Base 10

Used since the time of the Sumerians, the Base 10 System born because the man it found simplifies the calculations through the hands.

Historically other number base systems have been used, but Humans insist on using Base 10 because it is the most convenient for ten fingered beings. Base 10 is the international standard of today and represents what is necessary in the mathematical language to every action of our life.

I think it is unnecessary for anyone, but for starters, I have to say that the numbers of Base 10 are: 0, 1, 2, 3 , 4, 5, 6, 7, 8 and 9.

The more common operations are :

** + ADDITION**

** - SUBTRACTION**

** X MULTIPLICATION**** **

**÷ DIVISION**

In any case, the most simple operations as the most complex and articulated can be developed with whichever numerical Base.

These operations can be used in Base 10 or in any different Base systems (binary, octal, hexadecimal, etc.)

This is the numerical table from 1 to 100 of BASE 10

In order to understand better, we begin to analyze the position of the numbers in the yellow table .

The result is amazing

Base 7

The system of Base 7 is composed from the numbers 0 , 1 , 2 , 3 , 4 , 5 , 6

This is the table from 1 to 100 in BASE 7 :

The positions of number 1 are equals but opposites to the positions of number 6

The positions of number 2 are equals but opposites to the positions of number 5

The positions of number 3 are equals but opposites to the positions of number 4

Number 0 is not present inside, but only on the perimeter

Same characteristics and harmonies all ready noticed in Base 10.

But inside the yellow table, using a Base 7 composed from 0, 1, 2, 3 , 4 , 5 , 6, we have this result :

Six numbers presents , six times present, while the 0 is present only on the external perimeter, nearly to form a line of border.

This is the harmonic numerical equilibrium of Base Seven.

Chromatic Numbers in Base 7

****

Now, let us build a Numerical Table of Base Seven associating numbers with the seven colors of the rainbow.

Our intention is to develop a system where the numbers will be chromatic with the Base 7 characteristics and harmonies.

The result is a polygonal table constructible with elementary geometry.

Hexagonal tiling called a Spiral Honeycomb Mosaic (SHM)

Director - iVEC @ UWA University of Western Australia

SHM consists of groups of 7n hexagons (n > 0) called super-hexagons.

It uses a base 7 numbering system for the hexagonal mesh,

Now we explore the graphic position of numbers on the previous yellow table

The positions of number 1 are equals but opposites to the positions of number 9

The positions of number 2 are equals but opposites to the positions of number 8

The positions of number 3 are equals but opposites to the positions of number 7

The positions of number 4 are equals but opposites to the positions of number 6

The positions of number 5 are different from those filled by the number 0

Now we explore the position of numbers

Base Seven Table / Koch Curve Comparison

Copyright (C) 1987 - Paolo Di Pasquale

For this association, please visit also:

“An Orthogonal Oriented Quadrature Hexagonal Image Pyramid”

**Exploration between Base 7 and Base 10**

In this exploration we investigate the definition, reason, quality and quantity in elementary arithmetic

and how we can easy characterize the substantial differences between Base 10 and Base 7

We obtain a chromatic shape of hexagram similar to the Koch snowflake.