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unnihilator

Member

Registered: 2009-03-16

Posts: 3

New area of mathematics:

" 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.)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: New area of mathematics:

This is a copy-and-paste job from here, as well as several other places.  Typically I'd remove such a post, but it looks like the author actually went through the trouble of getting all the math tags in.

Seems to be a rewording of basic calculus... is there anything else going on here?

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: New area of mathematics:

Yes, a lot of math tag work!

---

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

unnihilator

Member

Registered: 2009-03-16

Posts: 3

Re: New area of mathematics:

I have given 10 items. The general opinion on this theme can be any. Some items contradict some mathematical bases. I would be grateful, if somebody has shown me though one mistake in each separate item of this work.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: New area of mathematics:

Lets take a look at your first integral:

You use x twice for two completely different things.  Inside the integral, we think of x as varying over the region of integration.  On the other hand, x as a limit of integration must be fixed.  You can't use the same symbol for multiple meanings.

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

unnihilator

Member

Registered: 2009-03-16

Posts: 3

Re: New area of mathematics:

What you see a mistake in:
1.

     

.
----------------------------------------------
"Structurual geometry" answers on problems on which more nothing will give the answer. For example:

.

- Volume of the cylinder.
As, applying the formula

to receive:
1. " volume of the cylinder" (

) = " volume of a cone " (

)  + "...? " (

);
2. " volume of the cylinder " (

) = " volume of a hemisphere " (

) + "...? " (

).

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: New area of mathematics:

You didn't respond at all to my criticisms of using the same variable for different meanings.  What does "Structural geometry" have to do with it?

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."