/sci/ - Science & Math

[Anonymous No.6394046]

Prove that pi doesn't equal 4.

>filename

[Anonymous No.6394049]

>>6394046
no

[Anonymous No.6394050]

>>6394046
So I suppose the diagonal of a square which sides measure 1 is 2 units long?

[Anonymous No.6394052]

>>6394050
lol

[Anonymous No.6394054]

>>6394046

A=pi*r^2

radius=0.5

A=pi*0.25

4A=pi

for the square

A_s=1^2

A_s=1

A_s > A, because you took shit away

therefore A_s > pi/4

therefore 1 > pi/4

therefore 4 > pi

therefore 4 =/= pi


||| cogito ergo sum

[Anonymous No.6394057]

>>6394046
The folded square will always be 4 units in length, but even it it folds to the infinitesimal, such that it depicts a circle, it will never be continuous, and it will never accurately depict the circle's continuous circumference

[Anonymous No.6394068]

>>6394054
>A=pi*r^2

Nice one pulling that out of your ass.

[Anonymous No.6394076]

When I was in 3rd grade or something like that we took a rope and put it around a picture of a circle, we then measured the rope and calculated the ratio of its length versus the diameter.

I can't remember how many decimal places we got.

[Anonymous No.6394081]

>>6394057
What proof do you have? Then why does integration work?

[Anonymous No.6394082]

>>6394068
divide a circle into n slices and approximate the slices with right-angled triangles. the area of each triangle is then hr/2, and we see that as n tends toward infinity, the area of the triangles tend to the area of the circle, and n*h tends toward C, i.e. n*hr/2 -> A, n*hr/2 -> Cr/2, and because a sequence can only have one limit at infinity, A=Cr/2=π*r^2

[Anonymous No.6394085]

>>6394081
Because it works on areas, not lengths.

[Anonymous No.6394087]

>>6394081
this has nothing to do with integration

[Anonymous No.6394089]

>>6394057
rotate the folded square 45° degrees clock-wise about the center of the circle. it is now continuous.

[Anonymous No.6394094]

>>6394089
that's not how it works

[Anonymous No.6394103]

>>6394089