If we don't know the actual value of PI then how can we use it in formulations or rely on it for real world calculations?

Question

Possible Duplicate:
Do We Need the Digits of $\pi$?

Are we at best, estimating things when we use formulas involving pi to describe the area, etc. of things?

"how can we ... rely on it for real world calculations?" - In the real world, there is no such thing as a "real" circle. The wheels, cans, and other such things are approximations to the real thing; manufacturing will always give things with a few imperfections. — J. M. ain't a mathematician, Dec 30 '11 at 08:02

score 2 · Answer 1 · answered Dec 30 '11 at 07:58

Not being able to write the exact value of $\pi$ does not mean we do not know it. It has many representations.

Some are well known, e.g. "the ratio between the circumference and the diameter of a circle",
Others are less known, e.g. $\sqrt{\sum_{n=1}^\infty \dfrac{6}{n^2}}$

The use of $\pi$ in calculations made in engineering, or physics, or other "approximates" is also fine because you know enough digits of $\pi$ to ensure that the error margin is small enough.

score 2 · Answer 2 · answered Dec 30 '11 at 08:03

2

No: When we say the area of a circle with radius $r$ is $\pi r^2$, and the circumference is $2 \pi r$, those are exact.

Yes: When we say the area and circumference of a circle with radius $2$ are about $12.56637$, those are approximations.

answered Dec 30 '11 at 08:03

Henry

157,058

If we don't know the actual value of PI then how can we use it in formulations or rely on it for real world calculations?

2 Answers2