Moving into any direction and reaching at the center is double division.Formula : ((n÷a)÷n) >=-1 and <=+1.

Moving into any direction and reaching at the center is double division. It can be stated as when the numerator will become the divisor of the quotient it will always be a point in the center. Formula : ((n÷a)÷n) >=-1 and <=+1.

Eg: a) A person had 90 dollars and given to 11 persons and out of the 11 person 1 person given what he has got to 90 person. What value is with the 90th person?

b) A person had 50 dollars and given to 11 persons and out of the 11 person 1 person given what he has got to 50 person. What value is with the 50th person?

n=90, 50 and a = 11. 

In both case answer is same ie. ((90÷11)÷90) = ((50÷11)÷50) = 0.090909

If the division process is repeated with the answer ie.  

((0.090909÷11)÷ 0.090909) = 0.090909.

In case of any direction take "n" as a number between 1 to 360 and divide by constant "a" as  number >1. 1 can be marked as a point anywhere in the circumference of a circle as value as a radius indicating direction of a choice.

See image below to know the geometry of the center and there will be fields like spatial frequency wave, sine wave in ascending and descending order and vice versa when more than such centers exist in parallel to each other from a common center..

If a = 0 ; then n = 0+(- or+)+n ;  n/a/n = 0+(+ or-)+n /(+or-)+0/ 0+(+ or-)+n = 1.

Why there is a common center = 1/1/1 = 1 , n/1/n = 1 or 0 , a/1/a = 1 or 0 etc..

When we know the answer need to bother about division by 0. 

Any given number can turn to a constant 9

 Any given number can turn to a constant 9

How to turn any number into single digit number 9. Excel file of calculation :

https://drive.google.com/file/d/0B03s-v1XHNIyOVA1QVFvMUVVc2s/view?usp=sharing

Any given number can be turned to single digit constant 9.
3Rules to Number 9:  Any given number(n) other than 0  can be turned to single digit number 9

1) Sort to Lowest or Lower Value(SLV), then deduct from Given Number(GN)  or RN to obtain Result Number(RN), if  GN is greater than the SLV. eg: n = 6174, SLV = 1467 ie. n-slv

2) Sort to Highest or Higher Value(SHV) , then deduct the SLV from SHV , If the GN or RN and SLV are Equal and obtain RN  eg: slv = 1467 , shv = 7641 shv-slv

3) Add the same number to the GN or RN, if all elements of number is same or single digit number and obtain RN eg: 111 (111+111) and obtain the RN

Repeat the steps applying above rules using RN will convert any  GN to 9

***If Given Number is negative then deduct the sort to highest value in rule 2

Eg: 6174, 9 and 1 are below:

Steps	Number	Input	Lowest to Highest	Highest to Lowest	Result	Rule
1	6174	6174	1467	7641	4707	GGR
2	6174	4707	477	7740	4230	GGR
3	6174	4230	234	4320	3996	GGR
4	6174	3996	3699	9963	297	GGR
5	6174	297	279	972	18	GGR
6	6174	18	18	81	63	HTL
7	6174	63	36	63	27	GGR
8	6174	27	27	72	45	HTL
9	6174	45	45	54	9	HTL

Steps	Number	Input	Lowest to Highest	Highest to Lowest	Result	Rule
1	9	9	9	9	18	EQL
2	9	18	18	81	63	HTL
3	9	63	36	63	27	GGR
4	9	27	27	72	45	HTL
5	9	45	45	54	9	HTL

Steps	Number	Input	Lowest to Highest	Highest to Lowest	Result	Rule
1	1	1	1	1	2	EQL
2	1	2	2	2	4	EQL
3	1	4	4	4	8	EQL
4	1	8	8	8	16	EQL
5	1	16	16	61	45	HTL
6	1	45	45	54	9	HTL

Division by 0 is clearly defined as per the rule of

1) Repetitive deduction with remainder addition back as First Step Rule

2) Rule of Multiplication inverse'  (Error /1)

Any number n/0 = n  or 0;  0/0 = 0  or 1

1) First Step

Eg: 6/2 = 3 , (2 x 3)+0= 6  ;  6/0 = (0 x 1)+6 = 6 ; 7/2 = 3+(1/2), (2 x 3)+1 ; 0/0 = 0 , (0 x 1)+0 =0

Steps 6/2	6	Steps 6/0	6	Steps 7/2	7	Steps 0/0	0
1	-2	1	-0	1	-2	1	-0
	4		6		5		0
2	-2			2	-2
	2				3
3	-2			3	-2
	0				1

2) Multiplication in verse (Error by 1).

Eg: 1/0 = '0/1 x 1/0 = 0/1 x Error = 0/1 x (Error x 1/1) = 0 x (Error/1) = 0

Logical conclusion : We have group of person representing number n and who don't want be  arranged in group (0 Divisions)so the value of number n remain as same. However division by zero is neither Error nor Undefined.
(01 x 09 = 09 = (01+01+01+01+01+01+01+01+01) - (09 x 01)=0, means from 09   nine (9) times 1 can deduct.

or nine(9) times 0 can deduct or nine(9) times 01 can deduct. Hence n/0 = n).

How to turn any number into single digit number 9. Excel file of calculation :

https://drive.google.com/file/d/0B03s-v1XHNIyOVA1QVFvMUVVc2s/view?usp=sharing

Any given number can be turned to single digit constant 9.
                                                                 

3Rules to Number 9:  Any given number(n) other than 0  can be turned to single digit number 9                                                                                           

1) Sort to Lowest or Lower Value(SLV), then deduct from Given Number(GN)  or RN to obtain Result Number(RN), if  GN is greater than the SLV. eg: n = 6174, SLV = 1467 ie. n-slv                                                                                  

2) Sort to Highest or Higher Value(SHV) , then deduct the SLV from SHV , If the GN or RN and SLV are Equal and obtain RN  eg: slv = 1467 , shv = 7641 shv-slv                                                                                             

3) Add the same number to the GN or RN, if all elements of number is same or single digit number and obtain RN eg: 111 (111+111) and obtain the RN                                                                                                                                                                     

Repeat the steps applying above rules using RN will convert any  GN to 9

***If Given Number is negative then deduct the sort to highest value in rule 2

Eg: 6174, 9 and 1 are below:                                                                             

Steps	Number	Input	Lowest to Highest	Highest to Lowest	Result	Rule
1	6174	6174	1467	7641	4707	GGR
2	6174	4707	477	7740	4230	GGR
3	6174	4230	234	4320	3996	GGR
4	6174	3996	3699	9963	297	GGR
5	6174	297	279	972	18	GGR
6	6174	18	18	81	63	HTL
7	6174	63	36	63	27	GGR
8	6174	27	27	72	45	HTL
9	6174	45	45	54	9	HTL

               

Steps	Number	Input	Lowest to Highest	Highest to Lowest	Result	Rule
1	9	9	9	9	18	EQL
2	9	18	18	81	63	HTL
3	9	63	36	63	27	GGR
4	9	27	27	72	45	HTL
5	9	45	45	54	9	HTL

               

Steps	Number	Input	Lowest to Highest	Highest to Lowest	Result	Rule
1	1	1	1	1	2	EQL
2	1	2	2	2	4	EQL
3	1	4	4	4	8	EQL
4	1	8	8	8	16	EQL
5	1	16	16	61	45	HTL
6	1	45	45	54	9	HTL

               

 Division by 0 is clearly defined as per the rule of                                                                                                              

1) Repetitive deduction with remainder addition back as First Step Rule                                                                                                

2) Rule of Multiplication inverse'  (Error /1)

                                                                                                           

 Any number n/0 = n  or 0;  0/0 = 0  or 1                                                                                                         

                                                                                                                                                                                                               

1) First Step                                                                                                       

Eg: 6/2 = 3 , (2 x 3)+0= 6  ;  6/0 = (0 x 1)+6 = 6 ; 7/2 = 3+(1/2), (2 x 3)+1 ; 0/0 = 0 , (0 x 1)+0 =0          

                                                                                               

Steps 6/2	6	Steps 6/0	6	Steps 7/2	7	Steps 0/0	0
1	-2	1	-0	1	-2	1	-0
	4		6		5		0
2	-2			2	-2
	2				3
3	-2			3	-2
	0				1

               

2) Multiplication in verse (Error by 1).                                                                                                    

Eg: 1/0 = '0/1 x 1/0 = 0/1 x Error = 0/1 x (Error x 1/1) = 0 x (Error/1) = 0                                    

Logical conclusion : We have group of person representing number n and who don't want be  arranged in group (0 Divisions)so the value of number n remain as same. However division by zero is neither Error nor Undefined.                                                                                                    

(01 x 09 = 09 = (01+01+01+01+01+01+01+01+01) - (09 x 01)=0, means from 09   nine (9) times 1 can deduct.

 or nine(9) times 0 can deduct or nine(9) times 01 can deduct. Hence n/0 = n).