Dog paradox graceli. New algebraic geometry.

Compared the graceli dog paradox with the paradox of Zeno's tortoise.
We see another calculus with infinite variables regarding the time, geometry and algebra, trigonometry and a variable and relativism. That is, a unified system.



Theorem graceli Paradox cube and square.

A number that multiplies added with another number that multiplies itself does not follow the same proportional increase of [another] to a number that is multiplied three times coupled with another number that is multiplied three times.

The relationship between the hub and the sum of the two numbers has a square growth [gradually], and irrational in most cases. Among cube and square.

2 + 3 [2] diff. Proportionality 2 + 3 [3].

2:03 = [sq] 13 [SC] 35 35/13 = 2.692 ........
3:04 = [sq] 25 [SC] 91 91/25 = 3.64
4:05 = [sq] 41 [SC] 189 189/41 = 4.6007 .......

        [Sq] = Sum of squares and [SC] = sum of the cubes.

In other words, one should not make the same comparison sums of squares, moving to sum cubes because the results do not follow the same order and growth of proportionality.

1] is not exactly square to the cube of a container.
2] And this difference increases as the container.


Geotrigonometria algebraic differential relative to concave and convex stable and variable.

A concave or convex and system dynamics and stable flow and the time or variable angles have pi hypotenuse, sine, cosine and tangent to vary in relation to these variables.

As an example, the paradox of the dog that runs up and down hills and has diagonal differential lateral movement towards the owner who runs in alternating convex and concave lines and ups and downs, and where the dog accompanies these movements, thus forming angles, triangles and pi variables in curved closed system in dynamic where the concave and convex alternate.


Concave and convex triangle differential as in Dog paradox.

Another example is the ball that rotates rotation and precession, and have variable frequencies flows on murchamentos and fillers parts of this ball.

That is also angles, triangles, pi, sine, cosine and tangent become variable and relative to each parts of buds of the ball.