Am I missing something here? How is this not the exact same definition? The rings have a circumference of 1 and they rotate in a circle. So it's effectively a unit circle.

>>15390934 (OP)

Actually it's even dumber because the diameter is 1. So the rings are irrelevant, you just have a vector radius spinning in a circle. It's literally a unit circle.

[eqn]\pi^2[/eqn] is also the circumference of a circle of radious [eqn]\frac{\pi}{2}[/eqn].

I LOVE SCIENCE!

>>15390934 (OP)

What's even more mind blowing is the area of a square with side pi is pi^2.

>circular reasoning 

very talmudic

Women wrote that tweet frfr ong

this is the least interesting thing I've seen in my entire life

and that the hypotenuse of a triangle of sides length pi is pi*root2

semetics is a very broad field

>>15390934 (OP)

It's a figure eight twisted around [math]\pi[/math] radians. The disks have diameter [math]1[/math]. The circumference of each circle is [math]\pi[/math] and when it is swept [math]\pi[/math] radians the surface area is [math]2\cdot\pi^2[/math].



So this math fact is actually incorrect. The surface area is double what is stated in the screenshot.

Actually, I did the math wrong. It does end up being [math]\pi^2[/math]. If you can't derive this answer then you don't know very basic geometry and should feel bad about your mathematical education

>>15390934 (OP)

>Am I missing something here? 

Yeah: the outer “half” of the shape has a much larger surface area than the inner “half”. Also consider that that same unit circle placed farther away from the axis of rotation could produce a much much bigger torus, but your calculation “area times radians” would still give the same value.



The correct method uses a double integral; a general theorem about it is Pappus’s Theorem.

Same error.

kek'd

If you take a cross section then it's a disk and then it's just a matter of making sure you "stack" them. The stack is distance to the center multiplied by angle of revolution. This logic checks out, for uniform solids all that matters for surface area and volume is the centroid of the cross section multiples by arc length of the "stacking" path.



Where is the error?

In fact, the uniform cross section could even be continuously twisted and this would still work by untwisting and restacking the uniform sections to get the total surface area and volume

sorry mathguys, but you can't math with infinite transcendental numbers.

>>15390934 (OP)

fucking stupid as hell

this is like saying, we define pi as the ratio of the circumference of the circle to its diameter

or in the case above

pi is the square root of the horn torus whose tubing is of unit diameter

pi is the ratio of a sphere to 3/4 times the cubed of its radius



fucking retarded play of math words



that stupid ass twitter poster wanted to use the words "tubing", "horn torus", "whose" "unit diameter" just to sound fucking smart "pi squared" etc.

>this is like saying, we define pi as the ratio of the circumference of the circle to its diameter

...we do.
