Today, I had the chance to introduce Boy #1 to the glory of the conic sections. And there was much rejoicing. Well, now he’s stuck solving systems of equations with one nonlinear equation, so there may not be too much rejoicing, but I’m rejoicing. 🙂
And as is fitting when discussing conic sections, orbits of planetary bodies was discussed, as were hypothetical situations where comets pass the sun in pure, infinite, two-body systems, versus the messier world we actually have in which there is more stuff and a quantum-ly limited world in which Planck-scale distances potentially fuzz the prettiness of asymptotically approaching but never reaching a line over infinity. It was sweet.
So, here’s to you, today, Apollonius! And here’s a quote from Apollonius that I would have loved to include in the recent mathematics-themed “Works of His Hands” article, but which, in the end, was a bit too far afield. He said in his treatise on conic sections back in the 3rd Century BC, like the pure mathematician he was, that although he was doing work that would be helpful in certain applications, “the subject is one of those which seem worthy of study for their own sake.” Looking forward to seeing you in the second resurrection, Apollonius!