Fibonacci Numbers




In plant kingdom, there happens to be a conspicuous display of fibonacci numbers through arrangement of leaves, florets & petals in many plants. The term is called phyllotaxis .The manifestation of Fibonacci numbers and patterns arise out of the dynamics of plant growth and not out of any innate love to conform to a math formula.A list of some common flowers is mentioned below petals of which belong to a number of fibonacci series--

Whitecalla Lily :                                                    1 petal

Lily, Iris, Trillium :                                                3 petals

Columbines, Buttercups, Larkspur, Wildrose :   5 petals

Delphinium, Bloodroot, Cosmos :                        8 petals

Corn marigolds,Ragwort :                                  13 petals

Asters,Shasta Daisy,Chicory :                           21 petals

Daisies :                                                              34,55,89 petals

Most pineapples have 5, 8, 13,21 spirals of increasing steepness on their surface. Buds placed along a spiral and separated by divergence angle of 137.5 ° which is the golden angle are packed most efficiently along the spiral with no multiplicity on any radial line. In a growing plant & flower,the new primoridia ( cells that mature to leaves and flowers ) spring up in the least crowded spot along the growing tip of the plant which is called meristem & then move radially out at a rate proportional to stem or petals' growth. Hotmeister's Rule states that 2nd primoridium is placed as far from 1st and 3rd the same distance from 2nd in a manner no overlapping takes place as the number increases. The divergence angle progressively converges to golden angle.The spiral is known as the Fibonacci Spiral. Pineapple scales are also patterned into same type of spirals.Divergence angle being golden angle allows each leaf to be closest to the leaf below it in the previous whorl and farthest from the youngest previous leaf above it. In other words, the arrangement facilitates receipt of maximum sunlight and passage of rain or dew drops down to the roots.

Leonardo Da Vinci's famous painting MonaLisa's face is drawn on a golden rectangle.

Primoridia arrangement in circle, click