Question

Proving if diameter of circle = 1,
then (2pi) = 4,
then pi = 2

Reference:
https://i.stack.imgur.com/znQDV.png

Answer 1

I would try and help but I cannot view imgur.

Answer 2

Perimeter = 4

Answer 3

Perimeter still = 4

Answer 4

Perimeter still = 4

Answer 5

repeat to infinity
as you can see
pi = 4 !

Answer 6

So this is supposed to be false, and you need to explain why?

Answer 7

I thought of this myself and I'm dying to know why it's wrong.

Answer 8

how did you determine the perimeter of four?

Answer 9

You could do the same thing for the hypotenuse of a right-triangle:

Answer 10

pi is the circumference divided by the diameter. Here diameter is not taken into effect.

Answer 11

My view is that you are simply only diving it by itself to infinity, so its eventually going to get to 4 but wont get there

Answer 12

Oops you're right, I meant to say circumference = 4

Answer 13

how do you know its wrong, bad grade?

Answer 14

It's like common sense that the circumferences does not equal to 4 * diameter

Answer 15

I know that, but I was confused by your confusion. I agree with dude.

Answer 16

Here infinity is not a rational number, so to utilize infinity to find the circumference is inaccurate.

Answer 17

The actual formalized proof of why this doesn’t work is pretty complex and honestly beyond what I’ve actually learned, but this type of approximation only works for the area of the circle not the circumference. You cannot assume that the sum of the horizontal and vertical tangent lines approaches the adjacent arc length on the surface. I believe a better approximation of the arc length is sqrt(x^2 + y^2) but I’m not sure even that would work

Answer 18

I’ll also add that the approximation function will always be outside the circle and thus will always have a longer path length than the circle

Answer 19

@-@

Answer 20

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
the approximation function will always be outside the circle and thus will always have a longer path length than the circle
\(\color{#0cbb34}{\text{End of Quote}}\)

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
this type of approximation only works for the area of the circle not the circumference.
\(\color{#0cbb34}{\text{End of Quote}}\)

Going off what you said, I've decided to add this:

Answer 21

Basically before I had an outer square going in towards the circumference.
Now I added an inner going out towards the circumference.
So the area of the outer square - area of inner square appears to converge to the circumference. lol I'm not sure what the measurements of the inner square are but ye if I was a caveman I'd probably use this method to find pi xd

Answer 22

I would take a string around a cylindrical object and then measure the length of the string

Answer 23

or animal tendon if you wish