**Astronomy and physics
**

**©2004 author: Michael Köchling**

**The 5. postulate of the Euclid solved!?**

In the world of physics it is spoken very much of non-Euclidian areas,
as well as their effects on the area geometry of the universe. This is represented as area curvature in connection with the gravity strength.

However this is not sufficiently, the time is forced as dimension as well as a area time curvature is done from it.
It appears necessary to therefore first determine which are " non-Euclidian areas."
The Greek Euclid, by 300 v. Chr. ) was a mathematician and wrote the handbook "The elements", 13 volumes.
This handbook was over 2000 years long basis of the geometry instruction. Euclid defined the elements of its geometry as point,
line and surface - concepts, with which each schoolchild trusted today. Then, he positioned five main postulates:

**1. two points , that are connected together build one route.
2. every ( never ending) route, can be (infinitely extended ) evenly extended.
3. two points are given, you can constructed a circle from the two points, which the one point lies and its center is the second point.
4. all right angel corners are equal to each other.
5. if a straight line cuts two other straight lines to such an extent,
that the interior angels are together smaller than two right angels (180°) on the one side, then,
more final two straight lines cut themselves on this side.**

Would one cope completely broadly with the only 4 postulates then what did Euclid do with the 5. postulate and for what did he make it?
This was a big headache for all Mathematicians for centuries and whether the present-day interpretations really correspond to his statement,
remains open. Fact is, at the time of Euclid one reckoned only with even surfaces. They were only squares, rectangles, triangles and circles.
If we now relate these to bodies (areas), so we get a square, cuboids, prisms, tetrahedron and pyramids. They all have something similar.
It is the straight outer areas.

Therefore, on this occasion they are " Euclidian areas". Bodies like balls, cylinders,
cones and ellipsoids therefore they are " non-Euclidian areas" because they have partly curved outer areas, or completely curved.
To calculate the surfaces of the last mentioned bodies other prerequisites had to be created, because for example a selection of a ball are not equal.
It becomes even worse at the corners. Their additions are > 180°, against the angel of a corner / triangle are always 180° .

They who deal with the handling of a funnel from round to quadrilateral
already know that one has to determine the true lengths and angels, so that the handling of the real form will correspond. In other words:

we have other results for incurved surfaces angels and lengths versus straight surfaces.

So we are working with bodies, beside the surface as well,
they also comprise a content, the volume. I would like to point out, therefore that areas can never be change in the bodies.
Only the volumes are influenced. Even if the body extends through heating, it keeps the same form. Even one can bend bodies,
the volume remains largely untouched, unless, the body is stretched or is compressed. No matter, each body, no matter what form,
comprises a volume, which can be measured in length, width and height in all three dimensions.

A certain area, no matter which form,
remains stable in itself even if it extends, as our universe, or moves in together. On this occasion, only the volume changes,
the form stays the same. However, all distances of all reference points change automatically within the body (area).

Do you still remember the fifth postulate of the Euclid? Only the four postulates were completely comprehensible. However why are there so big understanding difficulties with the fifth? Could it be that a mistake was done translating it from Greek? If so maybe the sentence was twisted completely. My realizations tell me that some translations are said differently in English as in German. What did Euclid wanted to testify or say. What did he want to represent us with? In the first postulates, he gives us instructions how one has to proceed in order to construct a route, an infinite straight and a circle. Thereupon, he still says that all right angels resemble themselves, independently their thigh lengths. Correct, they are only instructions! However one instruction is still missing! Namely to his parade object, the triangle! Under these prerequisites, we have the following explanation to the statement in the 5. postulate:
Cross two straights with another straight with an angel smaller than 180° on a side, so these two straights cross themselves on this side even! All triangles with any angels are complete! It is mathematically expressed so:
Crosses the straights B and C the straight A in a angel together small 180° on a side, so the straights B and C cross this side even.

With this instruction, Euclid gave us the possibility, to construct each and any triangle!

©2004 author: Michael Köchling

**In the astrophysics, much is possible,
however, it should always be compatible with the natural conditions.
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