Saturday , July 24 2021

How mathematics helped China create an empire (and that her emperor managed to sleep with 121 women every 15 days)

From measuring the time to understanding our position in the universe, from mapping the Earth to navigating the sea, from the first inventions of man to modern technologies: mathematics was the axis of human life

The first steps in the mathematical journey of man gave the ancient cultures of Egypt, Mesopotamia and Greece, cultures that created the basic language of numbers and calculations.

But when ancient Greece fell, mathematical progress stopped … on the West. In the east it has risen to new heights.

Much of this mathematical inheritance often does not receive the merit it deserves.

We started recounting on BBC Mundo it history, something forgot, the development of mathematics in the East, which transformed the West and gave birth to the modern world.

In the distance

The Chinese wall, which spans thousands of kilometers, lasted nearly 2,000 years since it began in 220 BC. to protect the growing empire.

Never stop surprised. GOTTY IMAGES

A large defensive wall is an incredible engineering venture, built on a vibrant terrain and high.

As soon as they began to put it, the old Chinese had to calculate the distances, angles of height and quantity of material, and it is not surprising that inspired genius mathematical methods.

Its foundation was an incredibly simple system of numbers that laid the foundations for today's way in the West.

When they wanted to pay, small bamboo sticks were used.

The lines are arranged to represent numbers 1 to 9.

Then they were installed columns so each one represented units, tens, hundreds, thousands, and so on.

For example, if you wanted to present a number 924, it was enough for the symbol 4 to be in the unit column, the symbol 2 in column ten, and the symbol 9 in the column of a hundred.

The way the old Chinese have done their calculations is very similar to the way we are learning at school today.

The strength of these bars is to allow very fast calculations.

We call it system of decimal place values, and is very similar to the one we use today: we use numbers from 1 to 9, and its position tells us whether it's units, tens, hundreds, or thousands.

The ancient Chinese were not only the first to use a system with a decimal value, but they did it for over a thousand years before we accepted it in the West.

However, it was used only when calculating the bars.

Whenever they wanted write numbersEverything was complicated.

Since they do not have the concept 0, they must create special symbols representing tens, hundreds, thousands, etc., so they can be written down.

So the number 924 would be written as 9, 2, and 4.

924 написано.

It's notra so effective.

Without a zero, the written number was very limited.

However, this did not prevent old Chinese people from doing huge mathematical steps.

Cosmic Numbers

In ancient China, numbers were subject to great fascination.

The legend says that the first sovereign China, the Yellow Emperor or Huangdai, in 2800 BC N. Nr. He created mathematics and believed that the numbers were cosmically important.

And to this day, the Chinese still believe in the mystical power of numbers.

There are dangerous numbers like 4 and blessed as 8 (1 to 10 in Chinese, starting with the upper left corner). GOTTY IMAGES

Unusual numbers are men, even numbers, women. Number 4 should be avoided at all costs. Number 8 brings happiness.

Magical square

In addition, the ancient Chinese attracted numbers and developed a very early version of Sudoku. They were called a magic square.

Legend has it that thousands of years ago, Emperor Yu came to us sacred turtle which came from the depths of the Yellow River.

On the back, the numbers were placed on the magic market.

In this market, which is considered to have a great religious significance, all the numbers in each line (horizontal, vertical and diagonal) sumban same: 15.

Sum 15, in all directions.

Although it should not be more than a the puzzle fun, the game depicts the ancient Chinese fascination for mathematical patterns, and soon they created even larger magical squares with greater magical and mathematical powers.

In court

Mathematics also played a key role in the work of the Emperor's court.

The calendar and movement of the planets were extremely important for the ruler, which influenced all his decisions, including the way his day was planned, so that astronomers became valued members of the imperial court and astronomers were always mathematicians.

Everything in the life of the emperor led the calendar and he he dealt with his mathematical precision.

Everything, including your sex life.

Sexual mathematical problem

One of the tasks of imperial mathematical advisers was to create a system that would enable the emperor to lie with as many women as he had in his harem.

The legendary yellow emperor has traditionally ruled from 2698 to 2598 a. C. He was deserving of the introduction of wooden houses, cars, boats, arch and arrows, writing and using coins. His wife is responsible for the discovery of pigmeat (silk production)

The legend says that the emperor had relations with 121 women during the 15th night:

  • lfor empress,
  • 3 consortia or "women",
  • 9 women or "invited ladies",
  • 27 concubines or "hereditary women" and. t
  • 81 slaves or "visiting ladies".

Mathematical counselors found a solution based on an idea called geometric progression.

They noticed that this is a series of numbers in which it moves from one number to another, so that the same number is multiplied each time, in this case, 3.

Each group of women is three times larger than the previous group, so they can organize a rotation that ensures that in space 15 nightthe emperor will sleep with all the women of the harem.

The first night was reserved for Emperor. Next, for three senior associates. Nine women came later, then 27 concubines, in groups of 9 every night.

Finally, during the 9th night, 81 slaves passed through their beds in groups of 9.

This can not be denied sThe emperor is needed from a lot resistance.

In addition, the rotation ensured that the emperor slept with the highest women on the night closest to the full moon when his yin– their female strength – was at the highest level and could match with their own yangor male power.

The goal was clear and necessary: ​​to find the best possible imperial inheritance.

  • Mathematicians who helped Einstein and without which the theory of relativity would not work

9 chapters

Naturally, mathematics was also essential for the country's operation.

Ancient China was a vast and growing empire with a strict code of law, expanded taxes and a standardized system of weights, measures and money.

The empire needed a highly qualified state service, qualified for mathematics. And for the training of these officials, a textbook was written about 200 BC: "Nine chapters on mathematical art."

The Han Dynasty Han translates classic texts with scientists. GOTTY IMAGES

The book is a collection of 246 problems in practical areas, such as trade, salaries and taxes.

And at the bottom of these problems is one of the central themes of mathematics: how to solve equations.

The equations are somewhat similar to mysterious crosses. You get a certain amount of information about some unknown numbers, and from this information you need to find out what the unknown numbers are.

For example …

… until you conclude that each peach weighs 4 g.

If you know that:

  • 1 basin with 3 peaches weighs a total of 15 grams
  • 2 plums with 1 peach weigh together 10 grams …

… you can figure out how much weigh one plum and one peach.


If you take the first set-1 basin and 3 peaches weighing 15 grams and fold it, you will have:

  • 2 plums and 6 peaches that weigh 30 grams.

If we subtract the second set of -2 plums and 1 weighing peaches 10 grams– the result is interesting: not only do you know that you stay 20 grams, but now not plums.

So if the remaining 5 peaches weigh 20 grams, weigh one peach 4 gbouquets, and from this you can conclude that every plum weighs 3 gbouquets.

… until you conclude that each peach weighs 4 g.

The old Chinese continued to use similar methods for the increasing number of unknowns, which were used to solve increasingly complex equations.

The unusual thing is that this is a system of solving equations in the west did not appear until the beginning of the 19th century.

In 1809, when analyzing a rock called Pallas in the asteroid belt, Carl Friedrich Gauss, known as the "Prince of Math", re-discovered this method, which was formed in ancient China centuries earlier.

  • Genius of Charles Gauss, prince of mathematics

The importance of others

The Chinese have solved even more complex equations, which included a much larger number.

In what is known as Chinese saying of rest, have come up with a new kind of problem.

Here we know the number that remains when we divide the unknown number of the equation with a given number, for example, 3, 5, or 7.

Although it is abstract mathematical problem, the ancient Chinese have expressed this in practice.

For example …

A woman on the market does not know how many eggs she has. He knows, that …

  • if you correct them 3 in 3, 1 egg is left;
  • if you give them 5 in 5, 2 eggs;
  • if you organize them in lines after 7, discover this You have 3 eggs left
If you group them into groups of 5, you have 2 eggs …

The old Chinese people found a systematic way of calculating that the minimum number of eggs they could have on the tray, 52.

The most striking thing is that you can record as large a number as 52 a small number, such as 3, 5, and 7.

In the sixth century BC, the Chinese theorem on rest was used in ancient Chinese astronomy to measure the planetary movement.

And it still has practical use today.

Internet cryptography They encode numbers using mathematics, which originates from the Chinese saying about rest.

The best one has not come … GETTY IMAGES

In the thirteenth century, mathematics had long been in the curriculum of China, with more than 30 mathematical schools spread across the country.

The Efrom Oro od Mmathematics Chinas I came. And his most important mathematician was Qin Jiushao.

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