3.18.2011

About symmetry of mathematical actions

About symmetry of mathematical actions - is my first official publication. To all appearances, my flaming speech under the name "Mathematics forever!" remained unnoticed. It is clear. Reading a like, I would say that a next idiot rushed about on all Internet with the ridiculous idea. But... All, that is here written, I write exceptionally for you and publish here in an only copy, unlike other authors of raving ideas. With my article about symmetry of mathematical actions you are first can become familiar right here and now. I am herein anything interesting or no - decide. In brackets I will give some comments (specially for you) that in the printed variant of the article are absent.

Annotation: Rules of symmetry of mathematical actions allow to apply a commutative law to all mathematical actions: to addition, deduction, multiplication and division. (An annotation is this obligatory condition for the publication of the article. Such are rules of the bureaucratic playing science)

Changes in the surrounding world are expressed by mathematical actions. Quantitative changes are expressed by addition and deduction. Quality changes are expressed by an increase and division. No quantitative changes can cause the change of quality.

Quantitative changes reflect the change of amount of the separately taken unit. Addition and deduction are symmetric mathematical actions reflecting the quantitative changes of any unit. Addition and deduction are mirror symmetric relatively neutral element are points zero.

An increase and division similarly are symmetric mathematical actions reflecting the quality changes of units. An increase and division are back symmetric relatively neutral element are points one.

Rules of symmetry of mathematical actions:

1. Any mathematical action is begun with a neutral element.

2. A sign of mathematical action is the inalienable attribute of number before that he stands.
(This fragment is distinguished by me by fat text specially for you)

Application of these rules allows to apply a commutative law to all mathematical actions reflecting quality or quantitative changes.

0 + 3 + 7 + 4 = 0 + 7 + 3 + 4 = 14

0 – 3 – 7 – 4 = 0 – 7 – 3 – 4 = –14

0 + 3 – 7 – 4 = 0 – 7 + 3 – 4 = –8

1 х 3 х 7 х 4 = 1 х 7 х 3 х 4 = 84

1 : 3 : 7 : 4 = 1 : 7 : 3 : 4 = 1/84

1 х 3 : 7 : 4 = 1 : 7 х 3 : 4 = 3/28

A commutative law can not be used in the cases of the mixed implementation of mathematical actions reflecting quality and quantitative changes in one mathematical expression.

The change of the mathematical operating on symmetric gives a symmetric result, here the point of symmetry is a neutral element. Application of commutative law does not influence on a result.

0 – 3 – 7 – 4 = 0 – 7 – 3 – 4 = –14

0 + 3 + 7 + 4 = 0 + 7 + 3 + 4 = 14

0 – 3 + 7 + 4 = 0 + 7 – 3 + 4 = 8

1 : 3 : 7 : 4 = 1 : 7 : 3 : 4 = 1/84

1 х 3 х 7 х 4 = 1 х 7 х 3 х 4 = 84

1 : 3 х 7 х 4 = 1 х 7 : 3 х 4 = 28/3

Running the numbers in the mathematical operating on symmetric relatively neutral element of number gives a symmetric result.

0 + (–3) + (–7) + (–4) = 0 + (–7) + (–3) + (–4) = –14

0 – (–3) – (–7) – (–4) = 0 – (–7) – (–3) – (–4) = 14

0 + (–3) – (–7) – (–4) = 0 – (–7) + (–3) – (–4) = 8

1 х 1/3 х 1/7 х 1/4 = 1 х 1/7 х 1/3 х 1/4 = 1/84

1 : 1/3 : 1/7 : 1/4 = 1 : 1/7 : 1/3 : 1/4 = 84

1 х 1/3 : 1/7 : 4 = 1 : 1/7 х 1/3 : 1/4 = 28/3

Simultaneous change of the mathematical operating on symmetric and running the numbers on symmetric relatively neutral element of number abandons a result without changes.

0 – (–3) – (–7) – (–4) = 0 – (–7) – (–3) – (–4) = 14

0 + (–3) + (–7) + (–4) = 0 + (–7) + (–3) + (–4) = –14

0 – (–3) + (–7) + (–4) = 0 + (–7) – (–3) + (–4) = –8

1 : 1/3 : 1/7 : 1/4 = 1 : 1/7 : 1/3 : 1/4 = 84

1 х 1/3 х 1/7 х 1/4 = 1 х 1/7 х 1/3 х 1/4 = 1/84

1 : 1/3 х 1/7 х 4 = 1 х 1/7 : 1/3 х 1/4 = 3/28

The neutral elements of mathematical actions it is not accepted to write at the decision of mathematical problems and examples, as they do not influence on a result. Before application of commutative law introduction of neutral elements allows correctly to apply a commutative law.

All of it is written, certainly, not for blondes, and for mathematicians. In the future we yet not once will call to this article. And while... you know any more mathematician about symmetry of mathematical actions.

3.16.2011

Mathematics forever!

Mathematics forever!

You can congratulate me, my first scientific publication went out in light. There are "The papers of independent authors" in a magazine, producing № 18, to the page 110 the little article is printed under the modest name "About symmetry of mathematical actions".

At the last time (in a blog in Russian language) I promised you to show that needs to be done in order that impossible in mathematics became possible. In this little article, only on two pages of text, it is shown, as a commutative law works at deduction and division. If someone wants to look, can pass on this page (in Russian language), there is reference for a flush-off. Nothing difficult in this article is present - the half of text is occupied by examples on addition, deduction, increase and division. All at the level of middle classes of school. Such mathematics any blonde will understand.

Here so, unnoticed, we with you began to live in a completely another epoch - Epoch of Great Mathematical Opening. Doing these mathematical opening coming to you, I can only broadly speaking explain to you, what mathematics, where in mathematics, opening is hidden and as they need to be searched. By the way, my article is the first step on a way to dividing by a zero. Mathematical actions are symmetric: if in mathematics there is multiplying by a zero, means there is under an obligation to be dividing by a zero. If dividing by a zero is impossible, means multiplying is impossible by a zero. The third variant (that is known by us all) can not be. When I will show you, where and as there is dividing by a zero, you will understand that mathematics is this not паханное field on that we engage in the most primitive collector. To throw open and take the crop on the mathematical field, at a desire, any of you can.

3.11.2011

Four-valued mathematical tables for blondes

Four-valued mathematical tables of Bradis - this was the basic mathematical reference book of soviet schoolchildren, students, engineers to appearance of calculators.

A trigonometric table for blondes is done by me to the navigation more informatively saturated in a plan. It what you did not lose way and did not entangle trigonometric functions.


Trigonometric table of sines and cosines
- from 0 to 90 degrees punctually to the minute corner.

Trigonometric table tangent cotangent in degrees - from 0 to 90 degrees punctually to the minute corner.

Trigonometric table in radians - sin, cos, tan.

We will do justice to work of Bradis and we will remember a bit history. His book "Tables of the four-valued logarithms and natural trigonometric sizes" went out in 1921. This book was repeatedly reprinted, but already under more simple name "The Four-valued mathematical tables". This bestseller looked approximately so.

Four-valued mathematical tables of Bradis for blondes. The basic mathematical reference book of soviet schoolchildren, students, engineers
It is possible to say without a false modesty, that on these tables all Soviet Union was built, a man started to fly in space, a soviet nuclear club was created et cetera. Schoolchildren, engineers, scientists - all used the tables of Bradis. We will remember those distant times - the Internet is not present, mobile telephones are not present, computers and calculators are not present. Even televisions were not then! There were only books. In many books formulas were written for a calculation, and necessary for calculations numerical values were taken from the tables of Bradis. And what did numbers multiply by then? Not on accounts... Well and time was! As it was then possible normally to live??? But lived somehow.

An interesting question arises up. What mathematical tables did Americans build famous sky-scrapers on and created the nuclear club? In fact did not they steal for us tables of Bradis? Omniscient Wikipedia is quiet on this occasion, and information about the table of Bradis in Wikipedia in English language I did not find. There is there a mathematical reference book of Abramowitz, Milton and Irene A. Stegun with tables, but he is published was only in 1964. And that did Americans have to these tables?

I used the table of Bradis once. This whole art, to search the value of trigonometric functions punctually to the minute corner. Fortunately, today we have calculators.

Unfortunately, work of great soviet writer of mathematical tables Bradis me does not interest. Therefore the four-valued mathematical table into language of blondes transferred will not be. In the simplified kind the table of Bradis will be presented in the tables of sine, cosine, tangent and cotangent.