What are the three famous problems of ancient times?
short answers for big questions
The three famous mathematical problems of ancient times had their origin in the Ancient Greece. All of them are geometrical problems and their solution was tried by only using a non measuring rod (without marks) and a compass. These two instruments could only be used according to the rule of the first three Euclid’s postulates. It meant that the rod could only be used to join two points or to extend a line and the compass was only used to draw a circle from one central point and from one point of the circumference. Let’s see the list of the famous problems:
- Squaring the circle
- Duplication of the cube
- Trisection of the angle
These problems have puzzled the Greek ancient mathematicians since they were not able to find a solution that was good enough. Only recently, after 2000 years since the problems have emerged, it was proved the problems didn’t have a solution only by using the two proposed instruments.
What is the squaring of the circle?
It consists in building a square having exactly the same area of a certain circle. In spite of being considered difficult, the problem was not regarded as impossible. Several mathematicians have dedicated lots of time in order to search for a solution.
What is the duplication of the cube?
After being given the length of one edge of the cube, it is meant to build a second cube being twice the volume of the first. The Greek already knew that from a square it was possible to build a second square being twice the area. However, when they tried to apply similar procedures to the cube, they did not manage to arrive to the duplication.
What is the trisection of the angle?
Having an angle with amplitude no matter what, the aim is to divide it into three equal parts, that is, to obtain another one having a third of the amplitude of the first. All over the Internet we can find lots of “evidence” how to do this. However, all of them are false since it is impossible to perform this division.
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