Interesting facts about mathematics. Interesting facts from the history of mathematics
Numbers, functions and geometric shapes are pure pleasure. And mathematics itself is just a very good joke. When you understand this, you will definitely love the “queen of sciences” with all your heart. So says Alex Bellos, author of the book Beauty Squared. Here are some interesting facts from it that will help you immerse yourself in the madness. interesting world numbers and graphs.
How to incinerate a boar using a paraboloid
Parallel rays of light entering the paraboloid are reflected by its surface into focus. Therefore, paraboloids are widely used in solar energy technology.
For example, the Scheffler reflector, a parabolic metal bowl, is commonly used in developing countries for cooking. It is aimed at the sun and slowly turns after its movement in order to catch as much as possible sun rays, reflecting them to the same point (focus) where the slab is located.
The most powerful solar oven is a 45 meter high parabolic mirror located in the French Pyrenees, near Odeillot.
Due to its enormous size, the mirror itself does not move, but receives the reflected sunlight from 63 small flat rotating mirrors. The focus of the mirror is round shield, which in sunny days heats up to 3500 °C - enough heat, to boil lead, smelt tungsten, or reduce wild boar to ash.
Queen's Secret
One of the most interesting mathematical puzzles involves rolling one coin around another. Place two identical queen coins next to each other on the table, placing them crown side up. Roll the left coin around the right one. Which way will the crown point when the coin is on the right side?
Would you expect the coin to be upside down because it has only traveled halfway around the stationary coin? This is mistake. The Queen makes a full turn, which at first glance is counterintuitive. The fact is that a coin rotates around itself and around another coin. The movement occurs in two independent directions. For every degree the left coin moves around the right coin, it rotates two degrees around itself.
Why an even number cannot be mystical
The Sumerians came up with names for numbers using words available in their language. For example, to designate a unit, the word ges (“gesh”) was used, the second meaning of which is a man or phallus. The deuce was denoted by the word min (“min”), also symbolizing the feminine principle. Perhaps this emphasized the fact that the man occupies a dominant position, and the woman is only an addition to him, or characterized the male penis and female breasts.
The Greek thinker Pythagoras, who lived in the 6th century BC, proclaimed odd numbers to be masculine and even numbers to be feminine, thereby confirming the associative connection noted by the Sumerians between one and a man, as well as two and a woman. He argued that the reluctance to divide into two is a sign of strength, while the tendency to do so is a sign of weakness. In Christianity, this is reflected in the myth of the creation of the world: God created Adam first, and Eve second.
These prejudices have survived to this day. Only odd numbers are still considered mystical.
Number trick
If you count the frequency of the first digits in all the numbers that you find on the front page of any newspaper, you will notice an interesting pattern. You will see that numbers starting with 1 are the most common; then follow the numbers, the first digit of which is 2, then 3 - and so on until the number 9, which is used at the beginning of numbers least often. It's truly incredible. Try it yourself!
In 1938, General Electric physicist Frank Benford discovered the first digit phenomenon by noticing the tattered pages of books containing tables of logarithms. He studied the distribution of the first digits based on data such as the population of US cities, the addresses of the first few hundred people from the biographical directory of American scientists American Men of Science, atomic weight chemical elements, river basin area and baseball game statistics. In most cases, the results were close to the expected distribution.
The method of analyzing numbers for compliance with Benford's Law is increasingly being used to detect manipulation of data, not only in the context of financial fraud, but also in all those cases to which this law applies.
In 2006, Scott de Marchi and James Hamilton of Duke University wrote that the provided industrial enterprises information about the level of lead and nitric acid emissions does not satisfy Benford’s law, which indicates the likelihood of information distortion.
Based on Benford's law, University of Michigan political scientist Walter Mibane announced the possible falsification of the presidential election results in Iran. Scientists also use Benford's law as a diagnostic tool. Thus, during earthquakes, the upper and lower values of the seismograph readings obey this law.
How to sell a house for more money
Cornell University psychologist Manoj Thomas argues that the discomfort associated with large, non-round numbers makes them seem smaller than they really are: “We tend to believe that small numbers are more accurate, so when we see a precise large number, we instinctively we assume that it is less than it actually is.” As a result, according to Manoj Thomas, we pay more for an expensive product if its price is represented by a non-round number.
In one experiment, Thomas gave subjects photographs of several houses along with their prices, randomly presented as either a round number (say, $390,000) or a slightly larger exact number (say, $391,534).
When respondents were asked which prices they thought were higher or lower, they on average rated the exact prices as lower, when in fact the opposite was true. Advice for those who are planning to sell a house: if you want to get more money for it, its price should not end at zero.
In the world of prime numbers
Jerry Newport is a former taxi driver from Tucson who suffers from Asperger's syndrome. mental disorder, in which a person experiences difficulties in interpersonal communication, but has unique talents. When Jerry sees a large number, he immediately divides it into prime numbers - 2, 3, 5, 7, 11... that is, numbers that are divisible only by themselves and one.
“I only pay attention to numbers that have more than four digits. if there are fewer of them, it is like an animal crushed on the road. Yes exactly! - he declares indignantly. “Come on, show me something new!”
Sometimes Jerry can't factor a large number into prime factors, which means that this number itself is prime.
“When you come across a new prime number, it’s like looking at rocks and finding something unusual among them. Sort of like a diamond that you can take home and put on your shelf,” Jerry explains. “A new prime number is like a new friend.”
Infinity Paradox
The philosopher Zeno warned against using such a concept as infinity in a series of paradoxes. The most famous of these, Achilles and the Tortoise, demonstrated that adding an infinite number of quantities leads to an absurd result.
Imagine, Zeno said, that Achilles is trying to catch up with the tortoise. When the athlete reaches the place where she was when he began his run, the turtle will crawl a little further. When he gets to the second position, the turtle will advance further again. Achilles can continue running as much as he wants, but every time he reaches the place where the turtle was, it will already be a little ahead.
Mathematics is a beautiful science. One English scientist named Godfrey Harold Hadri put it this way or something like this. Einstein compared mathematics to poetry, and any musician will say that music is permeated with mathematics. And they are all right. Various people talk about this interesting facts about mathematics.
This is useful to know
The word “mathematics” comes from the Greek “mathema”, which means “study”, “science”, “research”.
In Thai, the number 5 is pronounced "ha", and some Thais type the slang number 555 instead of typing "ha ha ha".
0 — singular, which cannot be displayed using Roman numerals. How did the ancient Romans manage without it? Instead of a number they used the word "nulla".
The number 9 has a special magic. Multiply any number by 9, then add all the digits in that number until you get single digit number, and the resulting amount will always be equal to 9.
How to check if a number can be divided by 3? To do this, add up all the digits of this number. If what you get is divisible by 3, the same goes for the original number.
The equal sign (=) was invented by the English mathematician Robert Record in the 16th century. He was tired of writing the word “equals” in equations every time.
The name of the popular search engine Google comes from the word “googol”. This word means a number, namely one followed by one hundred zeros.
Of all shapes with the same perimeter, a circle has the most big square. Also, of all shapes with the same area, a circle has the smallest perimeter.
What is the Fibonacci sequence? This is an order of numbers where, when adding the two previous ones, the next one comes after them. Nature is replete with examples of this sequence. The seeds of many plants are arranged in a spiral, going from the center to the outer edges. For example, this is how sunflower seeds are arranged, and they imitate this sequence.
What is an inverted number? This is a number that can be read the same from the beginning and from the end: for example, 12421.
1089 x 9 = 9801.
In the following equation, the number 100 is obtained from the arithmetic operation of the digits in order:
12+3-4+5+67+8+9=100.
Extraordinary number 7
An interesting fact from mathematics concerns the number 7 - the only number in the chain of numbers from 1 to 10 that cannot be multiplied or divided so that it remains within this chain. For example, you can multiply 5 by 2 to get 10. 8 and 6 are divisible by 2.
There are seven deadly sins, seven wonders of the world, the same number of days of the week, colors of the rainbow, gnomes, seas and pillars of wisdom. As you can see, seven is also a number strongly associated with human culture.
On dice sum of points on opposite sides is always equal to seven.
This cannot be true, but it is true. Here's the proof.
If 10xN = 9.9999…,
Then N = 0.9999...
Subtracting N from 10N leaves 9N=9.
Then N=1. But we already know that N is also equal to 0.9999...
It turns out that 1=0.9999...
Cicadas use an indivisible number strategy in their evolution
The period of underground maturation in cicadas is 13 or 17 years. Both 13 and 17 are indivisible numbers. Presumably, these insects were less likely to come into contact with predators whose life periods were a divisible number of years.
Kaprekar's constant
Take any four-digit number, follow these steps, and the end result is 6174.
The only condition is that this number must have at least two different digits. Arrange the digits of this number first in descending order and then in ascending order. You will get two numbers. Subtract the smaller number from the larger one. Repeat this action again with the result obtained.
If you continue to do these two actions - arranging the numbers in ascending and descending order in each result obtained, and then subtracting the smaller number from the larger one - then you will eventually arrive at the number 6174. If after that you do all the same operations , then the number 6174 will be obtained every time.
The secret of the golden ratio
One of the most interesting facts about mathematics- this is the phenomenon of the golden section, or golden proportion - this is the number that is obtained if you divide a segment into two parts and correlate the larger part with the smaller one. In this case, the largest part of the segment will correlate with the smallest in the same way as the length of the entire segment correlates with its larger part.
From this follows the equation:
a/b = (a+b)/a = 1.618033988…
The number "Phi", named after the 21 letters of the Greek alphabet, is an infinite fraction, just like the well-known number "Pi".
The already mentioned Fibonacci sequence is closely related to the concept of the golden ratio. The ratio of any two Fibonacci numbers is very close to the number “Phi” (1.618033...), which expresses this proportion. Moreover, the greater the value of the numbers, the closer their ratio is to the golden proportion. For example, the ratio of 3 to 5 is 1.666. The ratio of 13 to 21 is 1.625. 144 and 233 are related as 1.618.
The number "Phi" has been discovered many times in different time. That's why it has so many names: the golden ratio, golden mean, golden proportion, divine proportion.
It is present in the architecture of ancient monuments such as Egyptian pyramids or the Greek Parthenon. The ancient pyramid at Giza has a base length of 230 meters on each side and a height of 146 meters from the base to the top. The ratio of these numbers is very close to the golden ratio - 1.5717.
The so-called golden rectangle introduced the principle of the golden section. It is considered one of the most visually harmonious geometric shapes. This explains his presence in art. The golden spiral is obtained by connecting adjacent rectangles with Fibonacci dimensions.
In the famous painting “The Last Supper,” the artist Leonardo Da Vinci used the golden ratio in the geometry of the table, walls and background. The golden ratio is present in the works of Michelangelo, Raphael, Rembrandt, Seurat and.
Much of art can be expressed using mathematics.
How can we not repeat ourselves now? Mathematics is a beautiful science.
Focused on calculations. However, this does not mean that everything in this kingdom is boring and boring. Not at all! Despite the seriousness of the study, surprising and interesting facts about mathematics appear. And you can find them in almost every corner of the globe.
Surprising but true
Let's consider the most interesting facts about mathematics concerning our country, as well as
Western states. As you know, in our country zero does not belong to the set natural numbers. But not everyone thinks so: in the West it is classified as a natural number.
Or here's another example. Many of us live and do not suspect that “now” flies away from us quite quickly - 86,400 times a day. This unit of counting was not given a name, but they found out how long a moment lasts: approximately a hundredth of a second.
As it turns out, some peoples are very superstitious about certain numbers. For example, in Japan and China there is nothing with the number four, since this number represents death itself. Therefore, it is not customary to use it even in hotels.
In Israel, they reject everything that is connected in one way or another with Christianity, so they do not write a plus sign in mathematical calculations, but just make do with an inverted letter “T”.
And in gambling (casino roulette), the number 666 is the sum of all the values that are present on the reel.
Entertaining examples
Every person knows from school what happens if you add up all the numbers from one to ten. You forgot? It’s okay, let us remind you: the amount will be 54.
Those people who are friends with the exact sciences know that if you add up all the values from 1 to 100, you get a very impressive number - 5050.
You can make a simple calculation and see what happens if you enter the first 3 digits of your phone number (without an operator) into the calculator, multiply them by 80, add 1, then you need to multiply all this by 250, add the last 4 digits of your number twice, subtract 250, divide by 2. The answer will be a surprising number. It will amaze you, we assure you!
Ig Nobel Prize
Everyone knows what the Nobel Prize is, to whom it is awarded and for what. But besides this, there is another unusual award. It is called the Ig Nobel Prize. Who can become a laureate? It is awarded at the same time as the Nobel Prize, but, unlike the famous prize, the Ig Nobel Prize is given for those ingenious projects that currently cannot be translated into reality. Or they will never do it because they are absurd. In 2009, this award was given to veterans who proved that a cow with a name produces more milk than one without a name.
Experiment
Surprisingly, scientists conducted an experiment that shows what distance
on the axis are represented in their imagination by people who do not have an education. The subjects included members of the Munduruku tribe and American schoolchildren who cannot count. They were given a certain number of dots to look at, and after some time they were asked to indicate where the numbers one to ten were. It turns out that for most people, the smallest values are the largest distances.
As it turns out, there are also interesting facts about mathematics in the field of cooking. For example, a cake can be cut in two ways into eight even pieces.
Many people do not know how to check the authenticity of a euro bill. But this is relatively easy to do. You need to take a letter from the serial sign and substitute a number (ordinal number in the alphabet) in its place. Then you need to add the resulting number with the remaining values. And after that, add the numbers of the result until you get one value - 8. It turns out that such interesting facts about mathematics can help verify the authenticity of banknotes.
If you take several figures (among which there will be a circle) with identical perimeters, then after a series of calculations it turns out that the circle has the largest area. It is impossible not to notice that if you calculate the perimeter of the circle and other figures, then it will remain in the minority. Yes, it has the smallest perimeter.
about mathematics
Today, all people use the decimal system, but this was not always the case. When our ancestors were just beginning to count, they used a system of 20 symbols using their fingers and toes. Later this trend changed. For example, in Babylon, people counted not only the fingers, but also the phalanges, which gave the number twelve.
Something else belongs to the section “Fun and Interesting Facts about Mathematics.” As far as everyone knows, the Romans were a smart people. They knew how to count well. However, there was one flaw - the number "0". It is used everywhere now, but it was not used in Rome. Don't believe me? But in vain! Confirmation of the above is the fact that zero cannot be written down by any of the known Roman numerals!
Albert Einstein was gifted since childhood. But, having a talent in mathematics, he was unable to enter the Polytechnic School of Zurich due to the fact that he failed to score the required number of points in other subjects. By the way, such developmental features have been noted in many geniuses. Soon, having improved his knowledge in the necessary disciplines, Einstein was admitted to classes at this school.
There are other interesting facts about famous mathematicians. At an American university, a graduate student was able to solve two problems that had previously been considered unanswerable. The fact is that the future mathematician was a little late for class. After which he copied these problems from the board, deciding that they were homework. They seemed complicated, but in just a few days George managed to solve a question that scientists had been thinking about for years.
As it turns out, you can learn mathematics not only at school or college, but also at home by looking at wallpaper. In any case, it worked out for
It so happened that as a child she looked in her room at sheets with lectures on integral and differential calculations. The whole point is that there simply wasn’t enough wallpaper for the children’s room. And thank God!
Surprisingly, with the help of mathematics you can find out when your last day on earth will be. Abraham de Moivre (a scientist from Britain) managed to achieve this through He noticed that he began to sleep 15 minutes more every day. What came of it? Abraham made a progression that indicated the date when he would sleep 24 hours a day. It turned out to be November 27, 1754. That’s when he died.
Interesting Facts Not everyone is familiar with mathematics. In modern times, mathematics is used everywhere, even despite technological progress. The science of mathematics is valuable to people. Interesting facts about her will interest even children.
1. People did not always use the decimal number system. Previously, a system of 20 numbers was used.
2. In Rome there was never a number 0, despite the fact that the people there are smart and know how to count.
3.Sofya Kovalevskaya proved that you can learn mathematics at home.
4.The records that were found on bones in Swaziland are the oldest mathematical work.
5.The decimal number system began to be used due to the presence of only 10 fingers on the hands.
6. Thanks to mathematics, it is known that a tie can be tied in 177,147 ways.
7.In 1900, all mathematical results could be contained in 80 books.
8. The word “algebra” has the same pronunciation in all languages of the world.
9. Real and imaginary numbers in mathematics were introduced by Rene Descartes.
10. The sum of all numbers from 1 to 100 is 5050.
11.The Egyptians did not know fractions.
12.Calculating the sum of all the numbers on the roulette wheel, you get the devil’s number 666.
13.With three touches of the knife, the cake is divided into 8 equal parts. And there are only 2 ways to do this.
14.You cannot write zero in Roman numerals.
15.The first woman mathematician is Hypatia, who lived in Alexandria, Egypt.
16.Zero is the only number that has several names.
17. There is a world mathematics day.
18.The bill was created in the state of Indiana.
19.The writer Lewis Carroll, who wrote Alice in Wonderland, was a mathematician.
20. Thanks to mathematics, logic arose.
21. Using arithmetic progression, Moivre was able to predict the date of his own death.
22. Solitaire is considered the simplest mathematical solitaire game.
23. Euclid was one of the most mysterious mathematicians. No information about him himself has reached his descendants, but there are mathematical works.
24. Most mathematicians behaved disgustingly during their school years.
25.Alfred Nobel decided not to include mathematics in the list of his prizes.
26. In mathematics there is braid theory, knot theory and game theory.
27.You won’t see the number 4 almost anywhere in Taiwan.
28. For the sake of mathematics, Sofya Kovalevskaya had to enter into a fictitious marriage.
30. Our whole life consists of mathematics.
20 interesting facts about mathematics for children
1. It was Robert Record who began to use the equals sign in 1557.
2.Researchers from America believe that students who chew gum during a math exam achieve more.
3.The number 13 is considered unlucky due to the biblical legend.
4. Even Napoleon Bonaparte wrote mathematical works.
5.Fingers and pebbles were considered the first computing devices.
6.The ancient Egyptians did not have multiplication tables and rules.
7.The number 666 is shrouded in legends and is the most mystical of all.
8. Negative numbers were not used until the 19th century.
9.If you translate the number 4 from Chinese, it means “death.”
10. Italians don't like the number 17.
11.Large number of people lucky number They count exactly 7.
12.The largest number in the world is a centillion.
13.The only ones prime numbers that end in 2 and 5 are the numbers 2 and 5.
14.The number pi was first introduced into use in the 6th century BC by the Indian mathematician Budhayana.
15.In the 6th century, quadratic equations were created in India.
16.If a triangle is drawn on a sphere, then all its angles will be only right angles.
17.The first signs of addition and subtraction familiar to us were described almost 520 years ago in the book “Rules of Algebra,” written by Jan Widmann.
18. Augustin Cauchy, who is a French mathematician, wrote more than 700 works in which he proved the finiteness of the number of stars, the finiteness of the natural series of numbers and the finiteness of the world.
19.The work of the ancient Greek mathematician Euclid consists of 13 volumes.
20. For the first time, mathematics was brought into a separate branch this science namely the ancient Greeks.
