How to measure perimeter without pi?

[menniandscience]

how to measure perimeter without pi? [before they knew about the pi ratio]

 

[Hurkyl]

I don't understand the question.

 

[menniandscience]

I don't understand the question.

how pi was discovered?

 

[chiro]

how pi was discovered?

Look up some info on archimedes.

Basically the way that pi was discovered was to inscribe a polygon in the circle and measure the sum of the sides. So basically you approximate the circle by some uniform polygon (each side is the same size) and add up all the sizes.

Then you basically increase the number of sides that the polygon has and you find that the ratio of the perimeter of the circle against its diameter reaches pi.

The same kind of process is used in calculus.

 

[menniandscience]

Look up some info on archimedes.

Basically the way that pi was discovered was to inscribe a polygon in the circle and measure the sum of the sides. So basically you approximate the circle by some uniform polygon (each side is the same size) and add up all the sizes.

Then you basically increase the number of sides that the polygon has and you find that the ratio of the perimeter of the circle against its diameter reaches pi.

The same kind of process is used in calculus.

i know who is archimedes, can you narrow it?

calculus wan't invented - as much as i know- in ancient times. and approximation is not good enough to genralize and find pi. it had to be someother way.
right now if one wants to know how long is permiter he needs to use pi. but to know there is pi - you need to know the premiter in total acuratly and divide by diameter. problem

 

[chiro]

i know who is archimedes, can you narrow it?

calculus wan't invented - as much as i know- in ancient times. and approximation is not good enough to genralize and find pi. it had to be someother way.
right now if one wants to know how long is permiter he needs to use pi. but to know there is pi - you need to know the premiter in total acuratly and divide by diameter. problem

Here is a webpage about pi:

http://ualr.edu/lasmoller/pi.html

Also the analogy between Archimedes with pi and Newton/Liebniz with calculus is the concept of using limits to find certain quantities. That's what I mean when I use those two things with the same analogy.

 

[g_edgar]

the fact that circumference/diameter is the same for all circles is in Euclid, so it predates Archimedes.

 

[HallsofIvy]

Yes, but Archimedes was the first to give a really good calculation of pi- that pi is less that 3 and 1/7 but larger than 3 and 10/71.

In fact, in the bible (I forget which chapter and verse) there is a reference to a cauldron that has circumference 3 times the diameter- so you could say that the earliest approximation to pi was just "3".