What is the third quarter angle problem? Why is there no solution to the third division angle, the d

The latest method is the segmented angular method, which can arbitrarily divide any angle.

Summary. Hello dear! I will be glad to answer for you, first of all, it is not that there is no solution to the third part of the angle, but only the ruler and the compass without a scale are used for any part of the third part of the angle without a solution.

If you can use other tools, or special corners, you can still do it by dividing a corner in three equal parts. Second, the three equal parts of arbitrary angles, the double cube, and the circle into a square are known as the three major problems of ruler and gauge diagramming, and their impossibility has long been proven by mathematicians. Third, the process of proof is complex.

Hello dear! I will be glad to answer for you, first of all, it is not that there is no solution to the third part of the angle, but only the ruler and the compass without a scale are used for any part of the third part of the angle without a solution. If you can use other tools, or special corners, you can still do it by dividing a corner in three equal parts.

Second, the three equal parts of arbitrary angles, the double cube, and the circle into a square are known as the three major problems of ruler and gauge diagramming, and their impossibility has long been proven by mathematicians. Third, the process of proof is complex.

The main reason is that the ruler can make all the lines or things with quadratic root numbers, or multiple quadratic root numbers. And the third angle needs to use the third root number, which cannot be made with a ruler.

Trisected angles were one of the three major geometric problems of ancient Greece. The trisect angle is a famous problem in the ancient Greek geometric ruler diagram, and the problem of square and double cube is one of the three major problems of ancient mathematics, and now it has been proved that this problem is unsolvable. The full description of the issue is:

A given angle is divided into three equal parts using only a compass and an ungraduated ruler. Under the premise of ruler drawing (ruler drawing refers to drawing with a ruler and compass without scale), there is no solution to this problem. If the conditions are relaxed, such as allowing the use of graduated rulers, or if they can be used in conjunction with other curves, a given angle can be divided into thirds.

InRuler drawingUnder the premise that there is no solution to this problem.

Septic angles. It was one of the three major geometric problems of ancient Greece. The problem of trisecting arbitrary angles may have appeared earlier than the other two geometric problems, and it is impossible to find relevant records in history.

But there is no doubt that it will appear naturally, and we ourselves can imagine it now. It has been proved that there is no solution to this problem when judging height under the premise of drawing a ruler and gauge.

Definition. In order to illustrate the sufficient and necessary conditions for the possibility of drawing a ruler and gauge.

The first thing you need to do is to translate geometric problems into an algebraic language. The premise of a plane drawing problem is always given some plane figures, for example, points, lines, angles, circles, etc., but a straight line is determined by two points, an angle can be determined by its vertices and a point on each side for a total of three points, and a circle is determined by a point at the center and circumference of the circle.

The latest method is the segmented angular method, which can arbitrarily divide any angle. The key point is to the m power where the longitudinal height is set to 2.

The basis of this problem is still the Liang's three-point angle fixed operation mentioned earlier. The principle is that the angle of the middle part after the quintile is both 1 3 in the upper part and 1 3 in the lower part. Thus, the quintile arbitrary angle can be seen as a continuation of the trisect arbitrary angle.

Fig. 1 is a schematic diagram of the quintile, and Fig. 2 is a schematic diagram of the operation of the Liang's three-point angle setting.

It is impossible to draw with a ruler. It has been proven by Vantis.

However, relaxing the drawing method can be done as well.

It is also impossible to draw 5 equal parts of general angles with rulers.

For more information, you can refer to some books on abstract algebra.