[Symbiote]

My maths teacher for much of secondary school, who was the "pure maths" teacher when we were old enough for that to be taught separately, started one year with an elaborate 4-colour drawing of a steam locomotive on the whiteboard. There was no explanation or further reference to it in that lesson.

As we learnt trigonometry, he'd sometimes draw just part of the scene, and explain how it related to what we were learning.

I remember the coupling rods: as the locomotive moves, each end traces a sine curve: https://en.wikipedia.org/wiki/Coupling_rod

And also the electric catenary, which has a hyperbolic cosine curve: https://en.wikipedia.org/wiki/Overhead_line

I think there were also the pistons on the steam locomotive, and the curvature of the track.

(Occasionally, it was like the intro to https://vimeo.com/77451201 )