Again... improper equations give meaningless answers.
pi is exact. It is a true and pure relationship. However, dimensions... to use your words, are approximations. There is no such thing as a "perfect" measurement. Measurements can only be taken to factors of precision. Therefore mathematics has what is known as significant digits. So... to answer your question..the circumference of a 10 cm circle is 31 cm. Because math is pure logic... it doesn't care how you feel about the result. It is what it is. The solution of a given equation will never change. If you change the equation, you may get a different answer... but it will always be the correct solution for that equation.
Example. If you had asked what is the circumference of a 10.00 cm diameter circle, then answer would be 31.42 cm. If, however, wanted the circumference of a circle with a diameter greater than 9 cm but less than 11 cm.... you would have defined a 10 cm diameter and the answer would be 30 cm- exactly. No probabilities involved. Always exactly one unchanging answer to every equation.
In summary... being pure and perfect logic, math is pure and perfect. It doesn't care about your world view, philosophy, likes or dislikes... it is always what it is and not subject to any "external" influences. People may not like it but math doesn't care. You have been striving to show pi as something "unknown". It isn't. it is a true and pure ratio. I'm believing you are basing your belief upon the fact that from time to time someone factors pi to another place. Remember how I said that applying logic to faulty assumptions will result in incorrect conclusions? You seem to keep trying to show that pi defines circumference. It does not... the relationship between the circumference and the diameter of a circle define pi. The only way to calculate pi to additional precision... is to be able to determine the diameter and the circumference of a circle with greater precision. pi doesn't change - the ability to measure to greater precision is discovered. With the question you posed... you were attempting to corrupt logic by not understanding the question you asked. Math doesn't care if you are wrong. It will continue to be what it is and give you a solution to the equation offered. And it won't care if you try to interpret it as something else.
I've tried to logically explain it. I doubt that it will make any sense to you. A week or two ago you insisted that shape is defined by dimensions... when by definition a shape is not constrained by dimension because that is a function of scale. A few months ago you insisted that Linux cannot be contaminated by malware... when the reality is that it has and can be. Again, if facts, truth, logic and reality don't exist... no datum point exists for debate.
the question was give me the exact circumfrence of a 10cm diameter circle and you couldn't, 31cm is not the exact circumference, it's an approximation with the data you used in the equation, ie:- pi to 1 decimal place.
no i'm not saying pi defines circumfrence what i said was any equation that relies on pi as a constant is not "pure and perfect".
not disagreeing with you about maths equations/formula being perfect and logical,
just your assumtion that they prove anything and that they only give one answer, the truth is the same equation will give you as many answers that you put the data into them for, and the accuracy of the answer returned is totally dependant on the accuracy of said data.
as you've rightly stated the data depends on the accuracy with which we can measure. so if we can't measure exactly then the equations can not give us exact answers so therefore can only give us approximations and probabilities.
A week or two ago you insisted that shape is defined by dimensions
actually no i never, i was trying to point out to you using your words and arguments that "same shape", if same means identical then the shapes(whatever they are or how you define/measure them) must be identical which would include area taken up by them, but if same meant similar then just how similar is similar for an answer to be correct?
A few months ago you insisted that Linux cannot be contaminated by malware... when the reality is that it has and can be. Again, if facts, truth, logic and reality don't exist... no datum point exists for debate.
again no i didn't, i stated it couldn't be infected with a drive by virus(actually tongue in cheek i said it was virus proof) which it can't as far as i'm aware. malware is not the same as saying virus, virus is a specific type of malware, a virus to survive needs to infect and spread faster than it is killed off in the wild, which again as far as i know it cannot do on a linux machine, more than willing to be proved wrong tho if there is any.
Edited by terry1966, 10 May 2011 - 02:35 AM.