Seashell surface

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Seashell surface with parametrization on left Seashell Surface.PNG
Seashell surface with parametrization on left
Wheel-like Star Shell Astralium calcar, Diameter 3,5 cm; Originating from the Philippines Astralium calcar 01.JPG
Wheel-like Star Shell Astralium calcar , Diameter 3,5 cm; Originating from the Philippines

In mathematics, a seashell surface is a surface made by a circle which spirals up the z-axis while decreasing its own radius and distance from the z-axis. Not all seashell surfaces describe actual seashells found in nature.

Contents

Parametrization

The following is a parameterization of one seashell surface:

where and \\

Various authors have suggested different models for the shape of shell. David M. Raup proposed a model where there is one magnification for the x-y plane, and another for the x-z plane. Chris Illert [1] proposed a model where the magnification is scalar, and the same for any sense or direction with an equation like

which starts with an initial generating curve and applies a rotation and exponential magnification.

See also

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References

  1. Dr Chris Illert was awarded his Ph.D. on 26 September 2013 at the University of Western Sydney http://www.uws.edu.au/__data/assets/image/0004/547060/2013_ICS_Graduates.jpg. Enquiries about his work can be directed to the University of Wollongong via Michael Organ. http://www.uow.edu.au/~morgan