Comments on: Unscheduled Post: The Silver Ratio

By: GerritE

GerritE — Thu, 08 Dec 2011 18:03:08 +0000

@Gelada: “This leads to two questions. Firstly (and easily), what is the natural continuation of the sequence that starts Golden Ratio, Silver Ratio?”

Golden Ratio: (1*A+B):A = A:B
Silver Ratio: (2*A+B):A = A:B
´Bronze´ Ratio: (3*A+B):A = A:B
etc….

By: gelada

gelada — Mon, 08 Nov 2010 17:29:03 +0000

Lovely reference. Strangely I used to share an office with Matt Finn, and did not know about this!

By: Joshua Bowman

Joshua Bowman — Mon, 08 Nov 2010 17:21:21 +0000

I learned about the silver ratio in terms of mixing efficiency: it describes the rate of blending extremely viscous fluids (such as taffy or molten glass) using efficiently organized stirring rods. A relatively accessible paper, with lots of pictures, is on the arXiv at http://arxiv.org/abs/1004.0639.

By: El número plateado | Gaussianos

El número plateado | Gaussianos — Mon, 16 Aug 2010 06:02:34 +0000

[...] Algunas interpretaciones geométricas del número plateado. MeneameBitacorasFacebookTwitter [...]

By: gelada

gelada — Thu, 07 Jan 2010 16:10:18 +0000

The Pell numbers are wonderful. If you look carefully they come into the final drawing. They also come directly in the continued fraction expansion in John Cooks original post.

This leads to two questions. Firstly (and easily), what is the natural continuation of the sequence that starts Golden Ratio, Silver Ratio?

Secondly (and I would love to know the answer) why do some of the geometric interpretations (such as the relationship to regular polygons) disappear after the first few terms?

By: Mark Dow

Mark Dow — Thu, 07 Jan 2010 03:10:25 +0000

It’s worth noting that the ratio of sequential values in the Pell numbers, analogous with the Fibonacci sequence:

0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741… (sequence A000129 in OEIS)

approaches the silver ratio. This leads naturally to a nested rectangle interpretation, with these integers as sides. See, for an example and riffs:

http://lcni.uoregon.edu/~mark/Geek_art/Simple_recursive_systems/Tesselations/Pell_spirals/Pell_spirals.html

By: The silver ratio — The Endeavour

The silver ratio — The Endeavour — Wed, 20 May 2009 13:25:52 +0000

[...] interpretation. I don’t know of a geometric interpretation of the silver ratio. (Update: See Maxwell’s Demon for geometric applications of the silver [...]