What is meant by a math

The basics of geometry

There is a simple multiplication table for arithmetic. In geometry there are these 4 objects that you always need:

  • Point
  • route
  • Ray / half line
  • Just



Take a closer look at their properties:

The point

One Point do you know from spelling. Each sentence ends with a period.

The math point

In mathematics, a point is the smallest geometric unit of meaning. Actually, a point is so small that you cannot see it. To prevent this from happening, mathematicians decided to mark the point with an x. The point is exactly where the 2 lines of the x cross.

Points are indicated in drawings with capital letters.

Example:

You write the lettering for a point diagonally offset next to the x.

There are also corner points in figures. You don't need to mark the corner points with an x. The point is where the boundaries (sides) of the figure meet.

You mark a point with an x.

The distance

You know the route from your life when it comes to: "What is the shortest route to school?" Or "How long is the route?"

Both questions do not mean the mathematical route. The shortest route to school actually means the shortest route. It's about getting to school as quickly as possible. You use curves and intersections on your way.
If you're interested in the length of a route, you want to know how long you're going. So you're actually asking about the time.

The mathematical route

The mathematical route describes the shortest connection between two points.

Important: A route is the "shortest connection". A route has no curve.

Example:
First you have the two points.



Connect the dots and you get the route.



This representation is more common:



The route usually has a lower case letter as the name.



You can also write $$ bar (AB) $$ for the route from $$ A $$ to $$ B $$. The line above the letter shows you that it is a route. It doesn't matter which way around you put the letters, but usually you start with the letter that is at the front of the alphabet.

A route is the shortest connection between 2 points. You can measure the length of a route.
You write the length of the segment $$ bar (AB) $$ as follows: $$ | AB | = 3 \ cm $$.

The term “beeline” describes the shortest distance between two locations. That’s a stretch.

A route that delimits a figure has the name page. A stretch that limits a body is called Edge.

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The ray / the half-line

You know the term "ray" from the sunbeam or ray of light, for example.

If you can imagine a ray of sun, it goes away from the sun. He goes on and on until he hits the earth.



Image: Panther Media GmbH (dzmitri mikhaltsow)

The math ray

A mathematical ray also starts from a point. However, it has no end. That means that it goes on indefinitely.
You already know the number line. It often starts at 0 and theoretically goes on indefinitely.

You cannot draw an infinite ray. That is why mathematicians have come up with a type of representation that symbolizes the infinite line.

Example of a beam:
At the beginning there is also the point, but only one.



The beam then starts from this point. It will look like that:



That the ray does not end is expressed by the fact that there is no end point.

Here, too, you usually see:



A ray can go in any direction. It depends on how you draw it. A ray is not curved.

A ray has a start point but no end point.
You cannot measure the length of a ray. He is infinite.

Not to be taken seriously: if you draw a ray in the exercise book, it will invisibly run on and on. He shoots into space! :-)

The beam will too Half straight called.

Straight

You probably say the word "straight" a lot.

You use "straight" in 2 ways:

  1. Something just happened. Then it is in time.
  2. One line is straight. This means that it is not curvy or bumpy.

The mathematical straight line

The straight line in mathematics is a line without curves. The straight line has no beginning and no end.

Points can lie on a straight line. But points do not begin or end a straight line.

Example of a straight line:



Even lowercase letters are given names.



Points A and B lie on this straight line.


A straight line has no start and no end point.
You cannot specify the length of a straight line. The straight line is infinite.

If you draw a straight line in your math notebook, it doesn't stop in your notebook. It goes on in both directions to infinity. So she shoots twice into space. And all of this without curves or bends.