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How mathematics helped China create an empire (and his emperor laid down with 121 women …) – La Prensa Gráfica

Forbidden City

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When Greece declined, China took over the baton.

From measuring time to understanding our position in the universe, from charting the earth to the navigation of the seas, from the first inventions of man to the advanced technologies of today: mathematics is the axis of human life

The first steps of the mathematical journey of man were given by the ancient cultures of Egypt, Mesopotamia and Greece, cultures that created the base language of number and calculation.

But when ancient Greece fell into decay, mathematical progress stopped … in the West . In the east it rose to new heights.

Much of this mathematical heritage often does not get the credit it deserves.

At BBC Mundo we started with a recount of Which history, something to forget , of the development of mathematics in the East that transformed the West and gave birth to the modern world.

In the distance

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

Section of the Great Wall of China

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It never ceases to amaze you.

The enormous defensive wall is an amazing piece of technology built on rough terrain and high.

As soon as they started to set it up, the old Chinese had to make calculations about distances, elevation angles and quantities of material, so it is not surprising that this has inspired ingenious mathematical methods.

The basis was an incredibly simple number system that has laid the foundation for the way we count in the West today.

When they wanted to make a sum, they used small bamboo sticks.

the bars they were willing to represent the numbers from 1 to 9.

Numbers in bars

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Then they put them in it columns so that each unit represented tens, hundreds, thousands, and so forth.

For example, if they wanted to display the number 924, it was sufficient to place the symbol 4 in the column of units, the symbol 2 in the column of the tens and the symbol 9 in the column of hundreds.

924 with bars

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The way the old Chinese did their calculations is much like the way we learn at school today.

The strength of these bars is that they allow very quick calculations.

This is what we call a value system with a decimal and it is very similar to the ones we use today: we use numbers from 1 to 9 and the position tells us whether they are units, dozens, hundreds or thousands.

The ancient Chinese were not only the first to use a decimal value system, but they did it more than a thousand years before we adopted it in the West.

But they only used it when calculating with the bars.

When they wanted write the numbers Everything was complicated.

Because they did not have the concept 0, they had to make special symbols to display tens, hundreds, thousands, etc., by writing them down.

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

924 while writing.

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924 written.

Nora so efficient .

Without zero, the written number was extremely limited.

That did not stop the old Chinese from taking gigantic mathematical steps.

Cosmic figures

In ancient China the numbers were objects of great fascination.

According to legend, the first sovereign of China, the Yellow Emperor or Huangdi, one of his gods, created mathematics in 2800 BC, believing that the numbers were cosmically important.

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

1 to 10 in Chinese, starting at the top left

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

Odd numbers are seen as men, even numbers, women. The number 4 must be avoided at all costs. The number 8 brings happiness.

The magic square

In addition, the old Chinese were attracted to patterns in numbers and developed a very early version of sudoku. It was called the magic square.

The legend says that Emperor Yu was visited thousands of years ago by a holy turtle coming from the depths of the Yellow River.

On his back, numbers were arranged in a magic square.

In that square, which was regarded as a major religious interest, all the numbers in each row (horizontal, vertical and diagonal) sum ba n the same : 15 .

The turtle with the magical photo.

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Sum 15, in all directions.

Although it may not be more than a puzzle funny , the game shows the ancient Chinese fascination with mathematical patterns and it did not take long before they created even bigger magical squares with greater magical and mathematical powers.

For the court

Mathematics also played a vital role in the functioning of the court of the emperor.

The calendar and movement of the planets were of the greatest importance to the ruler, who influenced all his decisions, even in the way his day was planned, so that astronomers became esteemed members of the imperial court, and astronomers were always mathematicians.

Everything in the life of the emperor was governed by the calendar and he he treated his business with mathematical precision .

Everything, including your sex life.

A sexual mathematical problem

One of the tasks of the imperial mathematical advisors was to create a system with which the emperor could lie down with as many women in his harem as possible.

Tribute to the Yellow Emperor

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The legendary yellow emperor ruled, according to the tradition of 2698 to 2598 a. C. He is credited with the introduction of wooden houses, cars, boats, bow and arrows, writing and the use of conceived money. His wife is credited with the discovery of silk culture (silk production).

The legend says that in 15 nights the emperor had to have relations with 121 women:

  • lEmpress ,
  • 3 senior associates or "ladies",
  • 9 women or "invited ladies",
  • 27 concubines or "hereditary ladies" and
  • 81 slaves or "visiting ladies".

The mathematical consultants found the solution on the basis of a given idea geometric progression .

They noticed that it was a series of numbers in which you go from one digit to another each time by multiplying the same number each time, in this case 3 .

Each group of women is three times larger than the previous group, so they could organize a rotation that guaranteed it, in space of 15 overnight stays the emperor will sleep with all the women of the harem.

The first night was reserved for the Empress. The next, for the 3 superior partners. The nine women came later, and then the 27 concubines, in groups of 9 each night.

Eventually, during a period of 9 nights, the 81 slaves passed their beds in groups of 9.

Broken bed

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That is undeniable se emperor required from a lot of resistance .

The rotation also ensured that the emperor slept with the ladies with the highest ranking on the nights closest to the full moon, when his yin – their feminine strength – was at the highest level and able to match it yang or male strength.

The goal was clear and compelling: to seek the best possible imperial succession.

9 chapters

Of course, mathematics was also fundamental to the functioning of the state.

Ancient China was a huge and growing empire with a strict legal code, widespread taxes and a standardized system of weights, measures and money.

The empire needed a highly educated official who was skilled in mathematics. And to educate these officials there was a textbook written around 200 BC: "The nine chapters on mathematical art."

Emperor of the Han Dynasty with scholars translating classical texts.

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Emperor of the Han Dynasty with scholars translating classical texts.

The book is a compilation of 246 problems in practical areas such as trade, payment of wages and taxes.

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

The equations look a bit like cryptic crossword puzzles. You get a certain amount of information about a number of unknown numbers, and from that information you have to deduce what the unknown numbers are.

For instance …

Plums and peaches in groups and their weights

BBC

If you know that:

  • 1 plum with 3 peaches weighs a total of 15 grams
  • 2 prunes with 1 peach weigh in total 10 grams …

… you can deduce how much a single plum weighs and a single peach.

How?

If you take the first set of 1 plum and 3 peaches that weighs 15 grams, take and fold, you have:

  • 2 prunes and 6 peaches weighing 30 grams .

If you subtract the second set-2 plums and 1 peach weighing 10 grams -, the result is interesting: not only do you know that you stay at 20 grams, but now there are no plums .

So, if the remaining 5 peaches weigh 20 grams, weighs a single peach 4 g ramos , and from that you can deduce that every plum weighs 3 g ramos .

The operation explained with images

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… until you realize that each peach weighs 4 grams.

………………………………….

The old Chinese continued to apply similar methods to an increasing number of unknowns, and used them to solve increasingly complex equations.

The special thing is that this specific system of solving equations it only came in the West until the beginning of the 19th century .

In 1809, when he analyzed the Pallas rock in the asteroid belt, Carl Friedrich Gauss, who would become known as the "prince of mathematics", rediscovered this method formulated centuries ago in ancient China.

The importance of the rest

The Chinese solved even more complicated equations with much larger numbers.

In what is known as The Chinese thesis of rest they came up with a new kind of problem.

Here we know the number that remains when the unknown number of the equation is divided by a certain number, for example 3, 5 or 7.

Although it is an abstract mathematical problem , the old Chinese expressed it in practical terms.

For instance …

A woman on the market does not know how many eggs she has. What he does know is that …

  • if you fix them 3 in 3, 1 egg remains ;
  • if you put them down 5 out of 5, 2 eggs left ;
  • if you organize them in rows of 7 , discover that you have 3 eggs left
Eggs organized in groups of 5

BBC

If you arrange them in groups of 5, you have 2 eggs …

The ancient Chinese found a systematic way of calculating that the smallest number of eggs they could have on the scale was 52.

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

In the sixth century AD, the Chinese theory of rest theory was used in ancient Chinese astronomy to measure the planetary movement.

And today it still has practical applications.

Internet cryptography encode numbers using mathematics that have their origins in Chinese rest.

Chinese abacus

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The best was yet to come …

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

the E pa O of the M atemáticas C HINAS I had arrived. And his most important mathematician was Qin Jiushao.

tomorrow: Qin Jiushao, the Chinese mathematician who was "as violent as a tiger and as poisonous as a scorpion" … Do not miss it!


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