Naked Science Forum

On the Lighter Side => New Theories => Topic started by: SFMA on 09/05/2008 15:29:33

Title: Pi and the circle
Post by: SFMA on 09/05/2008 15:29:33

A circle has a 360 degrees and the pi that describes a circle always produces
new fraction numbers. Can we relate 360 degrees with a pi and why does it never end
producing new numbers? 

Can one reason be that the cycle of the circle is in constant motions. It
needs no external output. It won't break or we can never get the ultimate 
value of a pi?

 

Title: Pi and the circle
Post by: lyner on 15/05/2008 16:15:17

It was quite arbitrary to choose 360 degrees for the circle (a quirk of history) but PI is the same for everyone in the Universe.
PI is not a 'fraction'. It cannot be expressed as the ratio of two integers and neither can it be expressed as the solution of a simple algebraic equation so it's more than just an irrational number - like 'root two'. It is a transcendental number, just like e.  It is   --   just PI! and it comes into many bits of Maths with no particular reference to circles, either.
Beware of getting involved in numbers, too much.
They can make you believe in magic if you're not careful. 

Title: Pi and the circle
Post by: Madidus_Scientia on 16/05/2008 13:04:56

Pi is exactly 3!

Title: Pi and the circle
Post by: caboose17 on 16/05/2008 19:12:45

pi is not infinite as spme people have come to believe. only a few things are infinite in this universe. dividing by zero and thought/ conscience.   

Title: Pi and the circle
Post by: science_guy on 16/05/2008 19:18:59

then again, seeing that thought and concience is indeed possible, would that not suggest that dividing by zero somehow produces a believeable result?

perhaps the fourth dimention is i/0 [;D]

Title: Pi and the circle
Post by: caboose17 on 16/05/2008 20:03:01

the fourth dimension is well believed to me time so i think what you mean is the fifth dimension and the answer being no because a dimension cannot be a number.

Title: Pi and the circle
Post by: lyner on 16/05/2008 21:40:34

Quote from: caboose17 on 16/05/2008 19:12:45

pi is not infinite as spme people have come to believe. only a few things are infinite in this universe. dividing by zero and thought/ conscience.   

How can PI be infinite? It is greater than three and less than three point two.
Dividing by zero is not infinity, it's just indeterminate. No one who actually knows Maths would make such a statement. You can produce absolutely nonsensical answers if you are as cavalier as that with your mathematical processes!

Title: Pi and the circle
Post by: science_guy on 17/05/2008 03:53:47

well actually, the definition of pi is circumference over diameter. the ratio always translates into 3.14... yada yada yada.

the reason we dont know what it is for sure is because the circumference is kind of hard to measure accurately, so we dont get an accurate number for pi

Title: Pi and the circle
Post by: Madidus_Scientia on 17/05/2008 14:03:03

Was just joking btw. Here is the real value of pi, but only to 4 million digits or so. http://zenwerx.com/pi.php

Title: Pi and the circle
Post by: science_guy on 18/05/2008 03:48:58

 [:0] [:0] [:0]

Title: Pi and the circle
Post by: Bored chemist on 18/05/2008 13:57:47

Pi is pretty close to 3, but 3! is exactly 6.
"the reason we dont know what it is for sure is because the circumference is kind of hard to measure accurately, so we dont get an accurate number for pi"
We do know what it is, it's pi. We calculate it as the sum of a series or some such. The series is infinite so you can never finish the calculation. On the other hand you can get any desired degree of accuracy given enough time. The accuracy with which we can measure circles has nothing to do with it.
Pi is finite in the sense that it's less than 4. On the other hand pi, expressed as a decimal number is infinite- it has an infinite number of places of decimals. This is related to the issue of "squaring the circle" and has been proven to be true. Caboose17 is, therefore, talking out of his hat.

Title: Pi and the circle
Post by: lyner on 18/05/2008 22:15:33

You cannot say that 'infinite' means the same as 'represented as the ratio involving a number of infinite length'. That is very loose terminology and not worthy of serious mathematical analysist. It is a number which CANNOT be represented by the ratio of two numbers or as the solution to an algebraic equation. It's part of the set of Number and you can always find two rational numbers whose magnitudes lie on either side of it. That's all.
We could consider a whole set of numbers which are multiples of PI and ratios which involve PI. They would sit in equally inaccessible points on the 'number line' / set of real, rational numbers. Take two rational numbers, as close together as you like and you can find a number, calculated using transcendental numbers which fits between them. There is nothing more 'normal' about the numbers we know and love than all the other ones.
The fact that there is a particular geometrical relevance to PI is only a small part of PI's persona.

Title: Pi and the circle
Post by: SFMA on 19/05/2008 16:45:04

The pi implies that we can never draw a perfect circle!

Title: Pi and the circle
Post by: lyner on 19/05/2008 18:09:47

Of course you can't. It's going to be full of knobbly atoms, for a start.
Maths isn't  real life. It's just a tool, fun though it may be for some.

Title: Pi and the circle
Post by: SFMA on 19/05/2008 18:20:09

The Pi certainly beckons us on further. For example it's impossible to conclude a circle there is always be a subtle slit remaining.

Why is a circle like it is? Until the final answer rests on the finding of its ultimate value what's concrete is its infinity. While the nature is finite it's this infinite stake that she has to place for a possible intersect with the infinite original matter is sensible.

Title: Pi and the circle
Post by: science_guy on 20/05/2008 05:02:11

thats like saying that you can never finish a clap... It can be done, but we just dont know the whole formula [:)]

Title: Pi and the circle
Post by: SFMA on 20/05/2008 10:16:02

Well the mankind have been calculating pi for over 3500 years. We are still
to discover a pattern in its endless fractions that curiously never repeats.
The destination is yet to be reached!   

Title: Pi and the circle
Post by: SFMA on 20/05/2008 22:18:58

By the way circle is the most beautiful shape the nature has. The pi
alone can not determine it.

Title: Pi and the circle
Post by: science_guy on 21/05/2008 03:59:39

pi is actually just a ratio.

The definition of a circle is all points with a given distance, the radius, from a given point, the center.

Title: Pi and the circle
Post by: Bored chemist on 21/05/2008 07:11:25

"By the way circle is the most beautiful shape the nature has."
Perhaps you need to get out more.

Title: Pi and the circle
Post by: SFMA on 21/05/2008 13:15:56

Quote from: sophiecentaur on 16/05/2008 21:40:34

Quote from: caboose17 on 16/05/2008 19:12:45

How can PI be infinite? It is greater than three and less than three point two.

Pi is infinite in the sense that it produces endless digits and  a pattern never appears.

Title: Pi and the circle
Post by: science_guy on 22/05/2008 04:35:28

umm... Did you mean to say something, but forget to include it in you're post?

Title: Pi and the circle
Post by: lyner on 23/05/2008 22:59:10

Are you agreeing or disagreeing or did you just like the classy words?

Title: Pi and the circle
Post by: SFMA on 28/05/2008 15:25:39

Quote from: sophiecentaur on 19/05/2008 18:09:47

Maths isn't  real life. It's just a tool, fun though it may be for some.

Maths is considered as the language of science. If it's not real only a tool what would you say the science is?

Title: Pi and the circle
Post by: lyner on 29/05/2008 00:15:03

The Science is always going to be an approximation to the 'real truth'. Science can only hope to get closer and closer to that truth.
Once Science uses a particular bit of Maths to construct a model you have to accept the consequence that there may be situations which the Mathematical model does not include. However good it is, the Maths will let you down if you follow it blindly.
For instance, you can use Newtons Law of Gravitation to give you some very accurate predictions of planetary motion. The sums are simple but they let you down in the end because you need a new Mathematical model to include the effects of relativity.
I am not 'knocking' Maths; I am just saying that you have to be aware of the limitations. As yet, there does not seem to be a better alternative.

Title: Pi and the circle
Post by: SFMA on 29/05/2008 11:42:25

Quote from: sophiecentaur on 29/05/2008 00:15:03

The Science is always going to be an approximation to the 'real truth'. Science can only hope to get closer and closer to that truth.

What you said here is applies to pi as well. That never end finding the perfect circle but always outpours new digits new hopes. It looks there is
a limit, there is a control. The question is what it's that containing and keeping the ballance? A simple answer could be nature. But can we break it down? 

Title: Pi and the circle
Post by: lyner on 29/05/2008 15:21:17

Why does 'not knowing the whole story' have to involve anything supernatural?
Looking at it that way doesn't help at all; it just clouds the issue.
We just have a basic problem of studying a system which includes us, ourselves. That's Philosophy, that is!

Title: Pi and the circle
Post by: SFMA on 31/05/2008 16:56:42

Quote from: science_guy on 22/05/2008 04:35:28

umm... Did you mean to say something, but forget to include it in you're post?

It does make sense. It always produce new digits and no pattern appears
among these continous digits.

Title: Pi and the circle
Post by: Bored chemist on 31/05/2008 18:35:59

Is this "It does make sense. It always produce new digits and no pattern appears
among these continous digits. " a comment about your post?

Title: Pi and the circle
Post by: MonikaS on 02/06/2008 10:57:08

Quote from: Madidus_Scientia on 17/05/2008 14:03:03

Was just joking btw. Here is the real value of pi, but only to 4 million digits or so. http://zenwerx.com/pi.php

Or perhaps a nice Pi singalong...
http://www.youtube.com/watch?v=27OQfd_Sq4c (http://www.youtube.com/watch?v=27OQfd_Sq4c) [;D]

Title: Pi and the circle
Post by: lyner on 02/06/2008 14:10:52

And what about all the other transcendental numbers?

Title: Pi and the circle
Post by: SFMA on 04/06/2008 15:06:19

Not all are same.

Title: Pi and the circle
Post by: lyner on 05/06/2008 22:47:04

Meaning what?
They are not rational numbers so they 'go on forever' without repeating etc.
They are not solutions to algebraic equations.
In what other way are they different - except that they don't actually equal PI!

Title: Pi and the circle
Post by: LeeE on 07/06/2008 23:50:50

If you can do a bit of computer progamming, it can be fun to work out Pi using random numbers and Pythagorus:)

To initialise, set up two counter variables (let's call them inside and outside) and then, for each iteration in the main loop, generate two random numbers between 0 and 1.  Sum their squares and then take the square root.  If the answer is >=1 add one to outside and if its < 1 add one to inside.  Finally, display the ratio between inside and outside.

Of course, you really have to do a _lot_ of interations, but like I said, it's just for fun:)