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Crosspost/Re: pi Gets Fixed (what's up with this guy?)
Posted:
Jul 5, 1996 7:11 PM


***begin forwarded post***
( found this on sci.skeptic, in case you want to track the author down and flame him (i've gotta make it *sort of* difficult;) > > Determining the Correct Value of pi > > The following insight into one of the profoundest mysteries confronting the > easily confused, resolves several questions while leaving others conspicuously > open. The value of pi is derived by dividing the circumference of a circle by > its diameter; a simple mathematical exercise that yields a frustratingly > irrational number. What confounds some is that pi should be an integer, > having no fractional component whatever, yet the most powerful computational > resources available can find no end to the fractional component the formula > returns. The solution is simple. > > The diameter of a circle is a measure of physical space, the circumference of > a circle is likewise a measurement, pi is the relationship between these > measures. The confusion exists because those hoping to describe a circle > have thought only in terms of numbers without considering what the numbers > represent. The fractional portion of pi historically derived from the > calculation of C/d belongs to one of the measurements and not to the > relationship between them. > > Suppose we calculate the diameter as d = d + (pi  3) and then use that value > to determine the curcumference of a circle, C/d = 3. We now have a rational > constant. There's good reason for doing this. By transferring the irrational, > fractional component to the measure of the diameter, we introduce another > value that accounts for the minute errors inherent in measuring anything, a > value we can call the Rendering Error. This leads to a more effective way to > measure not only circles but anything having physical dimentions. The actual > numerical value of the Rendering Error (RE) is, .0471975, so we can compute > the circumference of a circle this way, > > d (in some units of length) = d+(d*RE) > and then, > C=d*3 > > Consider that adding the fractional component of pi to the diameter of a > circle introduces very large Rendering Errors for small diameters yet is > insignificant for larger ones. This suggests yet another mistake traditionally > made is these kinds of measurements. Since all circles are always exactly > defined as a circumference of length d*pi regardless of their actual size, > the units of measure are irrelevant. It is far more informative to use a > fixed number of units to define a circle and then solve for the magnitude > of each unit. If we decide that all circles will have 1000 units for their > diameter and then divide the length unit by 1000 we achieve the same result > but in a way that reflects the unchanging description of the circle. A > circle having a diameter of 6 inches, for instance, is described as > d = 6 (units of length)/1000. > > Recall that, since the irrational, fractional component of pi is transferred > to the diameter as a Rendering Error, the value of the fixed 1000 units is > really 1000.1459..., an insignificant quantity. If we further distribute > that Rendering Error to each unit, the error becomes, 1.0001459..., far > beyond the precision required for most measurements. This phenomenon is > somewhat analogous to the Nyquist number in its effects. By increasing the > sampling rate (the number of fixed units used to define a circle), we > increase the resolution of each variable unit of length. > > To determine the true diameter of a circle, then, we establish some fixed > number of units plus the fractional portion of pi, use pi as a true constant > (3), distribute the Rendering Error to every fixed unit and divide the > variable unit of length by that number. Presto! We have solved the problem of > pi being an irrational number, created a meaningful formula for calculating > the circumference of circle and cleared up the fuzzy thinking that created > all the confusion in the first place. > > Does this mean that the ancients and the authorities they referred to > for these kinds of questions were as unsophiscated as some claim or > that the books and other sources they trusted are invalidated because the > value of pi was given as 3? Apparently not. Will any of this make the > slightest difference to those who've founded their prejudices on a > faulty definition of pi? Probably not. Even if no one accepts my > revised formula for calculating the value of pi, it seems pretty > interesting and should lead to some fruitful pondering in related > areas. > > > Bill
Actually, pi is a clever joke a couple of alien mathematicians came up with several thousand years ago. When they retired to Greece, they thought it would be a great laugh to keep the natives confused about mathematics for the next several thousand years!!:@)
 "New ideas come to be accepted not because their opponents come to believe in them, but because their opponents die and a new generation becomes accustomed to them" (Planck's other constant)
Post Food for The Mind, Not Spam!!!



