Someone privately requested the definition of "nome". Not to be confused with the garden pest ( http://alyssadolls.homestead.com/potterica.html http://www.angelfire.com/stars2/harrypotterland/degnome.html http://membres.lycos.fr/justpotter/studies4.html http://www.geocities.com/hogwarts_29/ww/2/2c.html http://meisetsu.topcities.com/enchantments/beasts2.html http://neocortex.by.ru/index/d1.html#Degnoming) a nome is merely a crude approximation to a pole, as in the Alaskan city whose famed beauty pageant annually crowns "Miss Nomer." It can also refer to the little dot on the bottom of a fruit opposite the stem, as in nome de plum, (in deference to Asian- Americans, no longer called "berry button.") Finally, of course, there is the dyslexic animated fish. Hmm. The guy with the funny cigarette is no longer upwind, so let's try again. For what might seem an unmotivated web of definitions, see http://mathworld.wolfram.com/Nome.html . In summary, "nome" is merely the name for the second argument of a theta function, and is usually denoted by q. This is the same q as the "base" in "basic-" or q-hypergeometric series, so they both could have been called "nome" or "base". In fact, q is just a parameter, i.e., it tends to remain fixed, undefined, or even implicit for a given application of theta functions. E.g., the tumbling of an asteroid can be described with quotients of theta functions wherein the first argument is proportional to time, while the nome remains fixed. See, e.g., www.emis.de/proceedings/7ICDGA/VI/puta.ps . No, that's the name of the author, not a piece of asteroid. So why didn't they call it "parameter" instead of "base" or "nome"? Because "parameter" was already usurped to mean two other things: modulus^2 in the case of theta, and (incompatibly) a constituent of a series coefficient in the hypergeometric case. Finally, do not be discouraged that there are four theta functions. They are just four translates of the same function, like sine vs cosine. But unlike sine and cosine, thetas almost never appear alone, but rather paired in quotients. It is as if you never needed sine, just tangent and cotangent. --rwg
Just a couple of comments on Bill's message which is given below. One very interesting and important thing which can be done with theta functions is to use a modular transformation, so there are times when q changes in a way I won't try to type while on vacation. The other thing is that there are a lot of times when a theta function appears alone, but more in the combinatorial side of basic hypergeometric functions. Dick askey@math.wisc.edu
For what might seem an unmotivated web of definitions, see http://mathworld.wolfram.com/Nome.html . In summary, "nome" is merely the name for the second argument of a theta function, and is usually denoted by q. This is the same q as the "base" in "basic-" or q-hypergeometric series, so they both could have been called "nome" or "base". In fact, q is just a parameter, i.e., it tends to remain fixed, undefined, or even implicit for a given application of theta functions. E.g., the tumbling of an asteroid can be described with quotients of theta functions wherein the first argument is proportional to time, while the nome remains fixed. See, e.g., www.emis.de/proceedings/7ICDGA/VI/puta.ps . No, that's the name of the author, not a piece of asteroid.
So why didn't they call it "parameter" instead of "base" or "nome"? Because "parameter" was already usurped to mean two other things: modulus^2 in the case of theta, and (incompatibly) a constituent of a series coefficient in the hypergeometric case.
Finally, do not be discouraged that there are four theta functions. They are just four translates of the same function, like sine vs cosine. But unlike sine and cosine, thetas almost never appear alone, but rather paired in quotients. It is as if you never needed sine, just tangent and cotangent.
--rwg
I was curious about how 800 different triangle centers moved around as the underlying triangle changed, so I generated lots of pictures. You can see them at http://www.mathpuzzle.com/TriCent/TriangleCenter.html . On my front page, I've added links to Kimberling's page, Weisstein's page, and a list of 2000 centers compiled by Edward Brisse. --Ed Pegg Jr, http://www.mathpuzzle.com
participants (3)
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askey＠math.wisc.edu -
Ed Pegg Jr -
R. William Gosper