Seashells: the plainness and beauty of their mathematical description

Examples: Cephalopods

Chambered Nautilus (helmet shape, [2, p. 248])

[alpha=80, beta=90, phi=0, mu=0, Omega=0, A=2, a=2, b=1.5, L=0]

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In old times, cephalopoda (class that includes octopus, cuttlefish, spirula, squid and nautilus) were one of the most numerous class of invertebrates of the sea; now, only some species survive, mainly in the seas of the Indo-Pacific region. The nautilus is a thin and light shell coiled in flat spiral. The interior has chambers serving as buoyancy tanks allowing the animal to change depth (they migrate vast distances up and down daily). It dwells deep along the steep slopes of Pacific Ocean coral reefs to avoid predators active above during the day. But at night it slowly rises, adjusting gas pressure in its chambers. Once it reaches its preferred depth, it pursues crustaceans using rapid jet propulsion, swimming as its powerful muscles expel water previously taken in.
Habitat: free swimming, Indo-Pacific waters mainly.

[2] S. Peter Dance, Shells, Dorling Kindersley, 2002.

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