How to use mathematics in real life?If figures, functions and geometrical figures always seemed to you something boring and far from reality, then time to be surprised came. Mathematics everywhere. She not only helps to understand better life, but also gives huge intellectual pleasure.
Alex Bellos will ship you in madly interesting world of numbers and will provide food for thought. You want to learn, than the figure “chetyre“ and how the parabola helps to cook food is terrible? The book “Beauty in a Square“ will tell about it. So, you are ready to encourage brains?
Caution to mankindProfessor of physics Albert Bartlett acts as
with the well-known lecture “The arithmetician, the population and energy“ since 1969. Every time it begins it with what the tone which is not foretelling anything good declares: “The greatest lack of the human race consists in its inability to understand an essence of exponential growth“.
Exponential growth takes place in case any size constantly increases in proportion to its value, for example by doubling: 1, 2, 4, 8, 16, 32, 64...
When size grows under the exponential law, the more it becomes, the quicker increases therefore everything after several steps it can reach the stunning value. An illustration from the book.
Present a bottle with bacteria which number increases twice every minute. At 11:00 in a bottle there is one bacterium, and by 12:00 the bottle will be completely filled with bacteria. “If you were the usual bacterium living in this bottle, - Bartlett asks, - in what timepoint you would understand that there will be no free space left here - here?“ It is amazing, but at 11:55 the bottle seems almost empty: it is filled for only 3 percent.
Bartlett`s bottle is a caution to inhabitants of Earth. If the population of the planet increases after an exhibitor, there will be no empty seat left on it much quicker, than it seems.
How to choose the wife: the theory of “an optimum stop“1611 the astronomer Johann Kepler decided to find
B to himself the wife. Process began not really successfully: he rejected the first three candidates. Kepler would take in the wife the fourth if did not see the fifth which seemed “modest, economical and capable to fall in love with adopted children“. But the scientist behaved so indecisively that he met several women who did not interest him. Then he all - married the fifth candidate.
According to the mathematical theory of “an optimum stop“ to make a choice, it is necessary to consider and reject 36,8 percent of possible options. And then to stop on the first which will be best of all rejected.
Kepler had 11 appointments. But it could meet four women, and then make the proposal of the first of the remained candidates who was pleasant to it more than those whom he already saw. In other words, he would choose the fifth woman at once and relieved himself of six unsuccessful meetings. The theory of “an optimum stop“ is applicable also in other spheres: to medicine, power, zoology, economy etc. of
the Phenomenon of the first figure
Write out all numbers which meet there from any newspaper. Now pay attention to the first figures in these numbers. You will see that the numbers beginning with figure 1 meet most often; then numbers which first figure 2, then 3 - and so to figure 9 which is used at the beginning of numbers most less often follow. It is really improbable.
In 1938 the physicist Frank Benford opened a phenomenon of the first figure, having paid attention to a potrepannost of pages in books with tables of logarithms. Then it counted distribution of the first figures in other sets of data: addresses of several hundred people from the biographic reference book, the nuclear weight of chemical elements, statistics of baseball games and so on. In most cases results were close to the expected distribution.
the Mystical four
you knew that not to find the floor number four in Asian hotels? In insides of planes there is no fourth row, and the companies do not let out products with the four in the name. This most widespread prejudice concerning numbers is connected with a word-play.
In Japanese, Cantonese and Mandarin dialects of Chinese, and also in Korean the word “four“ (shi, sei, si, sa) sounds in the same way as the words designating death. For this reason carriers of these languages in every possible way avoid number four.
The number four is associated with death so strongly that this communication turned into inevitably coming true prophecy. According to supervision in the USA, 4 - go numbers of every month among people of the Japanese and Chinese origin the quantity of heart attacks with death sharply increases.
the Sun - the cook
the Parabola is a curve which, being made of the reflecting material, reflects all rays of light, proceeding from focus (center). And vice versa - to collect sunshine in a bunch, the parabolic surface is necessary. Sheffler`s reflector, a parabolic metal bowl, is used in developing countries for cooking.
Sheffler`s reflector is directed to the Sun and slowly turns after its movement to catch as much as possible sunbeams, reflecting them in the same point (focus) where there is a plate. And the most powerful solar furnace is the parabolic mirror 45 meters high located in the French Pyrenees near Odeyo. From - for the huge sizes the mirror does not move, and accepts the reflected sunlight from 63 small flat rotating mirrors.
In focus of a mirror there is a round board which in sunny days heats up to 3500 degrees Celsius - rather high temperature to cook lead, to melt tungsten or to burn a wild boar to ashes.
Ability of mathematics to surprise made her entertaining of all intellectual disciplines. She takes and helps to understand how the world is arranged. Steep in the Universe of figures - you will not regret.
On materials of the book “Beauty in a Square“ of Alex Bellos.