why pi?

[nghosh@india]

why pi is used in math?i mean why always 3.14....

[swansont]

pi is the ratio of a circle's circumference to its diameter. It's a very useful value.

[Moontanman]

I'm sure you know that pi is the ratio of the circumference of a circle to the diameter but my guess it is due to space/time being flat that makes this constant.. well.. a constant. Maybe someone here who knows for sure can inform us..

 

oops, cross posted with swansonT

Edited April 14, 2013 by Moontanman

[Dekan]

OP makes an interesting point. Maths can be done with simple numbers. Without striving for any futile decimal equivalents of Pi.

 

If you want the ratio of a circle's circumference to its diameter, you just take 355, and divide by 113. That gives a value accurate to the millionth part. Which is enough for everything.

 

As Swansont wisely implies, useful values are the most important in Science.

 

 

[Daedalus]

My guess it is due to space/time being flat that makes this constant.. well.. a constant.

 

That would imply that we only know about [math]\pi[/math] because spacetime is locally flat. However, even if spacetime wasn't flat, we'd still know about [math]\pi[/math] due to the nature of circles in Euclidean geometry.

[Amaton]

why pi is used in math?i mean why always 3.14....

 

"Why?" is a question that sits rather uncomfortably in mathematics, for any topic it may hold in question. We can define [math]\pi[/math], describe [math]\pi[/math], show identities, derive relations, etc. in order to answer 'why' on a more trivial basis. Maybe the most intuitive reasoning for [math]\pi[/math] is that it is the ratio between the circumference and diameter of a circle (a bit untechnical phrasing there).

 

However, the fundamental "why" has a more philosophical flavor to it, and these kinds of questions are not so objectively answered.

Edited April 16, 2013 by Amaton

[ewmon]

I think it's easy to see that π is the ratio of two measurements, and that it's a constant that's independent of the size of a circle (shown using geometry). I'm guessing the question behind the OP is, Why 3.14159...?

 

And why isn't it a rational number, seeing as how it's the ratio of two measurements?

 

In other words, we can take a measurement of 1 as the radius and draw a circle, so why is the circumference 2π, an irrational number? How does the making of a circumference "transform" a rational number into an irrational number?

 

I don't think this is too off-topic, but judge for yourself.

[Amaton]

And why isn't it a rational number, seeing as how it's the ratio of two measurements?

 

It's not good enough to just be the ratio of any two quantities. Those quantities in the ratio must be rational numbers themselves. [math]\pi[/math] is irrational by definition. It's impossible to express it as a ratio of any two integers, though actually proving this mathematically is a bit complicated.

 

 

 

In other words, we can take a measurement of 1 as the radius and draw a circle, so why is the circumference 2π, an irrational number? How does the making of a circumference "transform" a rational number into an irrational number?

 

[math]C=2\pi r[/math], which is how we calculate the circumference in the first place. Since [math]\pi[/math] is irrational, [math]C[/math] can also be irrational, depending on what the radius is.

 

You still raise a good point, since this still doesn't settle the question. Why is [math]C[/math] equal to [math]2\pi[/math] times the length of the radius? What intrinsic property of circles makes this fundamentally true (and is there a formal proof)? note: I think this is possible using a bit of calculus and series representations.

Edited April 20, 2013 by Amaton