Rhapsody on the Proof of Pi = 4

Correction: when I mark where pi is on the graph, I meant pi/2!
Note: If this video were supposed to be teaching you, I'd probably have to make it boring and say that in one sense of limits, spoiler alert, you actually do approach a circle and a line, solving the apparent paradox by saying that the invariant of length does not hold over infinity. Luckily I am an artist, and this is a Rhapsody, and instead of "learning," you get to actually think, if you like.

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  Education

[demurgos]

In maths, lines have no thickness.

[TheButterbreze]

brain.exe has stopped working and deleted itself

[Ben Ramsey]

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[Benjamin U]

gurl stop fuckin ma braain

[reelle Zahl]

You have it right. Although here is there no slipping in of anything, rather a burying or ignoring of the formal definitions of Length and Measurement.

[reelle Zahl]

There is no "YOU" in Mathematics. That is the first problem. One needs to think of these processes as being purely formal. No sloppy imperfect human interaction happens, only the pure analysis. The collapsing is in a geometric sense perfect: the eckige lines DO converge geometrically. What fails is the measurement: measure-theoretic convergence, and a black-boxed convergence that occurs when computing lengths-via-integrals. I. e., lines L_n —> circle S alone does not imply MEAS(L_n) —> MEAS(S).

[reelle Zahl]

No. If π were rounded, not π but the rounding thereof would be 3. π remains π and his value remains 3,14159… = Lim(3; 22/7; 333/106; 355/113) = etc.

[reelle Zahl]

With respect to multiplication in the group: ℝ u {∞} (one pt. compactification) there exists an isomorphism so that ∞ and 0 are switched. So w.r.t. to multiplication are they similar. Similarity as you correctly observed breaks down with respect to more structure, so that one concludes, they are not the same.

[reelle Zahl]

Almost true. One fine adjustment. She never shows WHY the proof is invalid, but rather THAT it is invalid. The WHY/HOW is as follows: one performs an analysis on the in-Argument-occurring assumptions/principles and terms. Invalidity is shown either by discrediting the principles, the applied logic or uncovering an ambiguous use of terms. Here "Measurement" is being mishandled. Computations computing a length according to another metric… or 1-dim masses of mass-theoretic disjoint objects.

[Kirill Simin]

The sweater sleeves are approaching triangle.

[Zeb Németh]

...Sis?