Ramble, Part 5: Exhausting!

I mentioned earlier that Eudoxus made two major contributions to mathematics. The first was the theory of proportionality I discussed earlier; the second was a simple observation which led to a procedure, the method of exhaustion, for computing the areas or volumes of regions with curved boundaries. Archimedes used this method extensively, solving such problems as the volume of a sphere and the area of the region lying between a parabola and a chord of the parabola. I discuss these ideas in detail under the cut.

( Take It To The Limit )

Ramble Contents

"Dies the Fire"

I'm currently in the middle of S. M. Stirling's Dies the Fire. I doubt I'll do a full review; it's entertaining enough, but kind of run-of-the-mill - there's not much here that wasn't in Lucifer's Hammer, or in any of a number of similar works. I do want to mention a few things that I've noticed, however.

• It's remarkable how many of the characters here have some kind of personal connection to characters from the Nantucket trilogy. I've seen mentions of John Martin and the Walkers - plainly the family of the warlord William; one of the characters is an Arnstein; and there've been one or two other fainter connections.
• At one point, one of the characters thinks, Home isn't a place. Home is people. Do I need to mention that Stirling was on the Bujold list for a while?
• There is a scene involving a dog looking longingly at a marrowbone while lying, stomach distended, on top of a pile of other bones. Stirling used that same image, memorably, in the third of the Nantucket books.

I'll probably go ahead with the rest of the series, but it doesn't seem to me to be as good as the Nantucket trilogy.