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" Structural geometry ".

The basic purpose: To enter into mathematics, alongside with concept "number", one more fundamental concept: "structure".

The Main task: To become the basic part of mathematics connecting its other sections with each other.

The basic toolkit: " the formula of re-structuring (in a general view):

.

(Result of application of the formula:

- it is read "

re-structuring on

in

"), rules of differentiation and integration in "planimetry" and "stereometry".

Examples of application:

1.

- Some value of function

At the certain value

.

;

,

,

.

2.

- Without taking into account structure;

- Volume of a cone (elementary structure:

).

- Volume of a quarter of a sphere: (elementary structure:

).

3. The decision of the algebraic equation

(In the structural form:

) - The answer to a question: " on how many it is necessary to increase value of argument that value of function has increased on "

" ".

"

",(

). In the structural form:

.

4. Using rules " integration and differentiation in planimetry and stereometry " it is had such results:

- The area of a circle with radius "

". (el.str.:

),

- The area of a lateral surface of a cone in height "

". (el.str.:

),

- Volume of a cone in height "

". (el.str.:

),

- Volume of a hemisphere with radius "

". (el.str.:

),

- Volume of a sphere with radius "

". (el.str.:

),

- Volume of two cones in height "

", tops directed to each other. (el.str.:

).

5. In " a structural kind " "Bin of Newton" look so:

.

For example:

.

6.

in structure form:

- The sum of 2 functions.

7.

- Volume of the cylinder in the height equal to radius.

.

" The structural geometry " gives two answers to this question (

):

1)

(

- radius)

(The area of a lateral surface of the cylinder).

2)

(

- height)

(The area of the basis of the cylinder).

8.The structural geometry explains result of application

for

,

in the form of

that,

- does not exist. Exists only

.

- Special case.

9. A line named " the schedule of function

", the dividing area

on two areas:

and

in "stereometry" there is an area

, dividing a cube

on a pyramid

and two dual pyramids

.

To one of the main results of application of this theory becomes obvious, that " the fourth measurement of space on linear size " (to not confuse " the fourth measurement of space on time ") is that in the physicist "field" (electric, gravitational, etc.)