Why is the area a of the circle of radius r a = pi * r2 ?

because the area of a circle of radius 1 is π

:^)

Just set it as an axiom. Any other response would move the goalpost.

File: CodeCogsEqn(1).gif (3KB, 609x84px) Image search: [Google]

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Becouse, pic related. Use transformation [math]x=r \cos(\theta) \wedge y=r \sin(\theta) [/math]

More proofs: https://en.wikipedia.org/wiki/Area_of_a_disk

>>7927290
Then how come circumference of a circle is 2pi r?

>>7927270
>>7927307
You can always use the classic Archimedes (I think) method of trapping the circle between two polygons and taking a limit (you know what I'm talking about right?).
This will give you a converging sequence that converges to pi r ^2 for area or 2 pi r for circumference

File: Pie_Are_Square.gif (939KB, 632x812px) Image search: [Google]

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>>7927270

>>7927299
I hardly believe you remotely know what you just posted
>>7927328
?

>>7927391
Cut a circle into pizza slice. Arrange the pizza slices into approximately a rectangular shape as shown. The hiehg tof this rectangle is approximately the radius of the circle and the length is approximately half the circumference ((1/2)*2pi*r= pi*). The area of of a rectangle is the eight times the length, which is r time pi*r so pi*r^2.

As you cut the circle into smaller and smaller pizza slice it approaches a perfect rectangle.

>>7927402
Nice. Where did you see this?

>>7927402
What is the volume of a pizza height a radius z ?

>>7927391
>thinks nobody knows multivariable calc
Yeah, fuck off high schooler.

>>7927391
not him but it's obvious, a double integral over the area that defines a circle -> jacobian -> integral.
Although to be fair, it assumes a circumeference has 2pi radians

>>7927407
Nice

File: circleAreaProof.png (21KB, 240x260px) Image search: [Google]

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I propose that if you take a shape and translate it, rotate it, cut it, or any combination of them then the area of all the remaining pieces will equal to the area of the original shape. This picture shows a simple proof of the area of the circle. No calculus required.

>>7927420
this

>>7927437

End thread. I'm cringing at the try hard autists ITT.

[math]C=2\pi\ r[/math] is the circumference of a circle, and the transcendental number [math]\pi[/math] is computed from this formula. If you want to figure out the mysteries of pi, start with that one theorem that demonstrates how with a unit closed line segment the circle maximizes internal area. (the name of the theorem escapes me currently)

>>7927391
>?
It's a gif, click on it.

>>7927437
Well, some mathematical analysis is needed, becouse the bases of those triangles are infinitesimal

>>7927666
>non-mathematician detected
yes what you said is "true", but laughably moot

>>7927629
What is this?

>>7927629
this is pseudoscience