area of a circle (1 Viewer)

[muttiah]

i read in a book that in old times they inscribed a n sided polygon in a circle to estimate the area... but isnt it that u can fit infinity sided polygon in a circle.. so wont the area b infinity?

and how did they get the value of pi?

 

[acmilan]

The area cant be infinity, if you're sticking something inside a circle that has finite area, then the thing you stick inside it must have area less than or equal to it.

To get the value of pi, you inscribe an n sided polygon into a circle of radius 1 (the area of a circle of radius 1 is pi), and then work out the area of this polygon using trig. Take the limit as n->inf will give you the area of the circle, which is pi.

 

[muttiah]

oh ok.. i get the pi bit.. but i dont understand the area bit...

cant u put a billion sided polygon inside a circle? and keep going?

 

[acmilan]

Yes, you can put as many sides as you want. The more sides you put, the smaller the length of the sides becomes. As the amount of sides goes off to infinity the polygon actually becomes more and more like a circle.

Edit: http://ganley.org/software/pi.html


That shows graphically what happens

 

[muttiah]

oh mad.. kk cool....

but in a straight line the value of pi is 2.. in a hexagon the value of pi s 3...

how did they get those values?

 

[acmilan]

Well another way to get pi is using the circumference formula:

C = pi*d, ie. pi = C/d

so in the shapes they take C = perimeter, d = diameter. Thats how they get those values