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  2. 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.

  3. List of spirals - Wikipedia

    en.wikipedia.org/wiki/List_of_spirals

    Fibonacci spiral: circular arcs connecting the opposite corners of squares in the Fibonacci tiling: approximation of the golden spiral golden spiral = special case of the logarithmic spiral Spiral of Theodorus (also known as Pythagorean spiral) c. 500 BC

  4. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    A Fibonacci prime is a Fibonacci number that is prime. The first few are: [47] 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, ... Fibonacci primes with thousands of digits have been found, but it is not known whether there are infinitely many. [48] F kn is divisible by F n, so, apart from F 4 = 3, any Fibonacci prime must have a prime index.

  5. Golden ratio - Wikipedia

    en.wikipedia.org/wiki/Golden_ratio

    Both the Fibonacci sequence and the sequence of Lucas numbers can be used to generate approximate forms of the golden spiral (which is a special form of a logarithmic spiral) using quarter-circles with radii from these sequences, differing only slightly from the true golden logarithmic spiral. Fibonacci spiral is generally the term used for ...

  6. 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.

  7. Patterns in nature - Wikipedia

    en.wikipedia.org/wiki/Patterns_in_nature

    Phyllotaxis spirals can be generated from Fibonacci ratios: the Fibonacci sequence runs 1, 1, 2, 3, 5, 8, 13... (each subsequent number being the sum of the two preceding ones). For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2.

  8. Golden triangle (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Golden_triangle_(mathematics)

    Golden triangles inscribed in a logarithmic spiral. The golden triangle is used to form some points of a logarithmic spiral. By bisecting one of the base angles, a new point is created that in turn, makes another golden triangle. [4] The bisection process can be continued indefinitely, creating an infinite number of golden triangles.

  9. Spiral - Wikipedia

    en.wikipedia.org/wiki/Spiral

    Spirals which do not fit into this scheme of the first 5 examples: A Cornu spiral has two asymptotic points. The spiral of Theodorus is a polygon. The Fibonacci Spiral consists of a sequence of circle arcs. The involute of a circle looks like an Archimedean, but is not: see Involute#Examples.