* Transposition property *

* Direct form *

Of ferman: Fernando Mancebo Rodriguez---
Personal page.

You can see many of my works, in the following pages:

PHYSICS:

Double slit and camera obscura experiments: ferman experiment

In favour of the cosmos theory of ferman FCM |||
Theory of Everything: summary

Model of Cosmos. |||
Atomic model |||
Development speed of forces.|||
Magnets: N-S magnetic polarity.

Stellar molecules |||
Static and Dynamic chaos|||
Inversion or Left-right proof

Chart of atomic measures|||
The main foundations of the Cosmos' Structure

Positive electric charges reside in orbits.|||
Mathematical cosmic model based on Pi.

Inexactness principle in observations |||
Einstein and the gravity |||
The Universal Motion |||
Atomic particles

Cosmic Geometry |||
Bipolar electronic: semiconductors |||
Multiverse or multi-worlds

MATHEMATICS:

Radial coordinates.|||
Physical and mathematical sets theory. | Algebraic product of sets.

Planar angles: Trimetry.|||
Fractions: natural portions.|||
Cosmic spiral

Equivalence and commutive property of division. |||
Concepts and Numbers. |||
Bend coefficient of curves |||
Mathematical dimensions

Transposition property |||
Accumulated product: Powers |||
Dimensional Geometry: Reversibility

Priority Rule in powers and roots |||
The decimal counter |||
Paradoxes in mathematics

Direct formula for Pi: The Squaring Pi. |||
The pyramids of Squaring Pi. |||
Functions of Pi |||
Integration formulas Pi.

Squaring the Circle

OTHER:

Spherical molecules. |||
Genetic Heredity. |||
Metaphysics: Spanish only. |||
Brain and Consciousness. |||
Type of Genes T and D

Certainty Principle |||
From the Schrodinger cat to the Ferman's birds |||
The meaning of Dreams

Freely economy |||
Theoricles of Alexandria |||
Satire on the Quantum Mechanics

INVENTIONS:

Andalusian Roof Tile. |||
Rotary Engine. |||
Water motors: Vaporization engines.

Triangular ferman's Houses .|||
The fringed forest

ARTICLES:

Garbage Triangle: Quantum mechanics, Relativity, Standard theory

Fables and tales of the relativists clocks.|||
Nuclei of galaxies.|||
Particles accelerators.

Hydrocarbons, water and vital principles on the Earth. |||
Cosmos formula : Metaphysics

Ubiquity Principle of set.|||
Positive electric charges reside in orbits.

Chaos Fecundity. Symbiosis: from the Chaos to the Evolution.|||
Speed-Chords in galaxies.

METAPHYSICS:

Who is God

Email: ferman30@yahoo.es

* Direct Transposition property in equalities and equations *

The direct property of transposition is a work method by which we can move terms and operations from a side of the equality to the other one in inverted way.

Given a + b = c where a = c - b. Here we pass the term +b (that is adding) to the second member in inverse operation -b.Given a/b = c where a = c*b. Here we pass the term b (that is dividing ) to the second member that now is multiplying .

Given a^b = c where a = c^1/b. Here we pass the exponent b (in power operation) to the second member in root operation.

In the transposition method we also have to respect the priority rules of operations.

Given (a + b)/c = d

We must to transpose firstly the division by (c),

a + b = d*c

And later on, we can transpose the addition terms.

a = (d*c) - b

As we can see in the drawing, in the transposition of terms or operations we don't have to make any type of operations (addition, subtraction, multiplication, etc.) alone we move "physically" the terms to the other side of the equation, only taking its inverse value.

When any term or operation is transposed to the contrary side of the equality, the both members of the equality are increased/decreased in the same value.

The transposition is an easy and simple method of organizing equalities and equations due to in it we don't need to make operations, alone move terms.

Contrarily, in the current method we need to make double operations and double simplification when we want to move terms.

Why the transpositions work?

In equalities and equations the both members are equivalents, and then when changing any of them we also have the change the other in the same value.

Given 25 - 8 = 17

If we eliminate the term (-8) we have to compensate the second member with the value that makes again equivalent to the equality.

And what this term is? Of course, the inverse value of -8, that is, +8, and then:

25 = 17 + 8

This occurs with any type of operations:

8*5 = 40 and then 8 = 40/5

So the transposition is moving terms between the sides of the equations in its inverse value.

Why the cross-multiplication work?

--The cross-multiplication is explained by means of the double transposition of its denominators.

--But also could be explained with the equalization of members by means mixture of the same ones.

Certainly, the cross-multiplication one members is composed by the multiplication of the bigger numerator of a fraction by the minor denominator of the other fraction, and the other member is composed by the multiplication of the minor numerator by the bigger denominator.

For instance: Given 8/4 = 6/3 ----------> 8*3 = 6*4

As we see in the drawing, in the transposition of terms and operations between the members of equations and equalities, the terms (addition, subtraction) are independent and prior and should be passed directly with the contrary sign.

Contrarily operations are included and subject to terms, and so, we must to pass firstly the terms to be able the transposition of operations later.