Flat Geometry, Origin

VIEW:410 DATA:2020-03-20

Euclid de Alexandria is determined to have stipulated the principles of geometry. In ancient Greek times, people had the idea that the gods went to heaven and became constellations, that is, it became a cluster of stars. In order for people to be clear about which gods were there, they united the stars to form drawings.

With that it could be said that the stars were points. Point, Euclides defined that point could not have parts, that is, the point could not be divided. Thus, it was necessary to accept the point, without proving the point. For the point would end up being an object without volume, without area, and without length, an object of dimension 0. Thus, the point was defined as axiom. Axiom is something that is believed, but not proved.

When looking at the starry sky, and seeing nearby stars, they look like the formation of lines, and so the line is the junction of infinite points. And so, the drawings in the starry sky were seen in the imagination of the Greeks. When the drawing closed, due to the lines connecting to the points, until there was no way out, that drawing would be called a plane.

So, looking at the view of the Greeks' sky, we can imagine what Euclid defined. Let's make ourselves Euclid, and we are looking at the constellation of Orion, and now we can see the stars of the Orion constellation, and now we can see Orion himself drawn in the imagination, and how did they connect the stars to form a design?

And now we can define:

1. In a straight line, as well as outside it, there are infinite points. So, when we look at the sky, we can imagine that there can be infinite points in the sky, and that there can be infinite points on the line that joins two points.

Imagine that we are seeing a slightly cloudy sky, so the number of stars that we see is less than on a non-cloudy day, that is, there may be several stars that we do not see. And so, the generation of the idea that there can be infinite points.

Remember that in a closed drawing, we call it a plane. Thus, within the drawings created by the Greeks in the sky, there are several stars within it. What could define that in a plane there are infinite points.

To define such things, it was agreed for straight lines, use lowercase letters, and for points uppercase letters, and for plans Greek letters are used.

Now, looking at the drawing of Orion, we can define some things that help us to understand Geometry.

We can see the following points, or stars. A, B, C, R, and S. We can see three lines r, t, and u. And we also see the alpha plane. The alpha plane would be the representation of Orion's head.

We can see the line t, and we see two points, point A and B, all are connected to line t, so we can say that A belongs to t, and B belongs to t. They are on the t line. Points that belong to the same line are called collinear. So, A and B, are collinear to the line t. And when the points are in different places, they are called distinct. If it were in the same place they would be coincidental. That it would just be the same point, that different names were given.

So we can read the definition as A and B are distinct points, so the sign is different, and the two belong to the line t, which defines being collinear.

It is important to understand the mathematical way of writing, as it speeds up the understanding of what we are analyzing.

Looking at the constellation of Orion we have, that A and C are distinct and collinear to the line r. We have that B and C are distinct, and they are collinear to the line u.

Then we'll look at more definitions for geometry.