1. The first question: bisect any angle. Use an uncalibrated ruler and compass to divide any angle equally.

2. The second question: Turn the circle into a square. Convert a circle into a square of the same size.

3. The third question: Drawing with a ruler. Make beautiful symmetrical figures with uncalibrated rulers and compasses.

The four-color conjecture, one of the three major mathematical problems in the modern world, was put forward by Britain. 1852, Francis guthrie, who graduated from London University, came to a scientific research unit to do map coloring and found an interesting phenomenon. It seems that every map can be painted in four colors, which makes countries with the same border painted in different colors. Can this conclusion be strictly proved by mathematical methods?

He and his younger brother, Grace, who is in college, are determined to give it a try. The manuscript papers used by the two brothers to prove this problem have been piled up, but the research work has not progressed. 1852, 10/0 On October 23rd, his younger brother asked his teacher, Morgan, a famous mathematician, for proof of this problem, but Morgan failed to find a solution to this problem.

So I wrote to my good friend, Sir Hamilton, a famous mathematician, for advice. Hamilton demonstrated the four-color problem after receiving Morgan's letter. But until the death of 1865 Hamilton, this problem was not solved.