One: The world is full of wonders, and there are many interesting things in our mathematics kingdom. For example, in my ninth exercise book, there is a thinking question that reads: "A bus goes from Dongcheng to Xicheng at a speed of 45 kilometers per hour and stops after 2.5 hours. At this time, it is just 18 km away from the center of the east and west cities. How many kilometers is it between East and West? When Wang Xing and Xiaoying solve the above problems, their calculation methods and results are different. Wang Xing's mileage is less than Xiao Ying's, but xu teacher said that both of them were right. Why is this? Have you figured it out? You can also calculate the calculation results of both of them. " In fact, we can quickly work out a method for this problem, which is: 45× 2.5 = 1 12.5 (km),112.5+18 =130.5 (. In fact, we have neglected a very important condition here, that is, the word "Li" mentioned in the condition is "just 18 km from the center of the east and west cities", and it does not say whether it has not yet reached the midpoint or exceeded the midpoint. If the distance from the midpoint is less than 18km, the formula is the previous one; If it is greater than 18km, the formula should be 45× 2.5 = 1 12.5 (km), 1 12.5-65448. Therefore, the correct answer should be: 45 × 2.5 = 1 12.5 (km),12.5+18 =130.5 (km),/kloc-. Two answers, that is to say, Wang Xing's answer and Xiaoying's answer are comprehensive.

In daily study, there are often many math problems with multiple solutions, which are easily overlooked in practice or examination. This requires us to carefully examine the problem, awaken our own life experience, scrutinize it carefully, and fully and correctly understand the meaning of the problem. Otherwise, it is easy to ignore other answers and make a mistake of generalizing.

Two: the origin of pi. A long time ago, people saw that the ratio of the circumference of a circle to the straight meridian was a constant independent of the size of the circle, which was called pi. 1600, William Autolante of Britain first used pi to express pi, because pi is the first letter of "circumference" in Greek, and δ is the first letter of "diameter". Pi is π. 1706. Jones in Britain first used π. 1737. Euler used π in his works. Later, it was widely accepted by mathematicians and has been used ever since. π is a very important constant. A german mathematician commented: "the accuracy of calculating pi in a country in history can be used as an important symbol to measure the level of mathematical development at that time." Many mathematicians at all times and at home and abroad are tirelessly seeking the calculation method of π value. In 200 BC, the ancient Greek mathematician Archimedes first gave the correct solution of π value in theory. He approached the circumference of a circle from both big and small directions at the same time, and skillfully calculated about 150 years before π met. Ptolemy, another ancient Greek mathematician, gave an approximate value of π by the chord table method (multiplying the chord length by 360 and dividing it by the diameter of the circle at the central angle 1). In the past 200 years, Liu Hui, a mathematician in China, has provided a scientific method to find pi, which reflects this extreme view. The methods of Liu Hui and Archimedes are as follows. He only takes "internal engraving" instead of "external cutting". Using the inequality of circular area, he gets twice the result with half the effort. Then, Zu Chongzhi leads the world in the calculation of pi, and obtains the "divisor rate" and "secret rate" (also known as ancestor rate) to get 3. 14 15926.