3.14 vs. 3.141.../irrational pi for a circle

Oct 2019
3
0
US
I realize math can be used for abstraction...

Would using irrational pi for a circle other than 3.14 make the circle more eliptical?
Why use the irrational number for a circle, instead of 3.14, if the irrational size for a circle cannot even exist in reality?
why use it for a circle?
 

Plato

MHF Helper
Aug 2006
22,462
8,633
I realize math can be used for abstraction...
Would using irrational pi for a circle other than 3.14 make the circle more eliptical?
Why use the irrational number for a circle, instead of 3.14, if the irrational size for a circle cannot even exist in reality?
why use it for a circle?
You seem to think that we have a choice? Well we do not.
The diameter is the maximum distance between any two points on the circle.
If we want to know the length of the circumference, distance around the circle, then that number is equal to the diameter times $\pi$.
Moreover the area enclosed is $\left(\dfrac{D}{2}\right)^2\pi$ So we have no choice about the value of $\pi$ it is just given to us by reality.
Here $\pi\approx 3.1415926535897932384626433832795028841971693993751058$ quite a few decimal points.
 
  • Like
Reactions: 1 person

romsek

MHF Helper
Nov 2013
6,647
2,994
California
What the actual value of pi can provide is a measure of the local curvature of space.

If I have this right curvature will increase the radius of a circle while leaving the circumference unchanged.

This would lead to a smaller value of pi than in flat space.

I remember some scifi short story where one of the characters was checking on the local curvature by calculating the local value of pi.
 

topsquark

Forum Staff
Jan 2006
11,552
3,443
Wellsville, NY
What the actual value of pi can provide is a measure of the local curvature of space.

If I have this right curvature will increase the radius of a circle while leaving the circumference unchanged.

This would lead to a smaller value of pi than in flat space.

I remember some scifi short story where one of the characters was checking on the local curvature by calculating the local value of pi.
Is that from "Eon" by Greg Bear? One of the characters did that in that one, too.

-Dan
 

romsek

MHF Helper
Nov 2013
6,647
2,994
California
Yes! That was a wowser of a story.
I have to admit I don't understand how you could calculate the curvature of a space you and your measuring instruments are embedded in.
It seems to me the ruler you use to measure the radius would be curved in just the right way so as to read the same whatever the local curvature.

Probably just my lack of deep understanding of curved spacetime.
 

topsquark

Forum Staff
Jan 2006
11,552
3,443
Wellsville, NY
I have to admit I don't understand how you could calculate the curvature of a space you and your measuring instruments are embedded in.
It seems to me the ruler you use to measure the radius would be curved in just the right way so as to read the same whatever the local curvature.

Probably just my lack of deep understanding of curved spacetime.
Even more difficult to believe is that it also measured \(\displaystyle \hbar\).

-Dan
 
  • Like
Reactions: rico001
Oct 2019
3
0
US
Thanks for the help and feedback everyone. For computer science we make fake circles with squares, like the Bessenham Circle Algorithm, and DDA so I got confused and didn't know, I was wondering about metrology also. There are a bunch of books on squaring the circle. I would probably just use 3.14 (less than pi area) or 3.142 greater than pi, times radius squared. People also use these ideas for art.