Some plants have intricate patterns on their bodies that, at first glance, appear haphazard, but upon closer inspection, reveal amazing order and structure.
We are afraid that even the greatest mathematicians cannot be compared with this natural form of creation. It represents the most intuitive and natural expression of mathematical beauty.
Descartes was a famous French mathematician of the 17th century, renowned for his creation of the coordinate method. After studying the curvilinear characteristics of clusters of petals and leaves, he listed the curve equation x^3+y^3-3axy=0, which accurately revealed the mathematical laws contained in the forms of plant leaves and flowers.
This curve equation is named the "Cartesian leaf line" or "leaf-shaped line," also known as the "jasmine petal curve." By transforming the value of parameter 'a', the shape of different leaves or petals can be depicted.
The number of petals, sepals, fruits, and other characteristics of a plant fit well into a peculiar series called the Fibonacci sequence. In this sequence, each number, starting with 3, is the sum of the previous two terms.
The arrangement of sunflower seeds follows a typical mathematical pattern. Upon close observation of a sunflower disk, one can find two sets of spirals: one coiled clockwise and the other counterclockwise, nested within each other. Additionally, the number of petals tends to align with the Fibonacci sequence, often appearing in groups of 34 and 55, 55 and 89, or 89 and 144, where each group consists of two adjacent numbers in the sequence.
A closer look at the common plantain reveals that the size of the arc between its adjacent leaves is consistently approximately 137.5°. Many other plants have leaves similar to plantain, with an arc of 137.5° between two leaves. Scientists have observed that by following this 137.5° arrangement pattern, the leaves can occupy the most space, absorb the most sunlight, and receive the most rain.
In 1979, British scientist Vogel used a computer to simulate the arrangement of sunflower fruits and found that if the dispersion angle of sunflower fruit arrangement is 137.3°, there will be gaps between the fruits on the disk, and only a set of clockwise spirals will be visible. Similarly, if the dispersion angle is 137.6°, there will also be gaps, but a set of counterclockwise spirals will be seen instead.
Only when the dispersion angle is precisely 137.5°, the fruits on the disk exhibit two sets of interlocking spirals without any gaps. This statistic shows that choosing a dispersion angle of 137.5° results in the most numerous, tightest, and most uniform distribution of fruits on the sunflower disk.
What is so remarkable about 137.5°? If we divide the circumference of a 360° circle using the golden ratio of 0.618, the resulting angle is approximately 222.5°. The outer angle corresponding to 222.5° within the entire circumference is 137.5°. Therefore, 137.5° is the angle of the golden ratio within the circle, also known as the "golden angle."
Scientists have proven that the reason why plants arrange their leaves or fruits according to the "golden angle" - 137.5° - is due to the long-term influence of the Earth's magnetic field on plants.
Today, architects have designed innovative buildings based on the "golden angle" of 137.5°, inspired by the pattern of plantain leaf arrangement, to optimize light and ventilation in each room. Mathematics is a discipline created by human beings. It may surprise you to learn that many animals are also "good at mathematics." In fact, nature is home to many remarkable animal "mathematicians."
Every morning, when the sun rises at an angle of 30° to the horizon, the "scouts" among bees are entrusted with the task of searching for nectar. Upon their return, they communicate the location, distance, and quantity of nectar to their partners using a unique "dancing language."
Based on this information, the queen sends out just the right number of worker bees to collect the nectar. It's astonishing how adept they are at calculation, ensuring that neither too many nor too few worker bees are sent, guaranteeing efficient honey production.
Moreover, the beehives constructed by these worker bees exhibit a remarkable hexagonal structure. In the early 18th century, the French scholar Malarche measured the dimensions of numerous beehives and discovered that all the obtuse angles of the rhombuses within the hive's framework were 109°28′, while all the acute angles measured 70°32′.
Subsequently, French mathematician Knigge and Scottish mathematician Mark Loring deduced through theoretical calculations that this specific angle is the most efficient for minimizing material usage while maximizing the size of the rhombic containers. Hence, honeybees are often referred to as "genius mathematicians and designers."
We often use the term "magic" to describe nature, as rain, breeze, flowers, and greenery possess their own enchanting qualities. However, they are intricately intertwined with life, creating unique beauty within our existence.
