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(pi*d)+D=c
Even in wikipedia ,there is no proof that pi is a fixed number.How the mathematicians agreed ?https://en.wikipedia.org/wiki/Pi
It is approximately equal to 3.14159
its decimal representation never ends and never settles into a permanent repeating pattern).
Then it must be inner circle pi * d = Couter circle pi * (d+D)=C
where D is the diameter of the circles line.
Quote from: Thebox on 11/09/2017 16:07:18Then it must be inner circle pi * d = Couter circle pi * (d+D)=CI'm impressedQuote from: Thebox on 11/09/2017 02:03:40 where D is the diameter of the circles line. I understand what you mean but it would be better to describe D as the thickness of the line. Then your formula works. If you describe it as the diameter of the line it assumes measured from one side of circle to other and formula would be different eg. Inner diameter and outer diameter of line.
So they just determined ... Pi is a fixed number
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I would of thought that the thickness of the line would represent the depth of the line. Would it not be better to maybe say:Where d is the diameter of the inner circle and D is the diameter of the boundary line between inner and outer circle?
Quote from: Thebox on 11/09/2017 19:23:44[I'm impressedQuote from: Thebox on 11/09/2017 02:03:40 I would of thought that the thickness of the line would represent the depth of the line. Would it not be better to maybe say:Where d is the diameter of the inner circle and D is the diameter of the boundary line between inner and outer circle? Ok, bear with me here because we are using different terminology.To me a diameter is the measure from one side of a circle to the other across the centre, whereas the measure of the thickness of the boundary line would not cross the centre so I wouldn't call it a diameter.Draw 2 circles with same centre - you're good at drawing - call diameter of inner circle d1 and outer d2. Then d2-d1=half the distance between the edges of circles i.e. the thickness of the distances between their circumferences.
I have not seen proof that a pi of a 1 mm round closed line,Equal to the pi of a 100 mm round closed lineYou will not find such proof in Wikipedia as well.
d2 - d1 would not equal half the distance between circles.
It would have to be:+d1=halfway of the thickness between circles?
Quote from: Thebox on 12/09/2017 12:14:16d2 - d1 would not equal half the distance between circles. Sorry, I wasn't clear enough. The distance between the circles - the blue line in your diagram - is Quote from: Thebox on 12/09/2017 12:14:16 It would have to be:+d1=halfway of the thickness between circles?Yes, that is also correct. It is the diameter of a circle whose circumference is exactly halfway between the inner and outer circles.Now I'm doubly impressed. Not only are you using math to correctly describe your ideas, but you are also thinking real maths and making useful conclusions.