Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
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!!!
|
|
|
|
