What is the mathematical symbol for dimension

Basic concepts¶

Parallelism and angles¶

Two different straight lines run and along the same direction, they are called parallel to each other. [2] Both straight lines have the same distance at every point from each other and therefore no common point ("intersection").

The distance between a point and a straight line is always measured perpendicular to this straight line; this corresponds to the shortest possible distance between this point and a point on the straight line. The distance between two parallel straight lines corresponds to the distance between any point of one straight line and the other.

Angle and degree

Two rays go from a common point ("Vertex"), the difference in direction between the two rays is called an angle. Usually, angles are symbolized with Greek lowercase letters; if the angle describes a counterclockwise rotation of the beam, it is called positive, otherwise negative. Are the points on the two rays (also called "angle legs") and , that's how you write too .

The size of an angle is usually given in degrees. One degree corresponds to one -tel of a full turn; so becomes a ray at an angle of rotated, it is congruent with the original ray. Depending on the size of the angle, a distinction is made between the following types of angles:

  • Applies , that's how the angle is called "acute".
  • Applies , that's how the angle is called "obtuse".
  • Applies , this is how the angle is called "truncated".

Applies to an angle , so it is referred to as the "right angle" at an angle is called a "straight angle". In the case , ie a full turn, the angle is also referred to as a "full angle".

The units "angular minute" and "angular second" are also used for specifying very small angular values. One degree equals Angular minutes, an angle minute in turn Arc seconds. The following notation is common:

The radian measure, which is also often used to specify angles, is described in more detail in the section Degrees and radians.

Vertex angles and minor angles

If two straight lines intersect, two adjacent angles complement each other . For every two so-called "secondary angles" and so the following applies:

The opposite angles of two intersecting straight lines are called "vertex angles". The vertex angles are always the same in pairs, so the following always applies:

Step angle and change angle

If you draw a straight line parallel to one of two intersecting straight lines, the angular relationships at the second intersection point are identical to those at the first. The angles that lie on the same side of the straight lines intersecting the two parallels are called "step angles" (or "F" angles for short), the opposing angles are called "alternating angles" (or "Z" angles for short).

In the figure, step angle and alternate angle are for example and the same as a step angle, so it applies . The same applies , since these two angles are alternating angles. [3]

Angles perpendicular to each other

If the rays of two angles are perpendicular to one another, the two angles are equal. The reason for this is that the two are lying against each other -Angles represent vertex angles, i.e. they are equal. Since the sum of the angles in a triangle is always and an angle is the same in both triangles is follows from the equality of also the equality of .

A scientific application of this relationship is, for example, the force ratio on an inclined plane.


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