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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 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 ...
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 ...
The nautilus shell presents one of the finest natural examples of a logarithmic spiral, although it is not a golden spiral. The use of nautilus shells in art and literature is covered at nautilus shell .
Cutaway of a nautilus shell showing the chambers arranged in an approximately logarithmic spiral In mathematics , a spiral is a curve which emanates from a point, moving further away as it revolves around the point.
This shell has nine whorls. A whorl is a single, complete 360° revolution or turn in the spiral or whorled growth of a mollusc shell. A spiral configuration of the shell is found in numerous gastropods, but it is also found in shelled cephalopods including Nautilus, Spirula and the large extinct subclass of cephalopods known as the ammonites.
Spirals are common in plants and in some animals, notably molluscs. 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]
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 ...
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