Descartes, a famous mathematician who founded the coordinate method, listed the equation x3+y3-3axy = 0 according to the characteristics of a bunch of petals and leaf curves he studied. This is the famous "Cartesian Leaf Line" (or "Leaf Line") in modern mathematics, and mathematicians have also given it a poetic name-Jasmine Petal Curve.
Later, scientists found that the number of petals, sepals, fruits and other characteristics of plants are very consistent with a strange series-the famous Fibonacci series: 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89 .. Among them, from
The arrangement of sunflower seeds is a typical mathematical model. If you look closely at the sunflower disk, you will find two groups of spirals, one winding clockwise and the other winding counterclockwise, which are embedded in each other. Although the number of seeds in clockwise and counterclockwise directions and spirals of different sunflower varieties is different, it often does not exceed three groups of numbers: 34 and 55, 55 and 89 or 89 and 144. Each set of numbers is two adjacent numbers in Fibonacci series. The first number is the number of wires wound clockwise, and the last number is the number of wires wound counterclockwise.
Daisy's disk has a similar mathematical model, but the number is slightly smaller. Diamond scales on pineapple fruit. Line by line, 8 lines are inclined to the left, and 13 lines are inclined to the right. The cone of Norwegian spruce has three rows of scales in one direction and five rows of scales in the other direction. Larix gmelinii is a coniferous tree, and the scales on its pine cones are arranged in five rows and eight rows respectively in two directions, while those of American pine are arranged in three rows and five rows respectively in two directions. ...
If it is heredity that determines the number of petals of flowers and scales of pinecones, then why is Fibonacci series so coincidental? This is also the result of long-term adaptation and evolution of natural plants. Because the mathematical characteristics of plants are the inevitable result of plant growth in the dynamic process, they are strictly constrained by mathematical laws. In other words, plants can't live without Fibonacci sequence, just as the crystal of salt must have the shape of a cube. As the value in this series is getting bigger and bigger, the quotient of two adjacent numbers is getting closer to the value of 0.6 18034. For example, 34/55 = 0.6 182, close to it, the exact limit of this ratio is "golden number".
In mathematics, there is another numerical value called golden angle, which is 137.5, which is the opening angle of the golden section of a circle. A more accurate numerical value should be 137.50776. Like the golden number, Jinjiao is also favored by plants.
Plantago is a common grass, and the angle between its whorls is exactly 137.5. Leaves arranged at this angle can be well inlaid together without overlapping each other. This is the arrangement mode with the largest illumination area of plants, and each leaf can get sunlight to the maximum extent, thus effectively improving the efficiency of plant photosynthesis. Referring to the mathematical model of banana leaf arrangement, the architect designed a novel spiral high-rise building, and the best lighting effect made every room of the high-rise building bright. 1979, the British scientist vogel used many points of the same size to represent the seeds in the sunflower tray. According to the rules of Fibonacci sequence, these points are packed as closely as possible. His computer simulation of sunflower shows that if the divergence angle is less than 137.5, there will be a gap on the sunflower disk, and only a group of spirals can be seen. If the divergence angle is greater than 137.5, a gap will also appear on the panel, and another set of spirals will be seen at this time. Only when the divergence angle is equal to the golden angle will there be two sets of spirals embedded in the panel closely.
Therefore, in the growth process of sunflower and other plants, only by choosing this mathematical model can the distribution of seeds on the disk be the most effective, the disk become the strongest and the probability of producing offspring is the highest.