We know that pi is irrational. Also, the radical number 2 is also irrational for example. As we know, to get the geometric length of the radical 2 with a ruler and ruler, we first draw a line segment with a length of 1 unit, and then on the end or beginning of the line segment, we again draw a height equal to one by drawing the unit and connecting the end of the line segment which is considered as height to the other point of the base of a right-angled triangle, as a result, the chord of the obtained right-angled triangle will be the length of the radical 2. Now the question is whether there is another method in Is there a science of geometry that is similar or different from this method to get the length of the pi geometrically? Can we draw a circle with the radius of pi with our knowledge of geometry so far? If not possible, why? Is it related to algebraic or transcendental numbers? Thanks
Hi, see, for instance,
http://www.taharut.org/imo/I5771/Ruler_Compass.pdf
more thanks . but Professor, if a circle with a radius of 1/2 is drawn, its circumference will be π. Correct. Now, in a space outside of the ruler and ruler, if we draw a thread on the circumference of the circle, the length of that thread is equal to the circumference of the circle, i.e. π. But this seems impossible from the point of view of geometrical science, but interestingly, it was found experimentally in this way! What do you think about this? Is it at all because of obtaining the result as fractions like 3/22 and... is it correct? So, how did Ghiyasuddin Jamshid Kashani get a score very close to 3.14? Does any of the professors know the method of the old mathematicians regarding getting a follower? Thanks
Ahmad Jafariaghdam
Dear Ahmad, nice question. But what is it for? It also would be nice to get an answer from you.
My first answer to your question: “Do not trust thee complete content as Yuri gave you the path for!” Imaginary is out!
A litle help:
Where did you get the very exact length of `1´ for the radius from?
Buy more than one ruler, built by different companies. All will differ a bit, not?
So your taking `1´ is on definition, not?
What ever you take `1´, 1[mm] length, 12,093[m] length, ... , the circle constructed by that as taken for the radius, depents on two times this by π .
Now the true (first step for) help:
Take a straight line. Do a circle around one point of that line. Define that path as the lengh `1´. It´s only on measure! The additional constructed two points, the circle will cross the line, define a length on π.
Concrete it is on 1/π . At once I can´t do it better (π as the nominator).
A construct by number-theory is on `transcendental´, yes. π-square by this constructed line too?
A projection of that circle will depent on (number) π too, as I think.