Math - 10 numbers that hold the world together

To create a universe, even a small one, you need numbers without which it simply won't start. These are the fundamental constants. With the help of these ten numbers you can describe everything: the growth of snowflakes, the explosion of a grenade, the game on the stock market, and the movement of galaxies. But where they came from is unclear. Those who want to write them off as God's will. And militant atheists can only use them, explaining with their help the course of evolution and the temperature of the blessed fire.


Archimedes' number.

To what it is equal: 3.1415926535... Today it is calculated to 1.24 trillion decimal places.

Who discovered it and when: The exact authorship is unknown. Attributed to ancient Hindus, Greeks, Chinese and other good people. It was first designated by the Greek letter π in the early eighth century by the English mathematician William Jones. 

When to celebrate π day is the only constant that has its own holiday, and even two. March 14, or 3.14, corresponds to the first signs in the number entry. And July 22, or 22/7, is nothing more than a rough approximation of π by a fraction. Universities (e.g., the Faculty of Mechanics of Moscow State University) prefer to mark the first date: it, unlike July 22, does not fall on vacation

What is π? 3.14, a number from school problems about circles. And at the same time - one of the main numbers in modern science. Physicists usually need π where there is no mention of circles, say, to simulate the solar wind or an explosion. The number π is found in every other equation - you can open a theoretical physics textbook at random and choose any one. If you don't have a textbook, a map of the world will do. An ordinary river with all its bends and twists is π times longer than the straight path from its mouth to the source.

This is to blame for the space itself: it is homogeneous and symmetrical. That is why the front of the blast wave is a ball, and from the stones on the water there are circles. So the π turns out to be quite appropriate here.

But all this applies only to the familiar Euclidean space in which we all live. If it were non-Euclidean, the symmetry would be different. And in a strongly curved universe, π no longer plays such an important role. Say, in Lobachevsky geometry a circle is four times longer than its diameter. Accordingly, rivers or explosions of the "curved cosmos" would require other formulas.

The number π is as old as all mathematics: about 4 thousand. The oldest Sumerian tablets give for it a figure of 25/8, or 3.125. The error is less than a percent. The Babylonians were not particularly fond of abstract mathematics, so that π was derived by experiment, simply by measuring the length of circles. By the way, this is the first experiment in numerical modeling of the world.

The most elegant of arithmetic formulas for π is more than 600 years old: π/4=1-1/3+1/5-1/7+... Simple arithmetic helps calculate π, and π itself helps understand the underlying properties of arithmetic. Hence its connection with probabilities, prime numbers and many other things: π, for example, is part of the famous "error function" that works equally reliably in casinos and sociologists. There is even a "probabilistic" way to count the constant itself. First, you have to stock up on a bag of needles. Second, throw them, without aiming, on a chalked floor with strips the width of a needle. Then, when the bag is empty, divide the number thrown by the number that crossed the chalk lines - and get π/2.


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Feigenbaum's constant.

What is equal to: 4.66920016

Where it applies: In chaos and catastrophe theory, which can be used to describe anything from the reproduction of E. coli to the development of the Russian economy.

Who discovered it and when: American physicist Mitchell Feigenbaum in 1975. Unlike most other discoverers of constants (Archimedes, for example), he is alive and teaching at the prestigious Rockefeller University.

When and how to celebrate δ Day: Before general cleaning.

What do broccoli sprouts, snowflakes and Christmas trees have in common? That their parts replicate the whole in miniature. Such objects, arranged like a matryoshka doll, are called fractals.

Fractals emerge from disorder, like a picture in a kaleidoscope. Mathematician Mitchell Feigenbaum was interested in 1975 not in the patterns themselves, but in the chaotic processes that make them appear.  Feigenbaum was concerned with demography. He proved that the birth and death of people can also be modeled by fractal laws. That's where he got this δ. The constant turned out to be universal: it is found in descriptions of hundreds of other chaotic processes, from aerodynamics to biology.

With Mandelbrot's fractal began a widespread fascination with these objects. In chaos theory it plays approximately the same role as a circle in ordinary geometry, and the number δ actually defines its shape. It turns out that this constant is the same as π, only for chaos.

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