Comments on: Why Seashells Are So Alluring? http://www.inspirationbit.com/why-seashells-are-so-alluring/ Knowledge comes from inspiration - one bit at a time Wed, 20 Aug 2008 23:59:12 +0000 http://wordpress.org/?v=2.5 By: Clement Falbo http://www.inspirationbit.com/why-seashells-are-so-alluring/#comment-4661 Clement Falbo Mon, 09 Jul 2007 19:23:19 +0000 http://inspirationbit.com/why-seashells-are-so-alluring/#comment-4661 Well, the spirals found in sea shells are often approximated by a logarithmic spiral. In genral, however, these spirals do not fit into a rectangle with the golden ratio proportions. (1.618.. to 1). They usually fit into rectangles whose proportions range from about 1.08 to 1 for the "olive" shells to about 1.33 to 1 for the nautilus. The Fibonacci Sequence is a special case of a quadratic recursion equation. x(n+2)= p x(n+1)+q x(n). p and q can be any positive numbers. In Fibonacci, we use p=1,q=1. The golden ratio is the limit of x(n+1)/x(n), as n increases indefinitely. In the genral series, that limit is phi(p,q) = (p+Sqrt(p^2+4q))/2. These numbers phi(p,q) provide general versions of every "magical" and "divine" poperty you can ascribe to phi. Well, the spirals found in sea shells are often approximated by a logarithmic spiral. In genral, however, these spirals do not fit into a rectangle with the golden ratio proportions. (1.618.. to 1). They usually fit into rectangles whose proportions range from about 1.08 to 1 for the “olive” shells to about 1.33 to 1 for the nautilus. The Fibonacci Sequence is a special case of a quadratic recursion equation. x(n+2)= p x(n+1)+q x(n). p and q can be any positive numbers. In Fibonacci, we use p=1,q=1. The golden ratio is the limit of x(n+1)/x(n), as n increases indefinitely. In the genral series, that limit is phi(p,q) = (p+Sqrt(p^2+4q))/2. These numbers phi(p,q) provide general versions of every “magical” and “divine” poperty you can ascribe to phi.

]]> By: Vivien http://www.inspirationbit.com/why-seashells-are-so-alluring/#comment-1985 Vivien Mon, 07 May 2007 19:03:39 +0000 http://inspirationbit.com/why-seashells-are-so-alluring/#comment-1985 hmm... thank you for a very interesting comment. As you can see I've based this post on a couple of other related articles/sites on the Web. Does it mean that those sites talk nonsense as well? I think, I did define the Fibonacci series correctly as well as the Golden mean number. In your opinion, what would've been the right way to explain the nature of shells? hmm… thank you for a very interesting comment.
As you can see I’ve based this post on a couple of other related articles/sites on the Web. Does it mean that those sites talk nonsense as well? I think, I did define the Fibonacci series correctly as well as the Golden mean number.

In your opinion, what would’ve been the right way to explain the nature of shells?

]]> By: Clement Falbo http://www.inspirationbit.com/why-seashells-are-so-alluring/#comment-1984 Clement Falbo Mon, 07 May 2007 18:36:39 +0000 http://inspirationbit.com/why-seashells-are-so-alluring/#comment-1984 Of course, almost everything you have written about sea shells and the golden ratio is nonesense; especially with regard to the Nautilus. Every other so-called "devine" property of the golden ratio and of Fibonacci numbers are simple results of a quadratic equation and there exists an uncountable infinity of such "devine proportions" and "extreme means." (Look up Uncountable infinity). There also happens to be countably infinitely many odd polygons that exhibit the "devine" property that a - b= 1/a, where a is a longest diagonal and b is a second longest diagonal. Belief in the divinity of the golden ratio requires one to be a polytheist. Of course, almost everything you have written about sea shells and the golden ratio is nonesense; especially with regard to the Nautilus.
Every other so-called “devine” property of the golden ratio and of Fibonacci numbers are simple results of a quadratic equation and there exists an uncountable infinity of such “devine proportions” and “extreme means.” (Look up Uncountable infinity). There also happens to be countably infinitely many odd polygons that exhibit the “devine” property that a - b= 1/a, where a is a longest diagonal and b is a second longest diagonal. Belief in the divinity of the golden ratio requires one to be a polytheist.

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