1. King Heluo of Syracuse asked the goldsmith to build a crown with pure gold. Because it was suspected that there was silver in it, Archimedes was asked to identify it. When he entered the bathtub to take a bath, the water overflowed outside the bathtub, so he realized that although the weight of objects made of different materials was the same, the discharged water would be different because of their different volumes. According to this truth, it can be decided whether the crown is adulterated.

2. When I was in Central China, in a math class, the teacher gave the students a famous question: "There is a number, three, and two; 5 digits, 5 numbers, and the remaining 3; There are seven places in seven, and there are two left. What's the date? " While everyone was thinking, Hua stood up and said, "23". His answer surprised the teacher and won his praise.

There are 20 pianos sold by manufacturers. One day, four children came and they all took the 20 pianos. Only Yaya suddenly calmed down and said, "We can get a point!" "

The aunt who sold the piano said, "Yes, I didn't think of that." Then the star said, "Then how do we divide it?" Who can answer the question of the stars, Yaya said. A child named Honghong said, "I can answer that 20 divided by 4=5. So each of us can get five pianos. " Yaya, the star and the aunt said, "Great."

In 46 BC, Julius Caesar, commander-in-chief of Rome, designated the calendar. Because he was born in July, in order to show his greatness, he decided to change July to "Julian month", and all single months were stipulated as 3 1 day, and bimonthly was 30 days. In this way, there is one more day in a year. February was the month when prisoners were executed in ancient Rome. In order to reduce the number of people executed, 1 day was reduced in February to 29 days.

5. Red-crowned cranes always move in groups and form a herringbone. The angle of the herringbone is 1 10 degrees. More accurate calculation also proves that half the angle of the herringbone-that is, the angle between each side and the direction of the crane group is 54 degrees, 44 minutes and 8 seconds! And the angle of diamond crystal is exactly 54 degrees, 44 minutes and 8 seconds! Is it a coincidence or some "tacit understanding" of nature?