Lan Ruochan

Chapter 165 There was Yelang eight hundred miles in ancient times, and it is known that the Han family has tens of thousands of hectares
To define and divide the zodiac constellations, both Tianzhu and Central Plains use the moon phase method,

It also compares the relative change of the moon's position in a sidereal month, which is the division of the zodiac.

The so-called sidereal month mentioned here refers to the real cycle of the moon orbiting the earth with the star as the reference.

A sidereal month is about 27.33 days, so choosing whether to divide the whole day into 27 areas or 28 areas has its own advantages and disadvantages.

Just like the 12th house is taken between the 13th and the 12th when the west divides the zodiac by the sun phase method, this difference will always exist.

The method adopted in ancient China is to use 28 stars as a reference to divide, without doing mathematical equal divisions.
On the observation instrument, it must be fitted by the equal division method.

But the method adopted by ancient Tianzhu is the same as that of the West. Since the extra ones cannot be made up, they should be removed altogether, and only 27 are taken.

I don't know if it's a coincidence or out of belief, but the star that was specially filtered out by ancient Tianzhu is the ox constellation in the 28 constellations (Hinduism respects cattle).

Tianzhu admits that there is a gap in the division of the 27 constellations, and defines this gap as the winning domain of Hetian, which is the division of the zodiac where the moon lived when the Indian god Hetian was born in legend.

The angle corresponding to Heitian's winning field in the zodiac is only one-third of that of ordinary stars, but it is the shrine of the moon.

The other 27 constellations are all the wives of the moon. The moon rotates every month and turns around in room 27, which sounds very poetic.

However, this poetic division method has limited their development in observation instruments, and star observation instruments based on the 27 divisions of the ecliptic have never appeared.

The drawbacks of the Tianzhu Constellation Calibration Method were pointed out by a child, and the face of the holy minister was naturally a little unsightly.

In order to regain ground, he began to try to cover up this problem with mathematical knowledge,

"There is no mistake in Tianzhu's division method.

We have mastered the mysteries about the calculation of the ratio of circumference to diameter,
Through calculation, the sky can be divided into 27 parts very accurately. "

The ratio of the circumference of a circle is called pi in China.

Liu Xin of the Western Han Dynasty and King Fan of Wu during the Three Kingdoms period tried to use the method of squaring the circle to accurately calculate pi.

The so-called squaring a circle is to use the square to fit the area of ​​the circle and then deduce the circumference ratio of the circle.

The accuracy of this method is not very high, and the values ​​​​calculated by both people are around 3.15.

(Of course, the ancients did not write decimals. Modern decimals are used here for intuition. The following knowledge points will briefly introduce the ancient decimal notation.)
However, since Liu Hui invented the black algorithm of cutting circles, using the idea of ​​calculus to calculate the area of ​​a circle,
The problem of pi has been completely solved in China.

The remaining work is the number of times of actuarial fitting, which is the problem of calculating this value to the number of decimal places.

Liu Hui himself is "relatively" lazy. He only calculated the area of ​​the 96-gon inscribed in a circle, thus pushing the pi to 3.1416.

But Zu Dingzhi's father, Zu Chongzhi, is a ruthless man. He calculated the 24576 polygon in one go, and pushed the exact value of pi to seven decimal places.

This record has been proud for more than 1000 years, and there is no rival.

In fact, from the perspective of method, as soon as Liu Hui's cutting circle appeared, China had already won.

In fact, even in complex modern calculations, it is rare to really use so many digits after the decimal point of pi. In most cases, taking 3.14 is enough.

This is the sparse rate (evaluation for easy calculation) given by Zu Chongzhi - 22/[-].

When making the armillary sphere, each area of ​​the four images needs seven points, and the fraction expression with seven as the denominator is also conducive to the calculation of the armillary sphere for stargazing.

However, although the problem of pi has been satisfactorily solved in China, this number is infinite after all, and cannot be calculated absolutely, and it has always been a difficult point in mathematics.

Maybe Tianzhu really has a better way of expression that is worth learning from?
At this moment, not only Xin Dufang, but also Zu Dizhi and Tao Hongjing pricked up their ears.

The holy minister was full of confidence, saying that Tianzhu had already recorded the estimation of pi in Bai Yeroufei's pack as early as the period of the Sixteen Heroes, using the ancient method of turning the circle into a square, and the final value was about 339/108 (3.14 ).

This value is indeed sufficient for the calculation of the circumference, and it is much more accurate than the estimate of the Chinese Zhouzhisan in the same period.

But after these hundreds of years, Tianzhu is still obsessed with the backward algorithm of using squares to approximate circles, which is fundamentally unable to solve the problem of pi.

Xin Dufang was a child and didn't know how to speak in diplomatic situations, so she immediately pointed out the backwardness of Tianzhu's algorithm.

Calculation of square and radius is one of the special fields that the holy minister is most proud of.

At this time, being teased by a child like this was a bit over the top, and he had a fight with Xin Dufang at that time.

Xin Dufang was also unambiguous, striding to the middle of the school grounds, using tree branches as pens and yellow sand as paper, he explained the calculation formula of cutting circles and Liu Hui on the spot.

The holy minister is naturally not mediocre, his ability in arithmetic is second to none in the five Tianzhu.
So Xin Dufang gave a brief explanation, and he was able to hear the magical effect of cutting circles.

At this time, he had completely suppressed his initial arrogance, and after listening carefully for a while, he began to have questions and answers with Xin Dufang, interacting with each other.

In mathematics, sometimes discovering a new idea, a new method, is equivalent to opening up a new world, a new world.

That door has always been there, but opening and not opening is the difference between Tianchao and Tongtong.

Two years later, the holy minister completed his "Ariyahata Almanac",
Tianzhu's pi calculation has entered the era of the fourth decimal place.

At the same time, the holy minister used the word āsanna (approximation) to indicate that his calculations were not precise enough.

Many seal-supporting scholars have been proud of themselves for many years, thinking that the word of the holy minister proves his cognition of irrational numbers.

In fact, it was only because he knew that the accuracy of his calculation results was far inferior to the density rate used by Zhongyuan at that time, so he called his calculation an approximation.

As for the term irrational number, it was originally defined by the West.

Although this concept was not explicitly proposed in China or ancient India, it was recognized as early as Liu Hui's period that there were numbers that could not be fully fitted.

When calculating the ratio of pi, Liu Hui said: If you cut it thinner, you will lose less. If you cut it again and again until it cannot be cut, it will fit into the circle without losing anything.

This sentence is the true meaning of "approximation" in mathematics.

The calculation infinite approximation algorithm of square root and cube root has been formed in the era of "Nine Chapters of Arithmetic".

Most of the Chinese calculations are based on a pragmatic attitude to solve the problem of how to calculate, instead of putting forward too many concepts and theorems like philosophy books.

Counting one, although it is included in the six arts, it ranks last. It is a strange skill and obscene skill, and it does not enter the mainstream Taoism.

Therefore, books and biographies should be practical. If they are too theoretical, they will end up in the same way as the dragon slaying technique, just like Zu's secret book "Zhushu".

The holy minister was offended by Xin Dufang, and his attitude changed immediately after he talked about it.

He intended to rebuild the calendar for Tianzhu, so he asked Xin Dufang for many details of the Central Plains calendar.

At that time, all the laws of the Tianzhu calendar existed side by side, and the system was complex. The sun, lunar, and yin and yang calendars coexisted.

However, the Central Plains calendar combines the strengths of various calendars, and it has been finalized. It can be used to know the new year, the time of cutting off farming, and its strong functionality.

The holy minister came to Middle-earth, and the errand of the Young Ri King is certainly one of the purposes.

But as far as he is concerned, being able to exchange academic knowledge with everyone in the Celestial Dynasty is also the main reason why he is willing to serve as the chief envoy.

He saw that all the children in the Central Plains had such attainments in arithmetic, astronomy, and calendar, so he knew that this trip must be rewarding, so he tentatively asked,

"Brother Xin really has good insights, but I don't know who taught these knowledge?
Central Plains is studying mathematics, who are the masters, can my brother recommend it for you?
I have a desire to learn, but I don't know immortals.

The well frog cries alone, where can the sky be seen? "

The last few ancient and five-word sentences are naturally not the original creation of the holy minister, but Sun Qing, the merchant of Shu, is very encouraged when he sees the soft power of the Central Plains.

Although the land of Shu belongs to Qi State in the south, the red flowers and green leaves belong to the same family. The cultural backgrounds of the northern and southern dynasties are the same.

So she was so overjoyed that she casually translated the holy minister's humble speech into a verse.

(End of this chapter)