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Yes, Brotherman, you are the closest to the solution. It does involve a clock face. However the solution is simpler than the one you described.
Brotherman
I'm not really sure but it appears you are hinting at modular arithmetic or clock mathematics. If so I am not sure how you use this to solve for area of a circle. I said before that it is possible to basically turn your circle into a polygon, I just don't remember exactly how that worked to calculate the area the more you evenly slice up the circle the closer your going to be to the area in which this method requires not a circumference nor pi. If it is clock arithmetic I'm interested in hearing how this works
so then you are using modulus 11 (if you are using 10) or you are using a different modulus in increments of 10 parts from 12 divided by Pi? or something to this effect? so essentially you are trying to gain the remainder to describe the amount of time or area inside your circle?edit on 10-12-2013 by Brotherman because: (no reason given)
so say every 10 minutes the clock moves 5inch
10M=5in there is 60inch on the face of the clock so equally 1Minute=1inch if this is known then it would be 60*pi?(assuming one increment moves at 5in in a 10min setting which is probably absurd but just for example) Am I getting close to what you are looking foredit on 10-12-2013 by Brotherman because: (no reason given)edit on 10-12-2013 by Brotherman because: (no reason given)
Can anyone offer a formula for the area of a circle that mentions neither the radius nor the circumference of the circle? Clue: This is possible, given enough time.
Yes, of course the the chord, happens to be the same length as the radius. It not the radius, nor is it derived from the radius, as are area-of-a-circle formulas involving the diameter of the circle.
CrastneyJPR
There are 12 points on the clock face, each number is 30 deg apart, any 2 numbers 2 apart are therefore 60 deg apart, measured from centre of circle. Make a triangle, two sides the same length, (radius to each number), and the angle between is 60 deg, and you have an equilateral triangle, all sides, and angles equal - so, all angles 60 deg and all sides equal to the radius (and the chord you've drawn)
so technically you're using the radius (or a value equal to the radius) without realising it.
Ross 54
Yes, of course the the chord, happens to be the same length as the radius. It not the radius, nor is it derived from the radius, as are area-of-a-circle formulas involving the diameter of the circle.
CrastneyJPR
There are 12 points on the clock face, each number is 30 deg apart, any 2 numbers 2 apart are therefore 60 deg apart, measured from centre of circle. Make a triangle, two sides the same length, (radius to each number), and the angle between is 60 deg, and you have an equilateral triangle, all sides, and angles equal - so, all angles 60 deg and all sides equal to the radius (and the chord you've drawn)
so technically you're using the radius (or a value equal to the radius) without realising it.
It's interesting that you should mention an equilateral triangle. The way the solution was presented originally had a larger equilateral triangle. It was drawn between the edge points nearest 12, 4 and 8 o'clock.
The largest possible square, the side being a 60 degree chord on the edge of the circle, from 5 to 7 o'clock points ,is drawn in through one side of the triangle, up to its inside edges, then across. It ends up looking like a crude drawing of a small square house with a large peaked, overhanging roof. The area of the circle is Pi times the area of the square within it.
It seems to be a novel solution for the area of a circle. The way it was presented was very unusual, too.edit on 12-12-2013 by Ross 54 because: added comma