Talk:Seashell surface

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These equations are wrong. There needs to be an exponential or other scale factor to take into account biological growth. There is a well established theory of seashell mathematics by Chris Illert.

Yes there is a question as to whether this article is intended to be a biologically accurate or just a mathematical curiosity. The Spiral page is somewhat bettern it at least refers to D’Arcy Wentworth Thompson's On Growth and Form. --Salix alba (talk) 11:08, 22 December 2007 (UTC)

it's not about actual seashells.Loud neighbors (talk) 04:03, 1 May 2008 (UTC)

Comment by Illert

The following was added by User:Chris Illert in this edit [1]

The equations for shell surface shape given above, as three separate equations are wrong and do not result in true to life shell surface shapes. The computer generated shell surface shown in the figure on the right is not true to life. Regarding the equation for seashell growth, one common mistake is to assume that there is one magnification for the x-y plane, and another for the x-z plane. This is wrong. It is known as the "Raupian" error, named after the late palaeontologist David Raup, working around the years 1970-2000. A whole school of palaeontologists believed it for decades and suppressed anything contrary. One could not write anything contrary and have it published anywhere. You were expected to write a spiral as three separate equations, as follows $x(\theta ,\varphi )=......,y(\theta ,\varphi )=.....,z(\theta ,\varphi )=.....$, for example, but actually these equations can represent anything, not just a spiral.

The equation given below, from Illert, results in true to life seashell surface. Actually, the magnification is scalar, and the same for any sense or direction. It is the same for the z, or the x, or the y axis. The same generally. $F\left({\theta ,\varphi }\right)=e^{\alpha \varphi }\left({\begin{array}{*{20}c}{\cos \left(\varphi \right),}&{-\sin(\varphi ),}&{\rm {0}}\\{\sin(\varphi ),}&{\cos \left(\varphi \right),}&0\\{0,}&{\rm {0,}}&1\\\end{array}}\right)F\left({\theta ,0}\right)$ Where a verbal description is: shell surface(vector) = scalar magnification x rotation matrix x generating curve(vector).

Thus when you look at Illert's equation, above, for the shell surface you see actual different levels of scale; you see one scalar part (the magnification), times a matrix (rotation), times an initial vector (the equation of the shell aperture). Wow. This is the correction to the "Raupian" error. Raup's equation doesn't see the above effect. Others make this error too, for regular conispiral shells. Of course there are some abhorrent second order spirals, and they are a different story. But for first, and most second order, surfaces the Illert's equation, above, is exactly correct. (References C .Illert)

This clearly needs some work to clear up to fit wikipaedia style. There are also questions of WP:OR as the user name matches the referenced author and many of the cites in the article.--Salix alba (talk): 08:53, 18 August 2014 (UTC)