Starring the Circle: Exploring the Balanced "Circle"lation of Number Sequences

8/14/2019 Starring the Circle: Exploring the Balanced "Circle"lation of Number Sequences

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nn == 00

STARRING THE CIRCLESTARRING THE CIRCLESTARRING THE CIRCLESTARRING THE CIRCLEExploring the Balanced "Circle"lation of number sequences

Joyce P. Bowen, Ph.D.


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STARRING THE CIRCLESTARRING THE CIRCLESTARRING THE CIRCLESTARRING THE CIRCLEExploring the Balanced "Circle"lation of number sequences

Joyce P. Bowen, Ph.D.Joyce P. Bowen, Ph.D.Joyce P. Bowen, Ph.D.Joyce P. Bowen, Ph.D.

JJJJuuuunnnneeee,,,, 2222000000009999

CONJECTURE: Any sequence of numbers placed in a circle, regardless of sign, has

increments that sum to zero with balanced binaries.

This paper is written as a companion document to my two previous publications, The

Law of Digit Balance andBen Franklins Most Magical Magic Square: New Analysis,in order to further illustrate the efficacy of Increment Analysis, the Unimath component

of Uniphysics, the Science of Synthesis. It has been found that ALL number sequences

have increments that sum to zero when zero is added to the beginning and ending of asequence. The reciprocals of seven, thirteen, seventeen, and other circular numbers do notneed zeros; they are naturally balanced without them, and when zeros are added, they

reveal additional balanced binaries.

In this paper, it will be demonstrated that the digits of ANY number sequence, when

placed in a circle regardless of whether positive or negative with random assignment,

sum to zero in all cases. In the examples please note that the iterations are color coded.The original sequence is:

The first iteration is:

The second iteration is:

The third iteration is:

The assessment can be taken clockwise or counterclockwise. They yield opposite but

balanced results; the gold circles represent the increments between two original numbers,and the blue circles are derived from increments between two gold circles. The white

circle numbers are derived from the blue circle increments. Though in this paper I have

only provided three iterations, I have found the system to be effective in four and fiveiterations or more. In order to assess these increments, determine the numerical space

between the numbers in like colors; add the resultants to come up with balanced binaries.For example, in the first circle-starring, the 1 9 sequence of numbers is assessed; theincrements between the numbers in the gold circles were analyzed to get the first

iteration; the blue circles to get the second iteration, and the white to get the third

iteration.

On the next page, the rules of analysis are provided for assessing increments.


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CONJECTURE

RULES OF ANALYSIS1. Select a number sequence and evaluate the increments between

adjacent numbers so that they become positive or negative inrelation to each other. Ignore decimal points and treat thenumber as a continuous sequence. For example, the reciprocal

of seven is a series of repeating numbers 0.01428571:

1 4 2 8 5 7 1:

The increment between 1 and 4 is +3 4 and 2 is 2 2 and 8 is +6 8 and 5 is 3 5 and 7 is +2 7 and 1 is -6

The resulting number string, therefore, is

+3 -2 +6 -3 +2 -6

2. Isolate the resulting binary patterns and cancel them to zero,leaving one or more remainders. In the above case, +3 -2 and 3 +2 cancel each other, and the +6 and 6 also cancel eachother, resulting in 0.

3. To see the underlying patterns of any sequence or sequencesegment that is not a circular number, you add zeros before andafter the sequence and proceed with the methodology outlined innumber 1 above. The digits will always cancel to zero.

4. Though it is important to keep in mind that each digit is anincrement that is ten times more precise than the last in thedecimal expansion of numbers, the numbers are taken at facevalue.


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1 - 9

n = 0 NUMBER SEQUENCE 1 2 3 4 5 6 7 8 9

1st

Iteration +9 -9

2nd

Iteration +9 -9

3rd

Iteration +18 -18

1

6

2

3

4

5

7

8

+9

9 +1

+1

+1

+1

+1+1

+1

+1

-8

+0

+0

+0

-9

+0

+0

+0

+0

+0

+0

+0

+0

-9

+18

-9

+0

+0


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3 5 8 1 2 6 4

n = 0NUMBER SEQUENCE 3 5 8 1 2 6 41

stIteration +10 - 10

2nd

Iteration +16 - 16

3rd

Iteration +27 - 27

3

6 5

8

1

2

4

-5

+1

-11

+1

-10

-6

+8

+3

+3

-2

+7

+2

-9

+3

-1

+1

-2+2

+4

-7

+18


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+1 - 4 + 3 +6 -7 + 4 -2

n = 0 NUMBER CIRCLE +1 - 4 + 3 +6 -7 + 4 -2

1st

Iteration +24 -24

2nd

Iteration +45 -45

3rd

Iteration +86 -86

-4

-2 +3

+6

-7

+4

+1

-41

-4

-12

-8

-16

+9

+24

+12

-17

-16

-17

+20

+26

+3

-5

+11

+3+7

-6

-13

+40


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8 2 9 4 4

n = 0

NUMBER CIRCLE 8 2 9 4 4

1st

Iteration +11 -11

2nd

Iteration +22 -22

3rd

Iteration +40 -40

2

9

4

4

8

-1

-12

-10

+5

+13

+4

-25

-14

+23

-5

-6

+0

+7

+4

+17


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As with my previous publications, it has been found that numbers are arranged in a Grand

Checkerboard of balanced positive and negative integers. Moreover, balanced numerical binaries are characteristic of different sequences: each one has its signature pattern,

which can be called a Phantom Value. The Phantom Value of a sequence is the balanced

binary that results, i.e., +12 -12, +4 - 4, +45 -45, etc. These numbers have meaning,

and it will be interesting to note the relationship between the Phantom Values and thenumber sequences they represent on an operational level.

Why is it important to know that number sequences are balanced, and that the incrementsreveal Phantom Values? The answers to these questions remain to be determined, but

these ideas do provide evidence of a beautiful, non-random, numerical homeostasisextant in mathematics.

-AB+AB

0


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all number sequences, whenplaced in a circle regardless

of sign,

have increments thatsum to zero

copyright 2009 Joyce P. Bowen

All Rights Reserved

Cover Illustration by Yaounde Olu

number theory

Starring the Circle: Exploring the Balanced "Circle"lation of Number Sequences

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