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A Fibonacci spiral approximates the golden spiral using quarter-circle arcs inscribed in squares derived from the Fibonacci sequence. A golden spiral with initial radius 1 is the locus of points of polar coordinates ( r , θ ) {\displaystyle (r,\theta )} satisfying r = φ 2 θ / π , {\displaystyle r=\varphi ^{2\theta /\pi },} where φ ...
Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae [1] and, as such, form part of the Hubble sequence. Most spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as the bulge.
In mathematics, the Fibonacci sequence is a sequence in which each term is the sum of the two terms that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers , commonly denoted F n .
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.
The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. [3] The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, ... .
Messier 81 (also known as NGC 3031 or Bode's Galaxy) is a grand design spiral galaxy about 12 million light-years away in the constellation Ursa Major. It has a D 25 isophotal diameter of 29.44 kiloparsecs (96,000 light-years ).
A spiral galaxy is a type of galaxy characterized by a central bulge of old Population II stars surrounded by a rotating disc of younger Population I stars. A spiral galaxy maintains its spiral arms due to density wave theory .
Subsequent studies (using the Hubble Space Telescope) show that the bulges of many galaxies are not devoid of dust, but rather show a varied and complex structure. [3] This structure often looks similar to a spiral galaxy, but is much smaller. Giant spiral galaxies are typically 2–100 times the size of those spirals that exist in bulges.