![]() These bi-directional spirals intersect each other, such as: 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, … The numerators or the denominators of this series are recognizable as the Fibonacci sequence. The head of a composite displays definite equiangular spirals running counter-clockwise and clockwise. Family members are distributed worldwide and have a recognizable, “unique disc-shaped inflorescence, composed of numerous pentamerous florets packed on an involucrate head, surrounded by ray florets (petals) on the outside.” The numbers of ray-florets and disc-florets vary from one plant to another, but they all are all “beautiful phyllotactic configurations” due to the arrangement of seeds in the seed head. Compositae (or Asteraceae) is commonly referred to as the aster, daisy, composite, or sunflower family. One of the largest families of the vascular plants, compositae, contains nearly 2000 genera and over 32,000 species (“Plant List”) of flowering plants. Many flowers display figures adorned with numbers of petals that are in the Fibonacci sequence:ġ petal: White Calla Lily 2 petals: Euphorbia 3 petals: Lily, Iris, Euphorbia 5 petals: Buttercup, wild Rose, Larkspur, Columbine (Aquilegia), Hibiscus 8 petals: Delphiniums, Bloodroot 13 petals: Ragwort, Corn Marigold, Cineraria, Black Eyed Susan 21 petals: Aster, Shasta Daisy, Chicory 34 petals: Plantain, Pyrethrum, Daisy 55, 89 petals: Michaelmas Daisies, the Asteraceae family (Sinha Akhtaruzzaman and Shafie) Spanish poet Salvador Rueda (1857-1933) eloquently said, “las flores son matematicas bellas, compass, armonia callada, ritmo mudo,” (flowers are a beautiful mathematics, compass, silent harmony, mute rhythm) (Spooner 38). Besides symmetrical number and arrangement of parts or petals, plants often illustrate the Fibonacci sequence in their seed sections or in the spirals that are formed as new parts and branches grow. Higher in the plant kingdom, many flowers exhibit Fibonacci-number petal symmetry, including fruit blossoms, water lilies, brier-roses and all the genus rosa, honeysuckle, carnations, geraniums, primroses, marsh-mallows, campanula, and passionflowers. ![]() For example, pentagonal symmetry (five parts around a central axis, 72° apart) is quite common in the natural world, particularly among the more “primitive” phyla, such as the water net ( Hydrodictyaceae Hydrodictyon), a green algae (“Live”). Structural symmetry is one of the simplest ways an organism will demonstrate this fascinating phenomenon (Livio 115). Nevertheless, mathematical principles do appear to govern the development of many patterns and structures in nature, and as time passes, more and more scientific research finds evidence that the Fibonacci numbers and the Golden Ratio are prevalent in natural objects, from the microscopic structure proportions in the bodies of living beings on Earth to the relationships of gravitational forces and distances between bodies in the universe (Akhtaruzzaman and Shafie).Īs it relates to the development and structure of a plant, it is not uncommon to find representations of the Fibonacci numbers or the Golden Ratio. Debate remains as to whether or not humans naturally prefer Golden Ratio (1.61803…) proportions in the organization and structural symmetry of art, music or nature, and some even deny that the Golden Ratio is as ubiquitous in nature as others proclaim. “Empirical investigations of the aesthetic properties of the Golden Section date back to the very origins of scientific psychology itself, the first studies being conducted by Fechner in the 1860s” (Green 937). ![]() ![]() The Fibonacci sequence of numbers forms the best whole number approximations to the Golden Proportion, which, some say, is most aesthetically beautiful to humans. (Previous Section: Disputation of Fibonacci in Art.) Buy Now on Amazon All citations are catalogued on the Citations page. This is an excerpt from Master Fibonacci: The Man Who Changed Math. ![]()
0 Comments
Leave a Reply. |