# Understanding ∏ and other mathematical constants

1. May 17, 2014

### Niaboc67

What exactly is ∏? I've never quite understood why it is apparent in so many different equations and formulas. Why is it there? Why is it apparent in nature so much? And ∏ it's just a infinite set of numbers why is it any more relevant than any other set of infinite numbers. Why is 3.14.... so important to the fundamental properties of this universe. The same goes with e and ψ and Ω and every other set of numbers. Are all constants just sets of infinitely repeating numbers that are set into different sequences?

I am in need of some demystification. Thank you!

2. May 17, 2014

3. May 17, 2014

### HallsofIvy

First, $\pi$ is NOT an "infinite set of numbers". It is a single number that happens, like almost all real numbers, to have an infinite number of digits in base 10 notation. And I don't see anything special about "$\pi$". It doesn't seem, to me, to be any more important than "e" and considerably less important than "0" or "1"!

4. May 17, 2014

### Niaboc67

I still do see why ∏ possesses this quality. What makes it any different from using other numbers? why is this set of numbers used as opposed to any other set of numbers, or single number as referred to? 3.14159265359, does it just so happened to be that number you get for the ratio of any circles circumference to it's diameter? so anytime we are referring to ∏ automatically it is in some relation with circles?

5. May 17, 2014

### micromass

Again, $\pi$ is a single number, not a set of numbers.

Yes, $\pi$ is defined as the ratio of a circle's circumference to its diameter. If you take an arbitrary circle and calculate that ratio, you will get $\pi$ (more or less exactly depending on your accuracy of measurement).
Any other use of $\pi$ must somehow have been derived from this definition. So everywhere you use $\pi$, there must have been some relation to circles, although this relation is sometimes very difficult to discover.

6. May 17, 2014