Introduction

The following numeric system is a side product of my over 10 year long research concerning geometry and higher dimensions (including Kissing number problem).
I'm also going to implement this system in a software that's going to search for kissing numbers in dimensions five and up.

----=== Balternalculator ===----




People who know how to add numbers in any other system than decimal (binary, octagonal, hexadecimal, ...), find this calculator easier to understand.
... But...
Children who are not yet familiar with the numbers we use today, could learn how to add, subtract, multiply and divide much quicker than they would do using the existing decimal numeric system

Lately I have found that the system that I reinvented is actually called a balanced ternary system
For convenience I'm going to call the digits trits

On the calculator, red(up) means positive (+),
brown/uncoloured means zero (0) and
green(down) means negative (-).

Let me give you an example:
Red(up) on the first field affront of the decimal point (rightmost) means that we add +1 to the current number,
red(up) on the second field affront of the decimal point means that we add +3 to the current number,
the next one +9, and so on...
In the contrary, greens(downs), from right to left, mean -1, -3, -9,...

Instead of writing a table, in which I would explain how numbers are represented using balternator, I've decided to make an online virtual calculator for you to get a glimpse of how this system works. Click here to give it a try.

Addition:

for adding two numbers there's only one rule: whenever pressing on a either of the two colours(red and green), you have to turn the neighboring trit accordingly(as shown in the video below).



Subtraction:

To subtract is equal to negate the number you are subtracting and then add it to the other number: [video link]

Multiplication:

Multiplying with this calc is a bit dodgy, but later on I'm going to show you another way.

[video link]



Division: [video link]

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Conclusions:



Imagine all the work and time saved by not having to learn multiplication table, building abacus, learning to divide and so on.

Also in computer science balanced ternary is very usable because:
- There's no need for an extra minus sign for representing the negativity of a number
- when cutting off digits behind the decimal point (=rounding numbers), you don't need to worry about rounding the number (i.e. - 1.44 rounds to 1.4 while 1.45 rounds to 1.5; and we encounter the same problem in binary)


Some people say: And I reply:
you need too many digits to write down a number. You can combine every two trits and get balanced nonary system which is very close to our currently used decimal(in terms of number of digits used for representing a number), and still use the same procedures to calculate numbers as in balanced ternary [video link]
There's loads of conversion to do Yes, but that is because we're used to decimal. If you have a balanced ternary ruler, no conversion is needed at all. [video/pic link]
Yes, but that is because we're used to decimal. If you have a balanced ternary ruler, no conversion is needed at all. [video/pic link]



other interesting things about this system -another multiplying:[pic link] ; as we see, the procedure for multiplication strictly follows the mathematic rules, as well as it corresponds to the behavior of two magnetic poles.
i.e.:
Let us say red means to repel - increase distance (+)
and green means to attract - decrease distance(-)
And also that red and green are the two opposite magnetic poles while brown/uncoloured is
-year
-3-digit letters

...Page under construction..

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