Also known as the lotus problem, it means: "A lotus flower 1/4 cubits above the water (ancient length unit), just immersed in the water, 2 cubits away from the original place. Seek the height of the lotus and the depth of the water. " This topic is also called the lotus problem. It was first recorded in the first book Annotations to the Yearbook of Ayabata written by an ancient Indian mathematician around 600 AD. In the12nd century, another famous Indian mathematician, Pushkar, expounded this problem for the second time in his masterpiece Lirowati. Only 1/4 feet above the water surface was changed to 1/2 feet, and recorded in the form of ballads, making the lotus problem one of the typical problems in the application of geometric theorems. /kloc-Narayana, another Indian mathematician in the 4th century, also described a similar problem in his works.

In fact, Nine Chapters of Arithmetic was written around A.D., which is the earliest ancient arithmetic book to record such problems in history. Among them, the sixth question in chapter 9 is described as follows: "Today there is a pool one foot high, and the height of one foot rises from its center. Lead it ashore, and it will be suitable for landing. What is the water depth and the geometry of the water depth? Therefore, mathematical historians believe that this is the result of ancient cultural exchanges between China and India. There are many similar topics in China's later ancient books, such as Zhang Qiujian's Calculation (5th-6th century), Encounter with Siyuan, Volume VI (1303) and Arithmetic Unity, Volume VIII (1593). The problem of "born in a pool" in China's arithmetic is the application of Pythagorean theorem, and the Indian Lotus problem is the application of the nature of intersecting chords in a circle. In addition, Alkasi, an Arab mathematician, gave a similar question in Arithmetic Rules (1427), and there were similar questions in English arithmetic books in the 6438+06 century.

Pingping Lake is clear, and the lotus is half a foot above the water. Suddenly, a strong wind blew the lotus off. The lake is no longer visible, and fishermen only find it in autumn. This flower is two feet away from the original one. How deep is it?

If the lake is x feet deep and the height of the lotus is (x+0.5) feet, it can be listed according to the meaning of the question:

x^2+2^2=(x+0.5^)2

x^2+4=x^2+x+ 1/4

4=x+ 1/4

x= 15/4=3.75

The lake is 3.75 feet deep.