Yeah... I worked out the geometry part... I think... and then I can write a program to start at one and keep feeding it the answer from the previous run until the previous answer is VERY VERY close to the current and next solution...
but.... how will I know if I ran it long enough? I mean... I can come up with *A* answer... but I can be 99.9% certain it won't be 100% correct since, even ONE more iteration would either cause me to run out of space in which to store the number, or bring me that much closer to a more accurate answer.
The true way to do this, I think, isn't to figure out the largest radius, but to determine a radius that it will NEVER be larger than, due to the fact that each new increment is smaller than the previous. By drawing it on paper I can say for SURE that it is less than 100. By doing a few runs on paper, I can say for SURE that the number is greater than 7.
The "right" way, I'm sure, is one of those "the limit of r as n approaches infinity" problems that we used to do in calculus.... but I'll be damned if I'm even 100% certain how to DRAW the problem, let alone SOLVE it.
I know from those days that, when you have one of these "limit" problems, finding the biggest radius is not the solution -- finding the radius that is one increment of undetermined accuracy larger than the largest possible value of the radius... THAT's the answer. I can give you an answer accuratue to say... 2 decimal places... how's that sound?
but.... how will I know if I ran it long enough? I mean... I can come up with *A* answer... but I can be 99.9% certain it won't be 100% correct since, even ONE more iteration would either cause me to run out of space in which to store the number, or bring me that much closer to a more accurate answer.
The true way to do this, I think, isn't to figure out the largest radius, but to determine a radius that it will NEVER be larger than, due to the fact that each new increment is smaller than the previous. By drawing it on paper I can say for SURE that it is less than 100. By doing a few runs on paper, I can say for SURE that the number is greater than 7.
The "right" way, I'm sure, is one of those "the limit of r as n approaches infinity" problems that we used to do in calculus.... but I'll be damned if I'm even 100% certain how to DRAW the problem, let alone SOLVE it.
I know from those days that, when you have one of these "limit" problems, finding the biggest radius is not the solution -- finding the radius that is one increment of undetermined accuracy larger than the largest possible value of the radius... THAT's the answer. I can give you an answer accuratue to say... 2 decimal places... how's that sound?
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Using R = L * csc((2*PI/N)/2)/2 I got the same answer over and over when rounded to 2 decimal places.
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Well done, sir.
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