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The spiral has polar slope 2ln(ρ)/π, where ρ satisfies ... Nautilus shell and plastic spiral, with ρ the positive root of x^3 = x + 1: Width: 2240: Height: 1680
The chambered nautilus (Nautilus pompilius), also called the pearly nautilus, is the best-known species of nautilus. The shell, when cut away, reveals a lining of lustrous nacre and displays a nearly perfect equiangular spiral, although it is not a golden spiral. The shell exhibits countershading, being light on the bottom and dark on top. This ...
Nautilus half-shell showing the camerae in a logarithmic spiral Section cut of a nautilus shell A nautilus shell viewed from above (left), and from underneath (right) Nautili are the sole living cephalopods whose bony body structure is externalized as a planispiral shell .
For example, in the nautilus, a cephalopod mollusc, each chamber of its shell is an approximate copy of the next one, scaled by a constant factor and arranged in a logarithmic spiral. [51] Given a modern understanding of fractals, a growth spiral can be seen as a special case of self-similarity. [52]
It is sometimes erroneously stated that spiral galaxies and nautilus shells get wider in the pattern of a golden spiral, and hence are related to both φ and the Fibonacci series. [3] In truth, many mollusk shells including nautilus shells exhibit logarithmic spiral growth, but at a variety of angles usually distinctly different from that of ...
Halved shell of Nautilus showing the chambers (camerae) in a logarithmic spiral (1st p. 493 – 2nd p. 748 – Bonner p. 172) Thompson observes that there are many spirals in nature, from the horns of ruminants to the shells of molluscs; other spirals are found among the florets of the sunflower. He notes that the mathematics of these are ...
Cutaway of a nautilus shell showing the chambers arranged in an approximately logarithmic spiral. The plotted spiral (dashed blue curve) is based on growth rate parameter b = 0.1759 {\displaystyle b=0.1759} , resulting in a pitch of arctan b ≈ 10 ∘ {\displaystyle \arctan b\approx 10^{\circ }} .
The aperture is an opening in certain kinds of mollusc shells: it is the main opening of the shell, where the head-foot part of the body of the animal emerges for locomotion, feeding, etc. The term aperture is used for the main opening in gastropod shells, scaphopod shells, and also for Nautilus and ammonite shells.