Sorry if it's a stupid question, but I just got out of grade school.
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While this is by no means a mathematical proof, consider this:
You are measuring something with a ruler. You find that it to be 1 and 1/8th inches long. However your measurement may not be exact. Your eye is only so precise. Who is to say that it is actually 1 inch and 9/16ths long> Think about the case when the thing you are measuring is in between the lines on the ruler. What is the value then? In that case you have to guess.
Every single measurement has uncertainty with it because when measuring you cannot be exactly precise.
You may be familiar with the following equation for calculating the circumference of the circle:
C = 2*pi*r or C = pi * D
However when pi was first found they measured the circumference and the diameter.
pi = C / D
Two numbers that can go on forever are being divided by each other. Thus pi must also go on for forever.
I hope this helps. It was not a stupid question by any means.
You are measuring something with a ruler. You find that it to be 1 and 1/8th inches long. However your measurement may not be exact. Your eye is only so precise. Who is to say that it is actually 1 inch and 9/16ths long> Think about the case when the thing you are measuring is in between the lines on the ruler. What is the value then? In that case you have to guess.
Every single measurement has uncertainty with it because when measuring you cannot be exactly precise.
You may be familiar with the following equation for calculating the circumference of the circle:
C = 2*pi*r or C = pi * D
However when pi was first found they measured the circumference and the diameter.
pi = C / D
Two numbers that can go on forever are being divided by each other. Thus pi must also go on for forever.
I hope this helps. It was not a stupid question by any means.
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Rational numbers can be expressed as a terminating or repeating decimal. For instance, 0.15 is rational. 0.333... (repeating) is also rational, and is equal to 1/3.
Irrational numbers cannot be expressed as terminating or repeating decimals. They "never end", as you put it. Pi is irrational; therefore, it never ends. All irrational numbers behave this way. For instance, the square root of 2 is also irrational, and its decimal representation never terminates or repeats.
As to why pi is irrational, there are proofs that show this, but they're pretty complicated; I've not looked at them, but Wikipedia has a page on it ( http://en.wikipedia.org/wiki/Proof_that_… )
Irrational numbers cannot be expressed as terminating or repeating decimals. They "never end", as you put it. Pi is irrational; therefore, it never ends. All irrational numbers behave this way. For instance, the square root of 2 is also irrational, and its decimal representation never terminates or repeats.
As to why pi is irrational, there are proofs that show this, but they're pretty complicated; I've not looked at them, but Wikipedia has a page on it ( http://en.wikipedia.org/wiki/Proof_that_… )