Base 10
Relationship between Base 7 and Base 10
Base 10
Used since from the time of the Sumerians, the Base 10 System is born because the man , having 10 fingers,
simplifies the calculations through the hands.
Then in time it has been adopted from all the people and represents what is necessary in the mathematical language
to every action of our life .
Through a simple reading of Base 10 for us therefore familiar, we can easy characterize which
are the substantial differences between Base 10 and Base 7 .
The numbers that compose Base 10 are: 0 , 1 , 2, 3 , 4 , 5 , 6, 7 , 8 and 9
The more common operations are :
+ ADDITION
: REMOVAL
/ DIVISION
x MULTIPLICATION
The simple operations, how much most complex and articulated , can be developed with whichever numerical base.
Therefore they can be used indifferently to Base 10 as far as Base 7 .
This is the numerical table from 1 to 100 of BASE 10
Adding the numbers that compose
Base 10 obtains the following
Multiplication Times Table
In this second table there are
only the numbers marked in yellow
in the previous Table of left
The table in yellow to the right seems to be much similar to does it look like a CHINESE SQUARE ?
In order to understand better , we begin to analyze the position that the numbers have in their entirety in the yellow
table .
The horizontal line correspondent to number 3 is equal but contrary to that one of number 7 when it comes read from
left towards right .
Same result is obtained reading in vertical the lines of the 3 and the 7.
Also the lines of number 2 and number 8 , like those of the 4 and the 6, like those of 1 and of number 9 has the same
characteristics .
We can try to always trace on the yellow table of the cross-sectional lines; we obtain also for these a perfect harmony
in the positions of the numbers.
All the numbers turn out to be balanced in the comparisons of number 5 that we find in the center position.
This is perfect , but we must to notice that in this balance with the numbers that compose Base 10 are present inside
of the yellow table more or less times .
In the yellow table :
number 1 is present 4
number 2 is present 12
number 3 is present 4
number 4 is present 12
number 5 is present 9
number 6 is present 12
number 7 is present 4
number 8 is present 12
number 9 is present 4
number 0 is present 8
times
times
times
times
times
times
times
times
times
times
Base 7
Relationship between Base 7 and Base 10
Base Seven
The system of Base Seven is composed from the numbers 0 , 1 , 2 , 3 , 4 , 5 , 6
This is the table from 1 to 100 in BASE SEVEN :
In order to familiarize with Base Seven , we make some simple operations:
1+1 = 2
2+1 = 3
3+1 = 4
4 +1 = 5
5 +1 = 6
6+1=10
10+1 = 11
1+2 = 3
1+3 = 4
1+4 = 5
1 +5 = 6
1 +6 = 10
2+6 = 1 1
3 +6 = 12
1x2 = 2
2x2 = 4
3x2 = 6
4 x 2=11
5 x2 = 13
6x2 = 1 5
10x2 = 20
1x1=1
1x2=2
1x3=3
1 x4=4
1x5= 5
1x6= 6
1x10=10
2x1=2
2x2=4
2x3=6
2x4=11
2x5=13
2x6= 15
2x10=20
3x1=3
3x2=6
3x3=12
3x4=15
3x5=21
3x6= 24
3x10=30
4x1=4
4x2=11
4x3=15
4x4=22
4x5=26
4x6= 33
4x10=40
5x1=5
5x2=13
5x3=21
5x4=26
5x5=34
5x6= 42
5x10=50
6x1=6
6x2=15
6x3=24
6x4=33
6x5=42
6x6= 51
6x10=60
Adding the numbers that compose
Base Seven obtains the following
Multiplication Times Table
In this second table there are
only the numbers marked in yellow
in the previous Table of left
The result is amazing.
Same characteristics and harmonies all ready noticed in Base 10.
Using a Base Seven composed from 0, 1 , 2, 3 , 4 , 5 , 6, inside the right table we discover this splendid result :
number
number
number
number
number
number
1
2
3
4
5
6
is present
is present
is present
is present
is present
is present
6
6
6
6
6
6
times
times
times
times
times
times
Six numbers presents , six times present, while the 0 are present only in the external perimeter, nearly to form one
true and own line of border .
This is the magnificent equilibrium of BASE SEVEN.
This magnificent numerical equilibrium obtained with harmonic Base Seven is reflected in all the aspects
of mathematics.
Now, let us build a Numerical Table of Base Seven associating numbers with the seven colors of the rainbow:
First number = 0
Ten numbers
Hundred numbers
BASE SEVEN
NUMBERS
1
2
3
4
5
BASE SEVEN and KOCH CURVE
For more information about it please, visit THE EXAGONAL LATTICE by Prof. Paul Bourke
http://masters.donntu.edu.ua/2009/fvti/hodus/library/article4/article4.html
Which importance must we reserve to Base Seven ?
Which is the reason that equilibrium is reflected in all the mathematic aspects , arithmetician, algebraic and
geometric aspects ?
Why is the history of the number 7 so important?
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