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  2. List of spirals - Wikipedia

    en.wikipedia.org/wiki/List_of_spirals

    logarithmic spiral (also known as equiangular spiral) 1638 [4] = Approximations of this are found in nature Fibonacci spiral: circular arcs connecting the opposite corners of squares in the Fibonacci tiling: approximation of the golden spiral golden spiral

  3. Golden spiral - Wikipedia

    en.wikipedia.org/wiki/Golden_spiral

    Golden spirals are self-similar. The shape is infinitely repeated when magnified. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. [1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.

  4. Patterns in nature - Wikipedia

    en.wikipedia.org/wiki/Patterns_in_nature

    For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2. In hazel the ratio is 1/3; in apricot it is 2/5; in pear it is 3/8; in almond it is 5/13. [56] Animal behaviour can yield spirals; for example, acorn worms leave spiral fecal trails on the sea floor. [57]

  5. Logarithmic spiral - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_spiral

    The golden spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every 90 degrees of rotation (pitch angle about 17.03239 degrees). It can be approximated by a "Fibonacci spiral", made of a sequence of quarter circles with radii proportional to Fibonacci numbers.

  6. Phyllotaxis - Wikipedia

    en.wikipedia.org/wiki/Phyllotaxis

    Examples can be found in composite flowers and seed heads. The most famous example is the sunflower head. This phyllotactic pattern creates an optical effect of criss-crossing spirals. In the botanical literature, these designs are described by the number of counter-clockwise spirals and the number of clockwise spirals.

  7. Chambered nautilus - Wikipedia

    en.wikipedia.org/wiki/Chambered_nautilus

    The chambered nautilus is often used as an example of the golden spiral. While nautiluses show logarithmic spirals, their ratios range from about 1.24 to 1.43, with an average ratio of about 1.33 to 1. The golden spiral's ratio is 1.618. This is visible when the cut nautilus is inspected. [13]

  8. Category:Spirals - Wikipedia

    en.wikipedia.org/wiki/Category:Spirals

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  9. Golden ratio - Wikipedia

    en.wikipedia.org/wiki/Golden_ratio

    The golden spiral (red) and its approximation by quarter-circles (green), with overlaps shown in yellow A logarithmic spiral whose radius grows by the golden ratio per 108° of turn, surrounding nested golden isosceles triangles. This is a different spiral from the golden spiral, which grows by the golden ratio per 90° of turn. [58]