Kepler and the cask

Kepler and Bucket Kepler were great mathematicians and astronomers. Because of his poor family, Kepler worked as a tutor and taught mathematics. In his spare time, he devoted himself to studying mathematics and became interested in finding the area of a circle. Ancient mathematicians used division to find the area of a circle, no matter how many times it was divided, it was an approximation. If you want to get more accurate results, you have to increase the number of segmentation. And the circle can be divided into infinitely many equal parts, which will never be finished. Kepler has his own ideas. He imitated the way people cut watermelons and divided the circle into many small sectors. The difference is that people used to divide the circle into similar hexagons, and Kepler divided the circle into infinite sectors as soon as he came up. After calculation, Kepler got the familiar formula of circular area: S=πr? Kepler was very happy to see this formula. In this way, he found out the area of many graphs. The verification results are all correct. So he wrote his research results into a book. What is the correct name of this book? Kepler lost his mind at the moment. One day, he went to a hotel to drink and found that the barrels in Austria were very different from those in his hometown. Why did you make it this shape? Can't it be shorter? Can't it be higher? How about a little flatter? Kepler's interest was aroused again. He took out a pen and paper to draw and count. As a result, he found it reasonable to make the Austrian barrel into this shape. This shape can hold the most wine with the same material. This discovery surprised Kepler and inspired him at the same time. So he named his new book "Solid Geometry of Barrels". In this book, Kepler introduced the volume of nearly 100 rotating bodies he calculated, and also introduced his new method of finding the area. For example, he calculated the volumes of various rotating bodies, which were generated by an arc rotating around a string. These rotating bodies have different shapes, some like apples, some like gourds, and some like lemons. No thinking, no creation. If people want to develop, they must keep thinking. grape