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Nipponites Mirabilis—A challenge to seashell theory?

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Il Nuovo Cimento D


Our earlier foundation paper for the new science ofTheoretical Conchology presented a general theoryexplaining seashell growth trajectories in terms of optimal, energy-efficient, tensile «clockspring» curves satisfying Hamilton's «least-action» principle. Meanwhile, working in isolation and publishing in Japanese, after the tradition of Wasan, Takashi Okamoto presented precise measurements and uncannily accurate 3D curveguesses which provide a finedescription of several bizarre, and previously little understood, «free-coiling» heteromorphic ammonites. One of these,Nipponites mirabilis, is so bizarre and wild that it provides the first good test of our new general theory. We are able to demonstrate that, merely by choosing the two fundamental constants of differential geometry to be complex numbers, our standard «clockspring” curves adequatelydescribe andexplain these geometries though one small improvement is possible. Even more surprising, considering the sheer wildness of the geometries, is the fact that Okamoto's guessed 3D «spheroidal» shapes agree with our correct, more general, «Lissajous» counterparts to several significant figures … a remarkable feat of precise measurement and intuition, on Okamoto's part, perhaps in its own way comparable to the achievements of Tycho Brahae and Johannes Keppler.

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Illert, C. Nipponites Mirabilis—A challenge to seashell theory?. Il Nuovo Cimento D 12, 1405–1421 (1990).

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PACS 87.10

PACS 46.30.Cn