„Study case“ or solution ?

„Study case“ or solution ?

Postby Guest » Wed Feb 17, 2021 3:13 am

„The solution of the problem of squaring the circle by compass and straightedge requires the construction of the number √π. If √π is constructible, it follows from standard constructions that π would also be constructible.“
„In 1882, the task was proven to be impossible, as a consequence of the Lindemann –Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients.“
From Wikipedia

This Paper was in the study cases category for the first three days:
https://drive.google.com/file/d/1AruLaitcjlSgIUQOUZ8AQlFk8nZun1zn/view?usp=sharing

It is now difficult to find it among hundreds of other…


related to the topic: How people find out pi? ; Area and circumference of a circle
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Re: „Study case“ or solution ?

Postby Guest » Thu Feb 25, 2021 11:24 am

Archimedes value Pi: 22/7

[tex]r=\frac{22}{7}[/tex]
[tex]a=r \sqrt {3,1640625}=\frac{99}{28}\sqrt{\frac{5}{2}}[/tex]


[tex]A=3,1640625(\frac{22}{7})^{2}=31\frac{397}{1568}[/tex]

[tex]A=(\frac{99}{28}\sqrt{\frac{5}{2}})^{2}=31\frac{397}{1568}[/tex]
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Re: „Study case“ or solution ?

Postby Guest » Sat Feb 27, 2021 3:37 pm

What do you mean by "find out pi"?

I believe it was Archimedes who first determined (or he copied what some other person had said- ancient Greece didn't have copyright laws) that the circumference of any circle is a constant multiple of the diameter. We call that constant [tex]\pi[/tex]. Typically we use an approximation such as "3.14" or "22/7" but those are NOT equal to [tex]pi[/tex]. (My favorite mnemonic, "May I have a large container of coffee" gives [tex]\pi[/tex] , 3.1415926, to 7 decimal places) [tex]\pi[/tex] is a "transcendental number". it has infinitely many decimal places and cannot be written as a fraction nor even as simple calculation, like [tex]\sqrt{2}[/tex]- there are complicated formulas for [tex]\pi[/tex] to any desired number of decimal places.
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Re: „Study case“ or solution ?

Postby Guest » Sun Feb 28, 2021 11:56 am

What do you mean by "find out pi"?



simply make a segment of length Pi
https://youtu.be/Z0UIshe0Fx8?t=408
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