But there are many ways to use other tools. The method is as follows:

Archimedes ruler trigonometry

Drawings:

1. Set any acute angle AOB；;

2. Take O as the center, make a circle O, ∠AOB and the circle intersect at point A and point B;

3. Extending BO to a considerable distance;

4. use a ruler to intersect with the circle o, one point is a and the other point is p;

5. At the same time, the extension line of ruler and Bo intersects at point C;

6. Adjust the position of the ruler appropriately so that PC = ao.

7. If communication is connected, ∠ACB=( 1/3)∠AOB.

It can be proved from the relation that the outer angle of a triangle is equal to the sum of two non-adjacent inner angles. (omitted)

Note: Although this method does not conform to the conventional ruler drawing, it provides a convenient and correct excellent means for triangulation in practical work.

Anasargeras studied "finding a square so that its area is equal to the area of a known circle" as a ruler drawing problem. At first, he thought the problem was easy to solve, but he spent all his time and got nothing. Anna Sa Golas was released from prison after rescuing her friend and politician Pericles. He published the questions he thought of in prison. Many mathematicians were interested in this problem and tried to solve it, but none of them succeeded. This is the famous problem of "turning a circle into a square".

The crescent area was proved by Xipolati before 2000, that is, the left figure: area (semi-circular AEC)= area (fan-shaped AFCO). His method is simple and ingenious, which makes people full of hope. It was not until Lin Deman proved that pi was greater than this number that he realized that it was impossible.

(Reprinted)