Logarithmic spiralA logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie"). More than a century later, the curve was discussed by Descartes (1638), and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous spiral".
PhyllotaxisIn botany, phyllotaxis () or phyllotaxy is the arrangement of leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature. The basic arrangements of leaves on a stem are opposite and alternate (also known as spiral). Leaves may also be whorled if several leaves arise, or appear to arise, from the same level (at the same node) on a stem. With an opposite leaf arrangement, two leaves arise from the stem at the same level (at the same node), on opposite sides of the stem.
SpiralIn mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. It is a subtype of whorled patterns, a broad group that also includes concentric objects. Two major definitions of "spiral" in the American Heritage Dictionary are: a curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point. a three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis; a helix.
Patterns in naturePatterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
Common sunflowerThe common sunflower (Helianthus annuus) is a species of large annual forb of the genus Helianthus. It is commonly grown as a crop for its edible oily seeds. Apart from cooking oil production, it is also used as livestock forage (as a meal or a silage plant), as bird food, in some industrial applications, and as an ornamental in domestic gardens. Wild H. annuus is a widely branched annual plant with many flower heads. The domestic sunflower, however, often possesses only a single large inflorescence (flower head) atop an unbranched stem.
Fibonacci sequenceIn mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
Golden ratioIn mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , where the Greek letter phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names.
