an epiphany--
here is a new calc i have on been working on( posted to my facebook page), that sprung from my efforts regarding "lateral tork", for all to inspect( love-it, or leave-it...i feel this way gets the best results)-- :o)
i am having fun with "PI" lately...but not cherry, apple, ect...nope, i am messing with 3.1415...yadda, yadda, into infinity...and even farther than that...and i am definitely messing with it, meaning, i am challenging it, out-right...for me, 3.14 just doesn't "get-it-done", not precisely...so, what to do?? here is what i am trying for everyone to "roll-around awhile"--
"the perfect slice"( "PI", even better)--
well, here is my thinking...360 degrees is a full circle, and i am working on deriving circular motion as of late, as a result of these efforts, i notice that if you slice a 360 degree circle( a pie, ect..), into 10 pieces, you get 36 degrees on the outer edge of each slice...so, the curve is 36 degrees for a circle...and i notice that we got that from division by an increment of ten, which led me to ponder about taking the diameter of a wheel and multiplying by 3.6 , to get the answer...neat, so i took a piece of tape, and marked it, to show the value of 1 inch, and then taped it to a lotion bottle, with a 1 inch top( in diameter), i then marked out a different piece of tape, to display a value of 3.6 inches, and taped it to the edge of the bottle...more neat stuff happened after that...the tape was only a tiny bit short, and then the issue became apparent to me, right way...3.6 is exactly right...but, we need to correlate it to our american system of measurement, to make it work...the degrees don't lie, 360 degrees divided into ten pieces, makes 36 degrees on each edge...period.
--( hmmm...my tape was not a perfect fit around my lotion bottle-cap)--
what to do??, inches "came-up short" a tad, so, i suggest that we utilize a change in measurement, that is based upon divisions of increments of ten( the metric system)...it may be, in this case, that we are having difficulties from trying to calc something with a fractal based system, that is about increments of ten...as a result of this issue, i contend that we might get better results via taking the original 1 inch measurement, and multiplying by a metric value( cm)...so, 1 inch x 3.6 = 3.6 cm in circumference( the distance around the edge)...afterward, we can calc back to inches, to regain our nifty american system of quantifying distances...by multiplying 3.6 x 2.54 to get 1.41732 inches, as the value of the diameter around the lotion bottle-cap that had a 1 inch diameter( across)...i feel that this gives super-good numbers, every time, and if a larger distance is being derived, the distance in feet is then multiplied to get meters...standard to metric, regardless of size, in larger and larger increments...to recap, i will put the math below to inspect--
radius x 2 = diameter
.5 x 2 = 1
diameter x 3.6 = circumference in cm
1 x 3.6 = 3.6
cm x 2.54 = circumference in inches
3.6 x 2.54 = 1.41732<<----short by 2 inches??
as we see, this concept above did not yield the desired "super-good" numbers...but, i feel that the concept is sound...meaning, that going from standard-to-metric, may be a viable option, in some cases, to "sync" the "exponent" to a situation that is best derived with a system of measurement that is not a "fractal one"...the metric system works nicely in decimal form, and is easy to calc with, for this reason-- :o)
"your first guess"--
i seem to be getting good at calcs, and deriving the correct answer without any field work...it occurred to me this morning, that my lotion bottle did not have a "cert" from "lloyds of london", or anywhere else...as a result, my tape was cut "less than nicely"...and it was still really close...this tells me that my first attempt, of 3.6 inches, must be spot-on...and the tape would indicate this fact, if i had a vernier calipers and a square, to cut the tape, and check the circumference to the item i am calcing the circumference of( a 1 inch circular block)...anyway, second guessing yourself is usually not-so-good...although checking, and re-checking, is very scientific...i am just going with "radius x 2 x 3.6 = circumference"...it's right--
the numbers( "the perfect slice")--
( inches) ( inches)
( radius) x 2 = ( diameter)
.5 2 1
( inches) ( "PI") ( inches)
( diameter) x 3.6 = ( circumference)
1 3.6 3.6
--( calc complete...happy time... :o) dancing is permitted depending on venue)--
the way that i know ( on paper)--
the first paragraph above denotes the epiphany for this new way to derive "PI"...if you divide 360 degrees into 10 pieces, you have ten 36 degree slices...this shows that a circle has a 36 degree angle, since 36 degrees x ten = 360 degrees, and if one of the 10 pieces is 36 degrees on it's outer edge, they all are...and it adds up( 360 degrees)--
circular math--
after we agree that the concept above is correct, we can contemplate "circular math"( no pun intended), i suggest, that if you are calcing numbers in two different ways, and each way is regarding the same shape( object), i feel that we will see the same similar numbers being generated, since one of the values is equal in both problems( 360 degrees, in this case), i will show this in numeric form below--
360 % 10 = 36 degrees
36 x 10 = 360 degrees
( diameter) x 3.6 = ( circumference, or "360")
1 inch 3.6 3.6 inches
summary--
here we see the same numbers coming up, again and again..due to the math, relating to the same shape...since the term "circumference" that we utilize when calcing a circle, is congruent with "360 degrees"...they are the same thing, and i suggest that this is the similar value in each problem...lastly, if this new way to calc "PI" is correct at 1 inch, i feel that i will be correct at any value, although i have not "real-world tested" it...at all, the numbers tell the tale--
--( and so, there we have it...the "perfect slice", "PI"...even better)-- :o)
--feel free to tape stuff to bottles of what-you-have at home, and see for yourself( caution...ask mom-or-dad first, definitely applies here though, and i suggest utilizing "validated" measuring tools)-- :o)
best wishes, john kruschke--
