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  2. Golden rectangle - Wikipedia

    en.wikipedia.org/wiki/Golden_rectangle

    In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or ⁠:, ⁠ with ⁠ ⁠ approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.

  3. 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 ...

  4. Golden spiral - Wikipedia

    en.wikipedia.org/wiki/Golden_spiral

    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 ...

  5. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers , commonly denoted F n .

  6. Fibonacci numbers in popular culture - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_numbers_in...

    In The Phantom Tollbooth (1970), Milo (Butch Patrick) is given a set of numbers to identify in order to gain entry to the "Numbers Mine", and correctly answers noting that it is the Fibonacci sequence. Along with the golden rectangle and golden spiral, the Fibonacci sequence is mentioned in Darren Aronofsky's independent film Pi (1998). They ...

  7. Generalizations of Fibonacci numbers - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of...

    A Fibonacci sequence of order n is an integer sequence in which each sequence element is the sum of the previous elements (with the exception of the first elements in the sequence). The usual Fibonacci numbers are a Fibonacci sequence of order 2.

  8. List of works designed with the golden ratio - Wikipedia

    en.wikipedia.org/wiki/List_of_works_designed...

    It is claimed that the upper level of 21 rows and the lower level of 34 rows of the Ancient Theatre of Epidaurus form an approximation of the Golden number since 21 and 34 are successive Fibonacci numbers with their ratio at / and a careful examination of the theatre's center reveals two back-to-back triangles balanced by the Golden number.

  9. 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.