# „Study case“ or solution ?

### „Study case“ or solution ?

„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

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

Archimedes value Pi: 22/7

$$r=\frac{22}{7}$$
$$a=r \sqrt {3,1640625}=\frac{99}{28}\sqrt{\frac{5}{2}}$$

$$A=3,1640625(\frac{22}{7})^{2}=31\frac{397}{1568}$$

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

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 $$\pi$$. Typically we use an approximation such as "3.14" or "22/7" but those are NOT equal to $$pi$$. (My favorite mnemonic, "May I have a large container of coffee" gives $$\pi$$ , 3.1415926, to 7 decimal places) $$\pi$$ is a "transcendental number". it has infinitely many decimal places and cannot be written as a fraction nor even as simple calculation, like $$\sqrt{2}$$- there are complicated formulas for $$\pi$$ to any desired number of decimal places.
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### Re: „Study case“ or solution ?

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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