of interest to educational math geeks

[jrtom]

(Yes, I mean you, hypgnosis--as if there were any doubt. And probably amnesiadust, too.)

+plus magazine

Plus is an internet magazine published five times a year which aims to introduce readers to the beauty and the practical applications of mathematics. Whether you want to know how to build a sundial, how to keep your messages safe or what shape the universe is, it's all here.

(No, I'm not getting paid by these folks, I just think it looks interesting.)

Comments

fascinating, Captain

[amnesiadust.livejournal.com]

hm. When I hear "Hamiltonian" I immediately think of quantum mechanics, so I guess that wasn't necessarily the best lead-in... but what does it mean in graph theory? Different Hamilton I assume.

Re: fascinating, Captain

[jrtom.livejournal.com]

Actually, same Hamilton (http://scienceworld.wolfram.com/biography/HamiltonWilliamRowan.html) (although it's not obvious from that bio, oddly enough, although I got there from the Wolfram article on Hamiltonian circuits (http://mathworld.wolfram.com/HamiltonianCircuit.html)).

Basically, a Hamiltonian path is a graph traversal that visits each vertex exactly once; a Hamiltonian circuit is a H. path that ends up at the vertex that it started at. (Not to be confused with an Eulerian circuit, which passes over each edge exactly once.) The problem of finding a Hamiltonian circuit in a graph is more commonly known as the Travelling Salesman Problem, one of the more well-known NP-hard graph theory problems.

minor oops

[jrtom.livejournal.com]

(I should have said, for H. path: "visits each vertex exactly once, and passes over each edge no more than once".)

Re: minor oops

[(Anonymous)]

Dude. Is it possible to have a path that visits each vertex once but visits some edge more than once?

Re: minor oops

[jrtom.livejournal.com]

I emphasized the wrong aspect, apparently. What I meant to emphasize is that a Hamiltonian path need not visit every edge (unlike an Euler tour, in which each edge must be traversed). You are, of course, correct in suggesting that you can't have a path that visits each vertex once but some edge > once.

"I've got egg on my face from both sides now..."

Re: fascinating, Captain

[hypgnosis.livejournal.com]

This is fascinating.

1) I already knew the basic Hamilton bridge-carving story. This is not a surprise; when I was an undergraduate, my senior honors thesis for the math dept. involved quaternions.

2) I switched my major from physics to math just before I would have really started in on quantum-mechanical Hamiltonians, but I heard about them anyway (from my old high-school friend verin_the_brown, who was at the time majoring in physics at the U. of Chicago). Because of (1), I already knew it was the same Hamilton.

3) Despite (1) & (2) above, amnesia_dust, I also at first had a reaction to your initial comment similar to that of jrtom: "Oh, ha ha, I keep my whiskey in Klein bottles, ha ha" except that I assumed that the magazine was the source of the tomfoolery rather than you. Then once I read the article, I thought, "Ohhhh, that's right . . . "

And, let me just say it again, Mathworld rocks!

Re: fascinating, Captain

[(Anonymous)]

About #2, my experience in physics at my University (which is basically your University time shifted by a year or so)was that the undergrads never really learn analytical mechanics, and by extension never really learn what a "Hamiltonian" actually is in connexion with Quantum Mechanics. So it's likely you could have gone a bit further and still not had this particular meme burrow into your skull and lay its many eggs.

(I go back and forth over the years between believing this omission has seriously damaged my understanding of Physics and believing it has actually helped)