Talk:Metallic mean

Mathematics Start‑class Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-priority on the project's priority scale.

This article was nominated for deletion on 16 October 2014 (UTC). The result of the discussion was keep.

Lead too long?

I know that the lead is only two paragraphs, but they're somewhat long, and the article only has one content section, so maybe some of the content in the lead should be moved to the article's body. Care to differ or discuss with me? The N^th User 02:36, 28 August 2018 (UTC)[reply]

Powers of the Metallic Means and the Pascal Triangle

In equations describing the powers of the metallic means each term in the chain has a numerical coefficient and is also raised to a power of 10. It turns out that the particular coefficients are identical to terms in a (2,1)-sided generalized Pascal Triangle. In the classical Pascal Triangle terms along so-called shallow diagonals sum to give Fibonacci numbers. The same types of terms along shallow diagonals in the (2,1)-sided Pascal Triangle sum on one side to give Lucas numbers rather than Fibonacci, and Fibonacci numbers on the other (though upshifted one move). The shallow diagonal terms leading to Lucas numbers here in the (2,1) system are identical to the numerical coefficients in the terms of the equations describing the powers of the metallic means. Furthermore, in the classical Pascal Triangle the usually discussed side-parallel diagonals are associated with dimensional values. The outer 1's are 0-D, the natural numbers are 1-D, the triangulars 2-D, the tetrahedrals 3-D and so on. Equivalent dimensional labels apply to the side-parallel diagonals in the (2,1)-sided generalized Pascal Triangle as well. Interestingly, the dimensional labels belonging to the side-parallel diagonals that each numerical coefficient terms are found in are identical to the powers that each term is raised to in the equations describing the powers of the Metallic Means. 2601:89:C600:E521:6500:3D92:ABF6:9690 (talk) 21:50, 9 April 2019 (UTC)[reply]

How do you have a metallic mean between 2 numbers!?

the article states that the golden ratio is the metallic mean of 1 and 2, but both the continued fraction and the formula only have one input, n. where does this other number come from?

You've misquoted. The article says that the golden ratio is the metallic mean BETWEEN 1 and 2, not OF 1 and 2. So there is no problem. 2601:89:C701:9190:9089:70B3:33A7:F85D (talk) 17:26, 17 August 2021 (UTC)[reply]