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Source: Excerpt from “Science,” by Cristian Violatti, published in the Ancient History Encyclopedia.
...the development of Chinese science is strongly linked to government officials. The court astronomers were particularly interested in the sciences of astronomy and mathematics, since the calendar was a sensitive imperial matter: the life of the sky and the life on earth had to develop in harmony, and the sun and the moon regulated the different festivals. During the time of Confucius (c. 551 to c. 479 BCE), Chinese astronomers successfully calculated the occurrence of eclipses.
Geometry developed as a result of the need to measure land, while algebra was imported from India. During the 2nd century BCE, after many centuries and generations, a mathematical essay named The Nine Chapters on the Mathematical Art was completed. This work contained mostly practical mathematical procedures including topics such as determining the areas of fields of different shapes (for taxation purposes), pricing of different goods, commodities rate exchange and fair taxation. This book develops algebra, geometry, and also mentions negative quantities for the first time in recorded history. Zu Chongzhi (429–500 CE), estimated the right value of pi to the sixth decimal place and improved the magnet, which had been discovered centuries earlier.
Where the Chinese displayed an exceptional talent was at making inventions. Gunpowder, paper, woodblock printing, [and] the compass are some of the many Chinese inventions.
How did the technologies of gunpowder, printing, and the compass spread out of Asia? Where did these technologies spread to and what was their impact?



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There is a website with info about this inventions in China it’s
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Just search up 4 great inventions of ancient China answers those questions
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Gunpowder, printing and compass technologies spread around the world, by maritime or mercantile routes, these inventions revolutionized the world, and are used to this nowadays, to understand more.....

Gunpowder

Muslims acquired knowledge of gunpowder sometime between 1240 and 1280, when the Syrian Hasan al-Rammah wrote in Arabic recipes for gunpowder, instructions for purifying saltpeter, and descriptions of gunpowder incendiary behaviors. It is implied in the use of some terms that he derived his knowledge from Chinese sources: in his references to saltpeter as "Chinese snow", fireworks as "Chinese flowers", and rockets as "Chinese arrows".

The first western accounts of gunpowder appear in texts written by the English philosopher Roger Bacon in the 13th century. Various sources mention Chinese weapons and gunpowder weapons being used by the Mongols against European forces at the Battle of Mohi in 1241.

Printing

The Chinese invention of woodcut printing, sometime before the first book dated 868 (the Diamond Sutra), produced the world's first printed culture. According to A. Hyatt Mayor, curator of the Metropolitan Museum of Art, "it was the Chinese who really discovered the media that would dominate until our era." Printing in northern China advanced even further in the 11th century, as it was written by Song dynasty scientist and statesman Shen Kuo (1031-1095), that the common craftsman Bi Sheng (990-1051) invented movable ceramic type printing.

The Qing Dynasty court sponsored huge printing projects using movable type printing on wooden blocks during the 18th century. Although replaced by Western printing techniques, movable wooden block type printing still remains in use in isolated communities in China.

Compass

This location instrument was created by the Chinese and modified by different peoples. The large-scale use of the compass was undertaken in the period of the Great Navigations, especially by the Europeans, who relied on this instrument to carry out sea voyages to new colonial possessions.

With this information, we can say that Gunpowder, printing and compass went to the world for being revolutionary inventions, and the impact of these inventions in the whole world were from technological development to an improvement of techniques and tools.

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