) nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqmjjwe95dghhw434k4vsvxs5yl6gcr6kupghf5u0dgcvhga0w94sq9lxf95 (nprofile…xf95) The Stern-Brocot tree is suprisingly simple! One way of looking at it is that it "undoes" the gcf function.
So if you start with an "ideal" ratio that you want your gears to have, then you can use the Stern-Brocot tree to find fractions that are good approximations of the ratio you are seeking. This is approximately what Achille Brocot himself developed the Stern-Brocot tree to do; he was a partner at a small clockmaking firm in Paris, and used the Stern-Brocot tree to help select gear ratios in some of their mechanical clock movements.
So there's gotta be a hundred different ways to build off of this lesson and dip your students toes in some very interesting mathematics, from modular arithmetic and number theory to who knows what all else.
https://www.cs.ox.ac.uk/people/jeremy.gibbons/publications/rationals.pdf
So if you start with an "ideal" ratio that you want your gears to have, then you can use the Stern-Brocot tree to find fractions that are good approximations of the ratio you are seeking. This is approximately what Achille Brocot himself developed the Stern-Brocot tree to do; he was a partner at a small clockmaking firm in Paris, and used the Stern-Brocot tree to help select gear ratios in some of their mechanical clock movements.
So there's gotta be a hundred different ways to build off of this lesson and dip your students toes in some very interesting mathematics, from modular arithmetic and number theory to who knows what all else.
https://www.cs.ox.ac.uk/people/jeremy.gibbons/publications/rationals.pdf