Principle 80/20 % and binomiality
Why are phenomena divided according to 80/20% principle and similar principles?
Phenomena are divided by power binomially,
where each phenomenon is 2 times larger than nearest phenomenon in power
Series x+0.5x+0.25x+0.125x = 100 is numerically formed
and values are grouped by power
(x+0.5x)+(0.25x+0.125x) = 100
Solving in decimal numbers without fractions we get x=100/1.875 and x=53.33
Then 0.5x=26.67 and 0.25x=13.33 and 0.125x=6.67
Returning to integral of sum of power of phenomena, we get:
53.33+26.67 = 80 and 13.33+6.67 = 20 in sum of 100% = 80% + 20%
or
53.33+6.67 = 60 and 26.67+13.33 = 40
in total 100% = 60% + 40%
Inverse problem, starting with smallest power phenomenon
from equation x+2x+4x+8x=100, we get x =100/15 =6.67
Checking all options through natural and decimal fractions,
solution shows separation of 80% and 20% calculated exact
1 / 15 = about 6%
3 / 15 = 20% accurate
5 / 15 = 1/3 third exactly or about 33%
6 / 15 = 40% accurate or 2/5
9 / 15 = 60% accurate or 3/5
10 / 15 = 2/3 exactly or about 66%
12 / 15 = 80% accurate
Square 10x10 =100 is divided at point 2x3 cells
bounding areas 2x3=6 and 2x7=14 and 3x8=24 and 7x8=56
Rounding up =6% +14% +24% +56% amounts are obtained
=6% +14% = 20% and =24% +56% = 80%
and =6% +24% = 30% and =14% +56% = 70%
Having identified 80% of profitable goods and excluded 20% of little profitable
among remaining goods, fractal stratification by 80% and by 20%
Active 20% population includes 6% of most active and 14% of less active
and also passive 80% includes 56% of inhabitants and 24% of indifferent
Square 4x4=16 is simply divided into quarters
1 / 16 = 6%
2 / 16 = 13%
4 / 16 = 25% accurate
9 / 16 = 56%
12 / 16 = 75% accurate = (1+2+9) / 16
Expressing by multiples 5:
55% +25% +15% +5% = 100%
Presenting phenomena visually as a series of elements,
size of each element depends on ordinal location
Let's say binomial multiplier M = 1/2 = 0.5,
then size of E(0) element of 0th dependent on
size of E(N) element with number N
is equal to E(N) = E(0) * M^N
Check: E(0)=53.33 and N=3,
then E(3) = 53.33*0.5^3 = 6.67
Number of element N is calculated by inverse problem:
to what extent should multiplier be raised to get result
M^N = E(n)/E(0) and N = log(E(n)/E(0); M)
Check: N = log(6.67/53.33; 0.5) = 3
Trinity and ternary division are possible
=15% +30% +55% = 100%
Total: an expression of form
«20% of actions create 80% of results»
integrally consists of 2 independent phenomena,
each of which is distributed binomially
80/20% principle is commonly referred to as «Pareto principle»