# Why does Pi go on for infinity?

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• Jan 5th 2007, 01:09 PM
anthmoo
Quote:

Originally Posted by ThePerfectHacker
I never seen one, the best I can do is as follows...

That is a good approach but it seems more algebraic proof then geometric. Are you naturally good at mathematical induction? (If that is what its called..)
• Jan 5th 2007, 01:15 PM
anthmoo
Quote:

Originally Posted by TD!
Why still the gap? The paper doesn't know about real numbers, nor about our concept of 'meters'.
The only problem which we practically encounter is our inability to draw so perfectly.

For us, it's not harder/easier to draw a perfect 3-4-5 (5² = 3²+4²) right triangle, than to draw a 1,1,sqrt(2) (sqrt(2)² = 1²+2²) right triangle, although this last one has a side which has an irrational number as length!

Ah I understand now - blame the imagination, I had an image of a perfect machine (that copes with infinity) drawing a perfect circle and it could never complete the circle..

I've had this problem before, such as with

0.9999999...=1 then i realised 1/9 * 9 = 1

which similarly relates to the point that you made!
• Jan 5th 2007, 01:22 PM
topsquark
Quote:

Originally Posted by anthmoo
Ah I understand now - blame the imagination, I had an image of a perfect machine (that copes with infinity) drawing a perfect circle and it could never complete the circle..

I've had this problem before, such as with

0.9999999...=1 then i realised 1/9 * 9 = 1

which similarly relates to the point that you made!

Well, presumably we can never walk anywhere because you start by walking half the distance, then you walk half THAT distance, then half of that distance, etc, so you can never get to your destination. Blame Zeno (or whoever came up with that concept.) Of course, he never took Physics. :D

-Dan
• Jan 5th 2007, 04:38 PM
Quick
Quote:

Originally Posted by anthmoo
0.9999999...=1 then i realised 1/9 * 9 = 1

just an interesting way to look at it (I know I saw this on the forum here, I just don't know where)

Let's say that $n=0.9\bar{9}$

Then: $10n=9.9\bar{9}$

Therefore: $10n-n=9.9\bar{9}-0.9\bar{9}$

So then: $9n=9\quad\Longrightarrow\quad \boxed{n=1}$
• Jan 6th 2007, 02:09 PM
ThePerfectHacker
Quote:

Originally Posted by anthmoo
Ah I understand now - blame the imagination, I had an image of a perfect machine (that copes with infinity) drawing a perfect circle and it could never complete the circle..

I've had this problem before, such as with

0.9999999...=1 then i realised 1/9 * 9 = 1

which similarly relates to the point that you made!

There is nothing supprising with that. The decimal is Definied to be the convergent. One of the bad things about the reals is the a representation is not necessarily unique like heir.
• Jan 6th 2007, 04:05 PM
TriKri
Quote:

Originally Posted by anthmoo
Does this mean that the ends of a circle do not touch at all? (Apart from at infinity)

A circle is not defined as a line that bends so that it's ends meet (as far as I know), nor is there anything that says a line's length must have a finite number of decimal places. And what unity would the line's length in that case be measured in?
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