Divisional Segmentation
Abstract:
In this article I purpose the use of triangulation, divisional segmentation, mathematical logic and scientific method to create a comparison of accuracy to define the area and circumference of a circle or sphere.
Question One:
Is divisional segmentation more accurate for the precise calculation of the area and circumference of a circle or sphere?
Question two:
If the use of 3.14159265358979323846264 is correct is it mathematically usable to calculate the area or circumference of a 360 degree circle or sphere?
Research:
I first conducted this mathematical calculation without researching previous calculations and after identifying a whole number of divisional segmentations which functions, then a search was conduct where I discovered that Babylon had concluded the same information. Where I found a nonprofit organization detailing historical information about the origins and history of Pi. This information was found on: https://www.exploratorium.edu/pi/history-of-pi
Hypothesis:
That the use of divisional segmentation is more accurate when calculating the circumference or area of a circle or sphere in reference to today’s representation of 3.14159265358979323846264.
Calculation Experiment:
(Defining divisional segmentation intervals using mathematical methods)
Let’s begin:
Here is defined a simple concept for segmentation of a 360 degree circle or sphere verified forwards and backwards using division and multiplication.
An interesting calculation occurs at 360 divided by 115.2
360/115.2=3.125
3.125x115.2=360
So, our segmentation at 115.2 of the 360 degree circle of sphere ends on a whole number directly at 3.125. No repeats and no irrational actions.
But how can we use this?
If 1 equal 360 this is the completed circle or sphere. We can then start to use this to create an area calculation.
81 x 3.125 = 253.125/360 = 0.703125
This says that each degree from a 360 circle or sphere is a segment of 0.703125 of the area 253.125.
The area of 253.125 contains at each degree a measurement of 0.703125 and completes a 360 degree circle or sphere.
So, if we do not want to use a decimal point function, we can use two whole numbers:
360/1152 = 0.3125
Zu Chongzhi (429–501) 355 at 113 not quite, 360 at 1152 is the correct answer.
Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for Pi.
One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for Pi which is a closer approximation. (This is correct at 360/1152)
Let’s reduce this and see what happens:
360/2 = 180
180/2 = 90
90/2 = 45
This is where we lose our whole number so let’s calculate this from 360.
360/45 = 8
360/8 = 45
360
⸺
45
Is equal to when reduced using only whole numbers
45
⸺
8
Reducing this further removes the whole number which we want to maintain so no irrationality
appears and for simplicity.
So, let’s attempt to use this divisional segmentation for calculation:
360 = 253.125
253.125/45 = 5.625
5.625/8 = 0.703125
0.703125x360 = 253.125
Here we reduce the numbers to the lowest and back to determine accuracy without loss of data.
Before we move on, I want to explain this next bit of information. The number 3.125 is not an ending point of the number. The number actually continues but because the calculation and methods used for mathematics don’t include the remaining information, we assume it ends. It actually looks like
this:
3.1250000000000000000000000000000000000000000000000000000000000
Let's start by extracting and triangulating our comparison with Egypt at 3.16 now how did they get this number?
1/360 = 0.00277777777 x114 = 0.31666666578
Now when you calculate that backwards its over 360 its 361. (calculator flaw)
So, 3.16 is close but not quite. We don't want irrational (333666777999) numbers here so let's go backwards and verify it.
3.16 x 114 = 360.24 <--- we are so close but not quite.
The .24 remains over 360 so we regress again by reducing the number by one. We will use the process of elimination:
3.15 x 114 =359.1 <--- we went to low.
3.155 x 114 = 359.67 <--- here its higher
3.1559 x 114 = 359.7726 <--- almost but not there yet.
3.156 x 114 = 359.784 <---- bit more
3.157 x 114=359.898 <---we are so close!
3.1577 x 114 = 359.9778 <--not yet.
You continue this process till you reach 3.15789473684210526 by adding an additional number by
increasing by 1 digit without allowing the process to go over the desired 360.
Let's do this all together:
1/360 is 0.0027777777 x 114 = 0.31666666666
0.31666666666 x 360 = 114 divided by 360 - 0.31666666666
I think this is what Egypt used to identify the 3.16 at 114 markers.
So, 3.16 x 114 =360.24
360.2400/114 = 3.16 when entered into a calculator.
So, math says we remove this from the remainder through even segmentation.
0.2400/114 =0.002105263157894736
Now we subtract from 3.16 and you get 3.15789473684210526315789474
3.15789473684210526315789474x114 = 360.00000000000000000000000036
3.15789473684210526315789473x114 =
359.99999999999999999999999922
This is a fluctuating number which identifies that the correct number exists between a difference of
less then 1.
When this is repeated you reduce the number, it continues to repeat 3.15789473684210526 which identifies it as a digit between 26 and 27 as shown below.
3.15789473684210526x114 = 359.99999999999999964
3.15789473684210527x114 = 360.00000000000000078
Remember this is a fluctuating number which identifies that the correct number exists between a difference of less then 1.
Now let’s confirm this number another way:
360 divided by 114 gives us a repeating digit of 3.15789473684210526 which mathematically produces the mystical repeating digits of a radial curve.
360/114 = 3.15789473684210526
When calculated back using multiplication we get:
3.15789473684210526x114 = 359.99999999999999964
This gives us a remaining amount of 0.00000000000000036 which is very close.
We can then extend that digit by either allowing the repeat to continue or by extension of the original number for instance:
3.15789473684210526315789x114 = 359.99999999999999999999946
360-359.99999999999999999999946 =
0.00000000000000000000054
0.00000000000000000000054 remains when we do this and due to its ability to be instantly reduced by the repeating digit, we can define the accuracy as far as we want beyond even the atomic scale to such an extent, we would be accurate to 1/100000 of a quark and even more if you continue to extend.
So, what do we do with our remaining number?
If we choose we may calculate that back into our total circumference or area calculations, you simply treat the remainder as the circumference or area integer and add it to your total as seen below:
360/114 = 3.15789473684210526315789
(This integer was extended but the method is the same for any)
3.15789473684210526315789x114 = 359.99999999999999999999946
360-359.99999999999999999999946 =
0.00000000000000000000054
0.00000000000000000000054x 3.15789473684210526315789 =
0.0000000000000000000017052631578947368421052606
We will use 81 as this is simple as area and circumference at 9x9 or diameter as 81:
81x3.15789473684210526315789 = 255.78947368421052631578909
255.78947368421052631578909+ 0.0000000000000000000017052631578947368421052606 =
255.7894736842105263157907952631578947368421052606
Our absolute area or circumference calculation is:
255.7894736842105263157907952631578947368421052606
Regardless of what Pi you use this method is the same.
Data/Analysis:
Now let’s compare this to other Pi calculations side by side:
255.7894736842105263157907952631578947368421052606
(3.15789473684210526315789)
253.125
(3.125)
As you can clearly see there is a difference between these calculations.
0.0000000000000000000000000000000000000016 is the size of a Planck length.
So, using the values present we can determine at a scale in conjunction with our calculation and segmentation we can go far beyond the scale of a quark by easily repeating the digits as seen below:
81x3.15789473684210526315789473684210526315789473684210526315789473684210526315789 =
255.78947368421052631578947368421052631578947368421052631578947368421052631578909
360-359.99999999999999999999999999999999999999999999999999999999999999999999999999946 =
0.00000000000000000000000000000000000000000000000000000000000000000000000000054x
3.15789473684210526315789473684210526315789473684210526315789473684210526315789
=
0.0000000000000000000000000000000000000000000000000000000000000000000000000
017052631578947368421052631578947368421052631578947368421052631578947368421052
606
255.78947368421052631578947368421052631578947368421052631578947368421052631578
909+
0.0000000000000000000000000000000000000000000000000000000000000000000000000
017052631578947368421052631578947368421052631578947368421052631578947368421052
606 =
255.78947368421052631578947368421052631578947368421052631578947368421052631579
079526315789473684210526315789473684210526315789473684210526315789473684210526
06
Here we are mathematically over double the calculation of a Planck length. As such you might be off by a small amount, but that amount is at a value far past the atomic structure itself. Far beyond the value of a quark. Far beyond the value of a Planck length.
To determine which calculation is true we must perform an experiment to finalize what calculation is determined to be physically correct.
Physical Experiment:
(Physical experiment proposal)
This experiment will verify the results and considering the use of 3.14159 is used today, if both the above calculations are incorrect it shall appear as the result of the below experiment. One of three
results will be verified:
3.125
3.15789473684210526315789
3.14159265358979323846264
Take a micrometer and a vernier caliper and a cloth measuring tape to determine using all 3 which
reverse engineered radial curve is accurate.
The experiment will use a approximate 1 inch cylinder, measured by the micrometer to obtain the
diameter. The circumference will be verified by extending the measuring tape around the cylinder
and then extending it to full length and obtaining the circumference for physical measurement using
the vernier caliper.
The calculation of the diameter will use the mathematical equation:
C= circumference
D= diameter
π= Pi
C= π x D
Where it will be checked using the following formula:
C= circumference
R= radius
π= Pi
C= 2πR
These will be verified by calculation of the area from both entries using the following formulas forward and backward:
R= D / 2
A= π * (R * R)
This will be re-verified by measuring the micrometer using the interior vernier calipers measurement to re-verify each number for accuracy.
Once all measurements and numbers are acquired and verified, we should have ourselves a quantified result of which calculation is accurate.
Variables:
3.125
3.15789473684210526315789
3.14159265358979323846264
Diameter one: 1.0087
Diameter two: 0.4292
Tools:
Pittsburgh Digital Micrometer
5-7/8” L x 2-3/8” W
+/- 0.0001” accuracy
Up to 1” or 25mm measurement
Digital read out
Pittsburgh Digital Caliper
6” Jaw depth: 1-9/16” outside jaws 11/16” inside jaws
0.001” or 0.03mm
Digital read out
Controls:
All calculations preformed cannot exceed the circumference or area or diameter amount even when reversed.
All area calculations must be derived from a radius or diameter obtained by measurement or mathematically from a measurement.
All integer values used must be from or equate to a sum derived either by divisional segmentation or by measurement.
All parts of the mathematical calculations must apply a forward and backward algebraic methodology of mathematical logic.
All calculations or divisional segmentation must be derived from 360 degrees or physically from the measurement of a circle or sphere.
Diameter one:
D = 1.0087 -micrometer
C = 3.225 -caliper
1.0087x3.125 = 3.1521875
D = 1.0087 -micrometer
C = 3.225 -caliper
1.0087x3.15789473684210526315789 = 3.185368421052631578947363643
D = 1.0087 -micrometer
C = 3.225 -caliper
1.0087x3.14159265358979323846264 = 3.168924509676024439637264968
3.225/3.19718449489441855854069594527609794785367304451273916922771 (see attached note for full entry one) =
1.00870000000000000000000000000000000000000000000000000000000279089305426356
58914728682170542635658914728682170542635658991947716971143561084
(see attached note for full entry two)
Diameter two:
1.3845/0.4292 =
3.2257688723205964585274930102516309412861136999068033550792171481826654240447
343895619757688723205964585
(see note for full entry three)
1.3845/3.2257 =
0.429209163902408779489723160864308522181231980655361626933688811730787
(see note for full entry four)
D = 0.4292 -micrometer
C = 1.384(5) -caliper
0.4292x3.125 = 1.34125
D = 0.4292 -micrometer
C = 1.384(5) -caliper
0.4292x3.15789473684210526315789 = 1.355368421052631578947366388
1.384-1.355368421052631578947366388 = 0.028631578947368421052633612
D = 0.4292 -micrometer
C = 1.384(5) -caliper
0.4292x3.14159265358979323846264 = 1.348371566920739257948165088
1.384-1.348371566920739257948165088 = 0 .035628433079260742051834912
According to the data none of these are correct but our divisional segmentation is closer to the circumference at 3.15789473684210526315789 but is still not precisely accurate.
Possible Solution:
First understanding that 3.2257 was extracted at approximately 1.0087 and was found at both experiments to be closer than all others. 3.2257 is the closet and most accurate calculation found so far. We can obtain this variable by dividing the circumference by diameter.
There is one calculation that does seem to operate properly to obtain the information of the circumference, but it requires modification of the decimal value by use of true pi simplified (reverse engineering as a two-part calculation):
3.14159265358979323846264 x 114 = 358.14156250923642918474096
360 - 358.14156250923642918474096 = 1.85843749076357081525904
We have determined that a missing integer value of 1.85843749076357081525904 is missing from our circle or sphere.
1.85843749076357081525904 x 3.14159265358979323846264 =
5.8384535681386832994208494001339074123429622656
We now add our value to the total of the area calculation to obtain the complete area of the circle or sphere but requires for the value to calculate a modification of the decimal point.
When applied to our experiment above with the augmented decimal value it only works for experiment one and even then it calculates over the amount which indicates it is incorrect also and that through exponential growth the calculation will be far less and far more away from the exact integer meaning the higher the diameter the less accurate it becomes. When calculation goes to planetary size you will have massive amounts of missing data on a low end and a vast over calculation on the other.
1.0087x3.14159265358979323846264 = 3.168924509676024439637264968
3.168924509676024439637264968+0.058384535681386832994208494001339074123429622
656 = 3.227309045357411272631473462001339074123429622656
When applied to diameter two it goes well over the circumference.
Answer To Question One:
Is divisional segmentation more accurate for the precise calculation of the area and circumference
of a circle or sphere?
Answer:
Yes, it does produce a more accurate integer, and this is present in the data. As we see 1.355368421052631578947366388(one) is closer to 1.384 found from
3.15789473684210526315789 verses 1.348371566920739257948165088 (two) which is further away from 1.384 which is found from 3.14159265358979323846264. Where 3.125 produces a value even further.
Value one: 0.028631578947368421052633612
Value two: 0 .035628433079260742051834912
Answer To Question Two:
If the use of 3.14159265358979323846264 is correct, is it mathematically usable to calculate the area or circumference of a 360 degree circle or sphere as a constant?
Answer:
No and this is because the use of a constant function does not permit the use of a two-step calculation and produces an inaccurate variable due to lack of integer data. While a two-step function can seemingly complete a calculation which is obtained by use of true pi simplified method which takes the Pi integer in reference to a 360 degree circle or sphere to calculate the remaining loss of data quickly it still shows to be over. The missing integers create a pass of data and prove to be less accurate than divisional segmentation as a constant. When calculation begins as a constant
1.85843749076357081525904 is missing from the radius leaving it less accurate than divisional segmentation.
Proposal For Further Experimentation:
I purpose this experiment be conducted with more precise equipment at a facility that can utilize more advanced tools.
My proposal would be to use a laser guided method that is calibrated to remove all errors by calculating the circumference accuracy that monitors the distance traveled as it maps that outside of the object measured. The circumference should then be directly divided by the diameter.
Conclusion:
Mathematical comparison without physical comparison determines that the use of divisional segmentation functions produces when reverse engineering from a 360 degree circle or sphere that the area and circumference sum is modified based on the exact integer used and that each integer
used will produce a different calculation, this would identify that while we currently use a different radial curve, we obtain different area or circumference calculation results exponentially expressed
the larger our diameter or radius becomes.
While using a direct method to create and calculate the remaining loss of data through reverse engineering of the complete circle or sphere we obtain a proper method to identify more accurate
results. While it is clear from the data presented that without being able to reverse the process to verify accuracy, we find the data to be flawed and inaccurate. The use of forward and backward
mathematical functions must be present in order to quantify the result as true and accurate. We also conclude that a rational solution exists and is present which obtains many levels beyond existing concepts of measurement.
The use of direct circumference divided by diameter calculation produces a consistent value at 3.2257 and would be an accurate value based on physical experimentation to determine the radial curve.
