Comments on: The silver ratio http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/ John D. Cook Sun, 19 May 2013 18:03:10 +0000 hourly 1 http://wordpress.org/?v=3.5.1 By: Austin B http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14416 Austin B Thu, 31 Jan 2013 14:49:47 +0000 http://www.johndcook.com/blog/?p=2308#comment-14416 If you create the same continued fraction with 3′s, do you get a “bronze” ratio?

]]> By: Rational approximations to e — The Endeavour http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14415 Rational approximations to e — The Endeavour Wed, 30 Jan 2013 16:17:34 +0000 http://www.johndcook.com/blog/?p=2308#comment-14415 [...] The silver ratio Approximation relating lg, ln, and log10 [...]

]]> By: Rob Bell http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14414 Rob Bell Tue, 19 Apr 2011 04:00:08 +0000 http://www.johndcook.com/blog/?p=2308#comment-14414 I recently drew up a simple geometric derivation of the silver ratio and the corresponding silver rhombus. I came upon this blog entry searching for other references of which there seem to be very few and none for the silver rhombus. The image can be found in my entry about polar zonohedra and the silver ratio.

http://zomadic.blogspot.com/2011/04/pecha-kucha-inspire-japan.html

]]> By: Anton http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14413 Anton Thu, 10 Mar 2011 13:19:24 +0000 http://www.johndcook.com/blog/?p=2308#comment-14413 The Golden Ratio is also the worst case for the Euclidean algorithm.
http://en.wikipedia.org/wiki/Euclidean_algorithm#Algorithmic_efficiency

]]> By: Mats Granvik http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14412 Mats Granvik Wed, 16 Feb 2011 10:40:25 +0000 http://www.johndcook.com/blog/?p=2308#comment-14412 Yesterday I found out that the silver ratio can be found as a limiting ratio of this number sequence: oeis A179807. It begins as the FIbonacci sequence but begins to differ at the 6:th term. 1, 1, 2, 3, 5, 9, 17, 34, 71, 153, 337, 755, 1713, 3925, 9064… Example 9064/3925 tends to the silver ratio, but it doesn’t become apparant until the 250:th term.

]]> By: Recommended readings 6/5/09 « Division by Zero http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14411 Recommended readings 6/5/09 « Division by Zero Sat, 06 Jun 2009 04:02:54 +0000 http://www.johndcook.com/blog/?p=2308#comment-14411 [...] silver ratio ~ two bloggers describe it (I love continued [...]

]]> By: Daniel Black http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14410 Daniel Black Wed, 20 May 2009 23:22:37 +0000 http://www.johndcook.com/blog/?p=2308#comment-14410 At the risk of stating the obvious, this is also the sine or cosine of either acute angle of the right triangle formed by taking the diagonal of the unit square.

]]> By: Unscheduled Post: The Silver Ratio « Maxwell’s Demon http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14409 Unscheduled Post: The Silver Ratio « Maxwell’s Demon Wed, 20 May 2009 12:51:44 +0000 http://www.johndcook.com/blog/?p=2308#comment-14409 [...] Post: The Silver Ratio John Cook on The Endeavour has just mentioned the wonderful silver ratio. As this is probably my favourite number I can’t resist the chance to put up some pictures. [...]

]]> By: Mark Reid http://www.johndcook.com/blog/2009/05/20/the-silver-ratio/comment-page-1/#comment-14408 Mark Reid Wed, 20 May 2009 12:03:10 +0000 http://www.johndcook.com/blog/?p=2308#comment-14408 If you remove the largest possible square from an A4 sheet of paper you get a rectangle with side length in silver ratio proportions since the A4 (and any A family page) has side ratios 1:sqrt{2}.

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