Let no one say that scientists have no sense of humor. It is no coincidence that International Mathematics Day is celebrated every year on March 14. In the US spelling, the date reads 3/14 and is intended to remind us of the circle number pi – rounded to 3.14. In the US, the day is also called “Pi Day.”
But the season for this special day may also have been chosen deliberately. In spring, the importance of arithmetic for nature becomes particularly clear. For example, if you count the petals of flowers such as dandelions or daisies, you will discover something strange. Again and again, you come across the same, seemingly odd numbers: 8, 13, 21, 34, 55, or 89.
All these numbers have something in common. They belong to the so-called Fibonacci sequence. It was named after the Italian researcher Leonardo Fibonacci (approximately 1170-1240) and describes a sequence of numbers that has a special characteristic: each subsequent number is the sum of the two previous numbers. For example, 3 and 5 add up to 8. In turn, 8 and 13 add up to 21. And 13 and 21 add up to 34, and so on.
A place in the sun thanks to the golden angle
“Of course, the question now arises as to how nature came up with this idea,” says Prof. Marko Lindner from the Institute of Mathematics at the Hamburg University of Technology. “And the answer has to do with two things: the golden ratio and the golden angle.” The golden ratio is a special numerical ratio: 0.618 is the number that results when a sufficiently large Fibonacci number is divided by the next one. The golden angle, in turn, is an angular conversion of this golden ratio to a circle division: the golden angle is around 61.8 percent of a full circle (360 degrees), or in other words, approximately 222.4 degrees.
This is an irrational number. This means that it cannot be expressed as a fraction of two whole numbers. The mathematician explains why this is crucial using the example of petal growth. “Petals do not grow simultaneously, but one after the other from the center of the flower,” explains Marko Lindner. "Suppose nature had chosen a rational number, such as 180 degrees. In this case, the first petal would grow at one point on the circle and the second directly opposite. The third petal would grow at the same point as the first petal. This would block the sun from the very first petal.“ Another rational number such as 240 degrees – i.e., two-thirds of a full circle – would not be much better for the arrangement of the petals. ”Then, starting from the circle in the middle, there would only be room for a total of three petals that could capture sunlight. The next petals would grow in the circle in the same places. This would leave the previous petals in the shade.“
The ”odd" number of 0.618... or the angle of approximately 222.4 degrees, on the other hand, ensures that as many petals as possible get a place in the sun. They can be distributed as evenly as possible without overlapping. “Nature probably tried a thousand other angles first,” explains the mathematician. “But these variants died out. Only a crazy mutation that arranged the petals at this angle prevailed.”
The mathematics of the pineapple
Fibonacci numbers are also often found in other plants, such as the pineapple. The fruit grows in the tropics practically all year round, but the main harvest season begins in March. The hexagonal scales of a pineapple fruit are arranged in such a way that spiral-like arcs can be drawn in different directions. Depending on the counting direction, 8, 13, and 21 spiral arcs can be counted on a pineapple. All Fibonacci numbers. Similar spiral patterns can also be found, for example, in the seeds in the center of a sunflower.
Elsewhere, too, nature is full of mathematics, especially in spring. The first honey can be harvested in May. The hexagonal structures that make up honeycombs are pure geometry. Thanks to this special shape, space is used in the best possible way. “That's just what nature does,” says Prof. Lindner. “Some shapes are simply more efficient than others. Through selection, an optimal solution has been found.”
Given how useful it is in everyday life, it's almost surprising that mathematics isn't more popular in schools. Does the subject have an image problem? “Yes, I think so,” says Lindner. “Although it's also a cultural problem. In Germany, it's completely acceptable to say that you hated math in school. In other parts of the world, on the other hand, mathematics is considered a prestigious subject alongside medicine and physics.”
There – just like at the Hamburg University of Technology – people know that without mathematics, engineering achievements would be unthinkable. Numbers, formulas, and algorithms form the basis for a wide variety of achievements, from cell phones to aircraft technology, from computer tomography to weather satellites. But that's another story. Perhaps one for next year's Mathematics Day.
Further information for young scientists:
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