π=4

first let’s draw a circle with a radius of r, The circumference of the circle is 2πr
images.chesscomfiles.com/uploads/v1/images_users/tiny_mce/Phil224/php1MOqMD.jpg
now let’s draw a square enveloping the circle, the length of the square is 2r, so the circumference of the square is 2r·4=8r
images.chesscomfiles.com/uploads/v1/images_users/tiny_mce/Phil224/phpCLDSc9.jpg
now let’s cut four small squares into the big square, The circumference of the square has not changed. now let’s cut another, no matter how we cut the square its circumference is always 8r, until it finally coincides with the circle.
images.chesscomfiles.com/uploads/v1/images_users/tiny_mce/Phil224/phpZNZuRk.jpg
now The circumference of the square is still 8r, but the circumference of the circle is 2πr. so that means
2πr=8r
πr=4r
π=4
so anyone saying π is 3.1415926... is wrong.

@Phil224 said in #1:
> first let’s draw a circle with a radius of r, The circumference of the circle is 2πr
> images.chesscomfiles.com/uploads/v1/images_users/tiny_mce/Phil224/php1MOqMD.jpg
> now let’s draw a square enveloping the circle, the length of the square is 2r, so the circumference of the square is 2r·4=8r
> images.chesscomfiles.com/uploads/v1/images_users/tiny_mce/Phil224/phpCLDSc9.jpg
> now let’s cut four small squares into the big square, The circumference of the square has not changed. now let’s cut another, no matter how we cut the square its circumference is always 8r, until it finally coincides with the circle.
> images.chesscomfiles.com/uploads/v1/images_users/tiny_mce/Phil224/phpZNZuRk.jpg
> now The circumference of the square is still 8r, but the circumference of the circle is 2πr. so that means
> 2πr=8r
> πr=4r
> π=4
> so anyone saying π is 3.1415926... is wrong.
You're right

note: images.chesscomfiles.com/uploads/v1/images_users/tiny_mce/Phil224/phpbH7ox4.jpg

@Phil224 said in #3:
> note: images.chesscomfiles.com/uploads/v1/images_users/tiny_mce/Phil224/phpbH7ox4.jpg
Yeah

It is incorrect to believe that = 4 since a circle can be adjusted to fit within a square. The square's rearrangement changes the shape of the figure, and it no longer has the features of a circle. 's value is an irrational number that cannot be stated as a decimal or fraction. Its decimal expansion continues indefinitely without repetition. We typically use 3.1415926... as an approximation of since it is a good enough approximation for most uses.

@Phil224
You kinda had me til the last picture when you cut the sides of the square it you can no longer equate it's perimeter to that of the circle inscribed.
Also, it doesn't "coincide" coincide with the circumference of the circle anymore.

Your problem can be solved with a little bit of calculus. So when you integrate the small triangles, it never really becomes linear for you to say that "circumference of square becomes circumference of the circle". Pi is still 3.14.....

You're assumption makes the perimeter of the square > perimeter of circle . And then integrating the small triangles without taking into consideration the infinitesimally small changes. Neglecting that just makes the whole thing incorrect.

If you go deeper into it, it also violates the Pythagorean law. Say AB =1 BC = 1 are the two sides , then the hypotenuse should be root2 but based on your assumptions it's gonna be =2 which is simply incorrect.

Also, consider this : if you were in a race, and had the choice of whether to run on one of two tracks: 1. a square track of perimeter 400 meters, or 2. a circular track that is "inside" the square, touching the square only at the midpoints of the square's edges, which track would you choose?

P.S : I ain't great at explaining Math and going deeper into proofs. Mathematicians on here, feel free to add on to it and correct me if I'm wrong.

also ,
@thalassokrator Please come to our aid and guide us through this mathematical conundrum !

your in trouble now, phil! :P

you kinda had me for a while until i realized dots arent lines. just because it will melt for our eyes doesnt change that. the 90degree angles will stay and it will be a line, not a dot, no matter how small.

I dont want to waste my brain cells reading some nonesense .
pi= 3.14
You are proving maths wrong bro

Phill stop, please. You will make me forget maths . Ia m sending my Maths teacher at your house ASAP