Unified relativity geotrigonométrica algebraic graceli.

Graceli theorem of oscillatory rotation and precession, and geotrigonometria.


In an n-dimensional space, any movement of a rigid body that maintains a constant point in a rotation axis of a sphere form various triangles in relation to the shaft and outer points of the sphere.


And this being spin precession in these triangles wheelbase and external points become variable, oscillating, and indeterminate.


For these triangles must take into account the acceleration and the rotational acceleration of flows and scope of the precession / time.


R + p [acceleration, range] / time.


And taking into account that this solid or sphere can be deformed, one should take into consideration the variable deformation.


Or the relative deformation against time, wilting and filling.


That is, angles and triangles, and sides, and sine, cosine, and tangent to be relative and dynamic, and follow the dynamic variability of the relative differential geotrigonometria concave and convex graceli. [See already published on the Internet].


In other words, we have a rotation system and geotrigonométrica for hard or not solid, and their dynamics.



Theorem ellipses [eccentricities] and circumferences.

The extreme determining means.

The same goes for the eccentricity [ellipsis] and the circumference.

To find the ellipse should be the average of the extremes and the media.

Thus, if the value of pi is to ellipses.

The average of the extremes with the means of the diameters is divided by the average of the most distant rays with nearby. [Extremes and lower].


Theorem of hollows for pi.

For an ellipse with one or more of a hollow inside.

One should take into consideration the diameter and the radii of the concavities or all if any, and subtract the equation of the ellipse to pi.

And if this concavity is in oscillatory flow has a variable in the frequency flows through time.


Where angles and sides and the sine, cosine and tangent tend to also be variable.


And if this ellipse is rotated one must take into account the rotation which appear concavities and its flow by time, that is, convex portions to concave and vice versa.


Ie, just to pi and its possibilities, has an algebraic geotrigonometria.


Thus we have a trigonometry, a variable geometry for triangles with sides and angles and other shapes, and also to find the pI value with all these variables.

That is, an algebraic geotrigonometria dynamic, variable and relative.



Infinite theorem graceli by graphs.

Graceli system for graphs.

In a graph with the vertical and horizontal integer above zero.

A - The previous result multiplied by the horizontal.
B - The result is divided by the previous diagonal later.


As increases of integer values, the infinitesimal results increase proportionally.



Other options for graphs.

Or it can be the previous line, or vertical.
Or it can be raised and the progression or root, or even derivatives.

Using graphs can be done by vertical lines or horizontal, diagonal. As these results to find these results.


And can be derived parts or integrate the whole, or even of those parts. Or series limit.



Theorem and graceli paradox of the tetrahedron.

Graceli versus Pythagoras.

If a tetrahedron has a corner with a right angle, then the square of the area of ​​the opposite face to the corner with a right angle is different from the sum of the squares of the areas of the other three faces:


Thus, this conventional formula is false.


If a tetrahedron has a corner with right angle, so the square of the area of ​​the opposite face to the corner with right angle equals the sum of the squares of the areas of the other three faces:







Thus, it is not the same, but different. Because:


We have three triangles with their hypotenuses, ie a repeatable error. As we saw in Pythagoras.


That is, these terms have always an infinitesimal hypotenuse. As we have seen in the geometric and algebraic postulates graceli to the hypotenuse and results of sums of squares to another square.



And, as has been seen that any triangle with three equal sides, or two equal sides choose any one of the long sides to be the hypotenuse already has an area to the square of the longest side over the other minor, or an equilateral triangle will be always the most left side [i.e., a larger cathetus left]. Ie following the graceli theorem for the hypotenuse squared the above theorem is wrong.



However, in this case the tetrahedron we have are two major sides and a smaller, ie shorter cathetus of the square will be a surplus.


And the hypotenuse squared is an infinitesimal [endless]. In other words, will never be the same.


[See graceli postulates for squares and cubes as a result of squared sums and cubes].


Example:
The square of 2, and the square of 3 will give a sum of 13, then what we have is a number squared to be found should have it as infinitesimal function, since that number squared gives 13? = 3.6000001 .........................


Thus, we enter the relativity and changing dynamic mathematics involving geotrigonometria algebraic.


Thus, it opens another perspective to find elements of geometry, trigonometry and algebra as pi, angles, hypotenuse squared, and sines, cosines, tangents and variables, changing forms of parts such as ball concave flows that deforms the buds, dynamics and relative.