Nine questions about * * * in "Island Computing". They all use a ruler to measure repeatedly from different positions, take the difference between the measurements and calculate the height of the mountain or the depth of the valley. This is Liu Hui's theory of heavy difference.

As can be seen from the title text, all calculations are made by calculation. "Being true" refers to the numerator of the fraction, and "Being law" refers to the denominator of the fraction. The length units used are Li, Zhang, Step, Ruler and Inch; 1 Li = 180 sheets = 1800 feet; 1 ft = 10 ft: 1 step =6 ft, 1 ft = 10 inch.

This material is an island, with two tables, three feet high and a thousand steps back and forth, so that the back table is consistent with the front table. Walking 123 steps from the front table, the man looked at the ground and took Wang Daofeng to meet the bottom table. Walking 127 steps from the back table, the man looked at the ground and walked Wang Daofeng, also touching the end of the table. Ask about the height of the island and the geometry of the table. A: The island is four miles high, with a level of 55; Go to see 120 miles and 150 steps.

Note: Suppose measuring an island, the height of two meters is 3 feet, and the distance from front to back is 1000 steps, so that the back table and the front table are in a straight line, and the back table is 123 steps away from the front table.

Observe the peak of Niuchang Island with human eyes and step back from the back 127. The human eye observes the island peaks on the ground. How high is the island and how far is it from the front? Tip: it is true that the height of the table is multiplied by the space of the table; More is the law, except it. The height of the island is obtained by adding the height of the table to income. People who find the distance from the front table to the island: it is true that the front table is multiplied by the table; Many things are laws. Besides, you have to go to the island to count.

Island Calculation is a book of econometrics written by Liu Hui in Wei and Jin Dynasties. It is also the earliest book on surveying mathematics written by China scholars, and it also provides a mathematical basis for cartography.

Liu Hui (born around 250 AD) is a very great mathematician in the history of Chinese mathematics, and also occupies a prominent position in the history of world mathematics. His representative works "Nine Arithmetic Notes" and "Arithmetic on the Island" are China's most precious mathematical heritage.

The book "Mathematics Department of China" comments on "Calculation Classics of the Island": "Make China's surveying reach its peak. In western Europe, it was not until 16 and 17 centuries that the second measurement technique was recorded, and it was not until 18 centuries that the third and fourth measurement techniques appeared, which shows the deep artistic conception and wide functions of China's ancient measurement. The calculation of Liu Hui's Archipelago Calculation is earlier than that of Europe 1300 to 1500.