Five questions about the encounter of nine arithmetic classics.

The five encounter problems of the nine chapters of arithmetic classics are as follows.

Topic 1: Today I started from the South China Sea and went to the North Sea on the 7th. These geese set off from the North Sea and arrived in the South China Sea on the 9th. Wild geese are springing up today. Ask when to meet. Answer days: the third and sixteenth days 15. Operation days: the combined days are the rules, and the days are multiplied by the reality, just like one day. It means: wild ducks take off from the South China Sea and fly to the North Sea in 7 days; A wild goose took off from the North Sea on the 9th and flew to the South China Sea. Now the ducks and geese take off at the same time. Ask when to meet?

A: June 3rd 15/ 16.

Methods: Take the number of days as divisor, multiply the number of days as dividend, and divide the dividend by divisor to get the meeting time. That is, 7+9= 16 is the divisor. 7x9=63 is the dividend, and the meeting time is 63÷ 16=3 and 15/ 16 (days). Note: Fu refers to wild ducks, and Fa refers to divisor; Dividends in real terms.

Note: The method in "Nine Chapters Arithmetic" is consistent with the way we answer this kind of question now. Our current solution is1÷ (1/7+1/9) =1/(9/7x8+7/7x9) = 65438. The method in Nine Chapters Arithmetic is to find the reciprocal of the sum of 1/7 and 1/9.

Topic 2: There is a dime in Chang 'an today, and it will arrive on the 5th. B Depart from Qi and arrive in Chang 'an in seven days. B sent it two days ago, and A sent it to Chang 'an. Meet on Geometry Day. Answer day: one twelfth of the next day. Running days: the fifth and seventh days are considered as Dharma. Subtract seven days from the first two days of B, and press A for the rest ... It is as good as the law.

It means: A departs from Chang 'an and arrives in Qidi in 5 days; B Depart from Qi and arrive in Chang 'an on the 7th. B will leave for two days first, and A will leave from Chang 'an. Ask when to meet? Answer: 2 and112.

Methods: Add 5 and 7 together as a divisor, that is, 5+7= 12. If you subtract 7 days from 2 days when B leaves first, the difference is 7-2=5, and the dividend is 5×5 = 25. Divide the dividend by the divisor to get the meeting time: 25- 12=2 and112 (days).

Note: All refer to place names.

Note: Our current solution is (1-2/7) ÷ (1/5+1/7) = 7-2/7 ÷ 7+5/7x5 = 7-2/7x5.

Nine Chapters Arithmetic, as a mathematical monograph in ancient China, is the most important one among the "Ten Classical Books on Computing" (ten ancient books on computing between Han and Tang Dynasties). Liu Hui commented on "Nine Chapters Arithmetic" in Wei and Jin Dynasties, saying: "The Duke of Zhou made a ceremony, and there were nine numbers, while nine chapters were a ceremony." He also said, "Zhang Cang, Hou Peiping in Han Dynasty, and Geng Shouchang, a senior farmer, all made good use of fortune telling.

Because of the remnants of the old text, Cang and others called it deletion and supplement, so the purpose of the school is different from the ancient or different from the ancient, and the theory is closer. "According to research, Zhang Cang and Geng Shouchang of the Western Han Dynasty have made supplements. The final edition was written in the early Eastern Han Dynasty at the latest, but its basic content was basically finalized in the late Western Han Dynasty.