Talk:Plastic number

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Is there a source for golden ratio being the origin of the name? Septentrionalis 05:14, 1 December 2006 (UTC)

Why is it called the "plastic" constant/number ? Fathead99 (talk) 17:17, 12 February 2008 (UTC)

I've added some more on this. —David Eppstein (talk) 18:00, 12 February 2008 (UTC)

[edit] Solution to the other equations

How was it discovered that the Plastic Number is also a solution to all those other equations? —The preceding unsigned comment was added by Vjasper (talk • contribs) 23:04, 8 January 2007 (UTC).

Most of them are the result of multiplying the original equation through by another polynomial and then simplifying; doing this as often as necessary.

For example, multiplying by x2,

x^5 = x^3 + x^2 = x^2 + x + 1\;

This one can also be gotten by multiplication by x2 - 1. Some of them are wrong; and they are all questionable as bordering on OR. Septentrionalis PMAnderson 23:28, 8 January 2007 (UTC)

Ummm .. I agree they are not all particularly interesting, but none of them are actually wrong - they can all be easily derived from x3=x+1, as follows:
(1)\ x^3 = x + 1\
(2)\ x^5 = x^3 + x^2\mbox{ from (1)}
(3)\ \Rightarrow x^5 = x^2 + x + 1\mbox{ from (1) and (2)}
(4)\ x^4 = x^2 + x\mbox{ from (1)}
(5)\ \Rightarrow x^5 = x^4 + 1\mbox{ from (3) and (4)}
(6)\ x^6 = x^4 + x^3\mbox{ from (1)}
(7)\ \Rightarrow x^6 = x^4 + x + 1\mbox{ from (1) and (6)}
(8)\ \Rightarrow x^6 = x^2 + 2x + 1\mbox{ from (4) and (7)}
(9)\ x^7 = x^5 + x^4\mbox{ from (1)}
(10)\ x^4 = x^5 - 1\mbox{ from (5)}
(11)\ \Rightarrow x^7 = 2x^5 - 1\mbox{ from (9) and (10)}
(12)\ x^8 = x^6 + x^5\mbox{ from (1)}
(13)\ \Rightarrow x^8 = x^4 + x^3 + x^2 + x + 1\mbox{ from (3), (6) and (12)}
(14)\ x^9 = x^7 + x^6\mbox{ from (1)}
(15)\ x^7 = x^4 + x^3 + x^2\mbox{ from (3)}
(16)\ \Rightarrow x^9 = x^6 + x^4 + x^2 + x + 1\mbox{ from (1), (14) and (15)}
(17)\ x^{12} = 2x^{10} - x^5\mbox{ from (11)}
(18)\ \Rightarrow x^{12} = 2x^{10} - x^4 - 1\mbox{ from (5) and (17)}
(19)\ x^{14} = x^{10} + 2x^9 + x^8\mbox{ from (8)}
(20)\ x^{10} = x^9 + x^5\mbox{ from (5)}
(21)\ x^{10} = x^9 + x^4 + 1\mbox{ from (5) and (20)}
(22)\ x^{14} = 3x^9 + x^8 + x^4 + 1\mbox{ from (19) and (21)}
(23)\ x^9 = x^8 + x^4\mbox{ from (5)}
(24)\ \Rightarrow x^{14} = 4x^9 + 1\mbox{ from (22) and (23)}
Not saying these derivations need to appear in the article - just saying that all these relations are mathematically correct. Gandalf61 10:54, 9 January 2007 (UTC)
Very clever. Thanks for the explanation. Vjasper 01:38, 11 January 2007 (UTC)

[edit] Request to review edit by 165.234.104.24, 27 March 07

Could someone knowledgable in this subject please review the edit made by 165.234.104.24 on 27 March? This IP address has made a considerable number of vandalism edits on other articles, and I am reluctant to allow this edit to stand. -- Arwel (talk) 19:55, 10 April 2007 (UTC)

Looks ok to me. The new polynomial listed as having the plastic number as a root, x^7-2x^4-1, equals (x^3-x-1)(x^4+x^2-x-1), where the desired root occurs due to the left factor. —David Eppstein 20:38, 10 April 2007 (UTC)
OK, thanks. -- Arwel (talk) 21:45, 10 April 2007 (UTC)