Re: [math-fun] Apostol's Riemann song for your iPod
I'm quite excited after all these years to be able to solve a problem which is at least related to mathematics. The tune to which Apostol wrote the Riemannian lyrics is "Sweet Betsy from Pike" "Oh do you remember sweet Betsy from Pike, Crossed the wide border with her lover Ike With a [something] and [something etc......] Tweedle dum da daa di [something, with necessary number of syllables] Next Question? dg At 07:13 PM 8/1/2006, you wrote:
Henry,
Thanks for the link
< http://olimu.com/Riemann/Song.htm >
to John Derbyshire singing Tom Apostol's song, "Where are the Zeroes of Zeta(s) ?" Quite a nice little ditty.
The tune was so familiar, but I couldn't place it at first.
SO: Trivia question: What familiar old song uses the same tune?
--Dan
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Fifteen verses may found at http://www.ndsu.nodak.edu/instruct/isern/103/betsy.htm However, the tune is originally English and known as "Villikins / Villikens and his Dinah" On 8/2/06, David Gale <gale@math.berkeley.edu> wrote:
I'm quite excited after all these years to be able to solve a problem which is at least related to mathematics.
The tune to which Apostol wrote the Riemannian lyrics is "Sweet Betsy from Pike"
"Oh do you remember sweet Betsy from Pike,
Crossed the wide border with her lover Ike
With a [something] and [something etc......]
Tweedle dum da daa di [something, with necessary number of syllables]
Next Question?
dg
At 07:13 PM 8/1/2006, you wrote:
Henry,
Thanks for the link
< http://olimu.com/Riemann/Song.htm >
to John Derbyshire singing Tom Apostol's song, "Where are the Zeroes of Zeta(s) ?" Quite a nice little ditty.
The tune was so familiar, but I couldn't place it at first.
SO: Trivia question: What familiar old song uses the same tune?
--Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Suppose that one has four nonnegative integers in a row, A B C D. Create a subsequent row by abs(A-B) abs(B-C) abs(C-D) abs(D-A). Repeating this process will eventually produce 0 0 0 0, the end state. The object is to create a "long" chain of rows ending in 0 0 0 0. I can "backup" chains to create arbitrarily long chains, but the process seems a bit unwieldy. Is there any formulaic way of specifying an initial row that will produce a chain of length n? Bill C.
Let a(n) be the maximum number of steps required to reach 0 0 0 0 with starting values between 0 and n-1, includng at least one 0 and one n-1. Rather suprisingly, this sequence is not monotonic. It starts: 0,4,4,6,7,6,7,7,7,8,7,9,8,10,8,9,9,8,9,10,9,9,10,9,10,10,10,9,10,9,10,11, 10, 10,10,10,10,12,11,10,10,10,11,10,13,11,10,10,10,11,12,11,11,11,12,11,11, 11,11,11,11,12,11,12,13,11,11,12,12,11,11,12,11,11,12,13,12,11,12,11 This sequence is not in the OEIS, although its running maximums are A065677. The record-setting foursomes up to 600 are: 0 0 0 0 1 0 0 0 3 1 0 0 4 2 1 0 9 4 1 0 11 5 2 0 13 6 2 0 31 14 5 0 37 17 6 0 44 20 7 0 105 48 17 0 125 57 20 0 149 68 24 0 355 162 57 0 423 193 68 0 504 230 81 0 These are all unique, up to the obvious symmetries: rotation and reversal, plus complement (subtract each term from n-1). The maximums in this sequence are A045794, essentially the same as A065678. The second and third values are in A034803 and A034804. See those sequences for formulas; these are related to the tribonacci numbers. Franklin T. Adams-Watters -----Original Message----- From: Cordwell, William R <wrcordw@sandia.gov> Suppose that one has four nonnegative integers in a row, A B C D. Create a subsequent row by abs(A-B) abs(B-C) abs(C-D) abs(D-A). Repeating this process will eventually produce 0 0 0 0, the end state. The object is to create a "long" chain of rows ending in 0 0 0 0. I can "backup" chains to create arbitrarily long chains, but the process seems a bit unwieldy. Is there any formulaic way of specifying an initial row that will produce a chain of length n? Bill C.
participants (4)
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Cordwell, William R -
David Gale -
franktaw＠netscape.net -
Fred lunnon