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The golden perfection of the aortic valve

Published:December 14, 2015DOI:https://doi.org/10.1016/j.ijcard.2015.12.018
      The ratio a + b/a = a/b = 1.618 was defined the ‘golden section’ in the 19th century but was definitely known to Euclid as mean and extreme ratio [
      • Pasipoularides A.
      Historical continuity in the methodology of modern medical science: Leonardo leads the way.
      ,
      • Livio M.
      The Golden Ratio: The Story of phi, the World's Most Astonishing Number.
      ]. During the 13th century, the genial mathematician Leonardo Bonacci, better known as Fibonacci, described in the Liber Abaci his famous sequence, in which the ratio of every consecutive number approximates the value of 1.618 [
      • Ashrafian H.
      • Athanasiou T.
      Fibonacci series and coronary anatomy.
      ]. From this sequence it is possible to generate a spiral that is inscribed in a rectangle made of squares with the sides obtained from the same sequence (Fig. 1a ). The Fibonacci spiral with its sequence is a structure that is worldwide present: sunflowers, pinecones, shells, stars, phyllotaxis of leaves and geometric figures such as the regular hexagon and pentagon that can be cut into squares and smaller rectangles and triangles with the same aspect ratio [
      • Weib G.
      Golden hexagons.
      ].
      Figure thumbnail gr1
      Fig. 1‘The golden perfection of the aortic valve’.
      The ‘golden hexagon’ is a set of six points, which is projectively equivalent to the vertices of a regular pentagon together with its center
      [
      • Weib G.
      Golden hexagons.
      ]
      .
      A Fibonacci spiral is composed of quarter-circle arcs inscribed in squares of integer Fibonacci-number side, shown for square sizes 1, 1, 2, 3, 5, 8 (a).
      The figure shows the fascinating symmetry of the aortic valve that ultimately can be represented by six Fibonacci spirals inscribed in regular hexagon that includes golden pentagons, squares, rectangles and triangles with the same aspect ratio of 1.618 (m).

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      References

        • Pasipoularides A.
        Historical continuity in the methodology of modern medical science: Leonardo leads the way.
        Int. J. Cardiol. 2014; 171: 103-115
        • Livio M.
        The Golden Ratio: The Story of phi, the World's Most Astonishing Number.
        Broadway Books, 2002
        • Ashrafian H.
        • Athanasiou T.
        Fibonacci series and coronary anatomy.
        Heart Lung Circ. 2011; 20: 483-484
        • Weib G.
        Golden hexagons.
        J. Geom. Graph. 2002; 6: 167-182