Help sought: Does anyone recognize this series in physical systems?
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From: 7 on 5 Jan 2010 14:41 Help sought: Does anyone recognize this series in physical systems? ------------------------------------------------------------------- Interesting little pattern spotted. 2 x (1) 2 x (2x1, 2x3) 2 x (2x1, 2x5, 2x3) 2 x (2x1, 2x7, 2x5, 2x3) The convention is that the first column doubles what is to the right of the equation: So, expand that out with that convention in mind by doubling each line: (1) (1) (2x1, 2x3) (2x1, 2x3) (2x1, 2x5, 2x3) (2x1, 2x5, 2x3) (2x1, 2x7, 2x5, 2x3) (2x1, 2x7, 2x5, 2x3) Now, multiply out the numbers: 1 1 2, 6 2, 6 2, 10, 6 2, 10, 6 2, 14, 10, 6 2, 14, 10, 6 Now look at the periodic table, and you find the exact numbers of elements in each series in each row of the periodic table!!!! I'm wondering if any maths geniuses out there with some long recollections had spotted the same series as below or a similar looking series in action anywhere else in either a physical system, electronic system or gaming system, or came across it in pure maths. (Any clue or pointer appreciated.) 2 x (1) 2 x (2x1, 2x3) 2 x (2x1, 2x5, 2x3) 2 x (2x1, 2x7, 2x5, 2x3)
From: Ken Pledger on 6 Jan 2010 16:51 In article <HBM0n.22391$Ym4.4929(a)text.news.virginmedia.com>, 7 <website_has_email(a)www.enemygadgets.com> wrote: > .... > Interesting little pattern spotted. > .... > 2, 14, 10, 6 > > Now look at the periodic table, and you find the exact numbers of elements > in each series in each row of the periodic table!!!! > .... You may like to look at the third paragraph of <http://web.jjay.cuny.edu/~acarpi/NSC/4-pertab.htm>. The number of electrons to fill the nth shell is 2(n^2). Putting n = 1, 2, 3, 4 gives the numbers 2, 8, 18, 32, familiar from the periodic table. The electrons filling a sub-shell (s, p, d, f) build up each of those numbers to the next, so there are 2(n^2) - 2((n - 1)^2) = 4n - 2 such electrons. Putting n = 1, 2, 3, 4 gives the numbers 2, 6, 10, 14 which you noticed; so your method seems to be a rather indirect way of finding 4n - 2. Ken Pledger.
From: spudnik on 6 Jan 2010 22:52 also see: http://www.21stcenturysciencetech.com/Articles_2009/Relativistic_Moon.pdf > <http://web.jjay.cuny.edu/~acarpi/NSC/4-pertab.htm>. --l'OEuvre! http://wlym.com
From: 7 on 7 Jan 2010 12:10
Ken Pledger wrote: > In article <HBM0n.22391$Ym4.4929(a)text.news.virginmedia.com>, > 7 <website_has_email(a)www.enemygadgets.com> wrote: > >> .... >> Interesting little pattern spotted. >> .... >> 2, 14, 10, 6 >> >> Now look at the periodic table, and you find the exact numbers of >> elements in each series in each row of the periodic table!!!! >> .... > > > You may like to look at the third paragraph of > > <http://web.jjay.cuny.edu/~acarpi/NSC/4-pertab.htm>. > > The number of electrons to fill the nth shell is 2(n^2). Putting n = > 1, 2, 3, 4 gives the numbers 2, 8, 18, 32, familiar from the periodic > table. The electrons filling a sub-shell (s, p, d, f) build up each of > those numbers to the next, so there are > 2(n^2) - 2((n - 1)^2) = 4n - 2 such electrons. > Putting n = 1, 2, 3, 4 gives the numbers 2, 6, 10, 14 which you > noticed; so your method seems to be a rather indirect way of finding > 4n - 2. > > Ken Pledger. Thank you very much, this was exactly what I was looking for. |