I endeavour to keep this dying blog aloft. It’s not actually dying so much as it’s in a medically induced coma while I recover from the consequences of reproduction. I have been motivated recently by learning that someone has been enjoying reading some of the posts. A professor here where I work, we’ll call him Ben because that’s his name, popped his head into my office to let me know that a friend/associate of his had stumbled across this humble attempt and wondered who I was. In this world made small by the internet it turned out that Ben did indeed know who I was and told me so. It was great to know that something here has been of value. I’ve been putting some time into some more substantial posts on my teaching, philosophy of mathematics and some other errata that hopefully will become posts in the near future. For now, I can’t resist sharing a couple of neat websites I found yesterday.
In calculus 2 when I discuss related rates I like to model the motion of a piston in a 2-stroke engine as example. The up and down motion of the piston is related to the rotation of the crank shaft and deriving the equation for that relationship is a good review of the law of cosines, quadratic formula etc. The resulting equation is not too bad and it’s good for the students to see ‘messy’ functions that require the chain rule that are not simply dreamed up by their instructor. Animated Engines is a website which does what you’d expect. I used their animated 2-stroke engine to prime the students for the drawings and derivations I did thereafter (these engines, if you don’t know, are common in things like chain saws, weed trimmers, lawn mowers, etc)
When you visit Animated Engines they advertise a related site called 507 Mechanical Movements, again, no surprises when you visit. These are mechanisms from an 1868 book by a fellow named Henry T. Brown. Not all the movements have been animated but many have and I wonder if I couldn’t find some uses in my math courses. Take a look at Movement 68
I imagine displaying the animation and asking them to sketch a graph of the motion of the teeth on the red gear perhaps. Not a bad example of a piecewise function. Movement 38 is likewise fascinating.
My last thought for now is that Mechanical Movements would also be a great inspiration for some woodworking projects that result in interactive wall art for the home or office. Someday…when I’m rehabilitated.