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!
Thoughts En Route 
I actually understand most of that. 😀 But that one diagram really is worth a thousand words. I LOVE conic sections! 😀
Sorry Mr. Smith, but from an artist’s point of view, for a second or two I thought you had misspelled “comic sections”….:D
And on another topic altogether, Tabitha’s baby girl was born last night…..Annie Makenzie, 18” long and 6#11oz…..another cause for celebrations! 😀
How wonderful for them! Please pass on our congratulations! 🙂
Circles I know. Ellipses I know. I’m even acquainted with the wonders of the Parabola. But of what use is the hyperbola?
Much! 🙂 They are very often not as familiar to most, but they are a wonderful part of nature. You’ve probably seen them before in geometrical “strong art” where the two adjacent sides of a square are adorned with straight pieces of string, far point form the corner on one side tied to the point close to the corner on the other, progressing along the sides. Also, if you’ve ever shined a flashlight straight down a hall and been standing close enough to the wall so that the wall intersects the cone of light from the flashlight, the outline of that light on the wall is a hyperbola. In bigger views, the hyperbola is the local curve of planetary flybys, such as the Voyager 1 & 2 spacecrafts performed in their grand “tours” of the solar system, in which they used each planet’s gravity to “slingshot” them to the next planet. Those paths around each planet–getting closer and closer, faster and faster, until being slung around by the planet’s gravity in a new direction–were hyperbolas. A hyperbola could almost be considered an “origin-&-destination-minded parabola”–not the best description in a lot of ways, to be sure, but illustrative in others. A search around the Internet or a tour of Wikipedia’s related entries might be helpful. Thanks for stopping by!
All of this makes my head hurt…