# Geometry

## Roto-translation (rigid transformation)

The rigid transformation (or roto-translation motion) is the composition between reflection, translation, and rotation, and therefore it is an isometry, that is, a geometric transformation that leaves the distances unchanged. In other words, we …

## Rotation

Rotation is defined as rigid movement having as fixed points a point called center (in two dimensions) or a straight line called axis (in three dimensions) of rotation. This movement shifts …

## Translation

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or space by the same distance in a given direction. It can also be interpreted as …

Midpoint.

Line segment.

Polygonal chain.

## Geometry

Euclidean geometry. Non-Euclidean geometry.

## Vector

Vectors are indicated in the scientific literature with a letter, generally lowercase, with an arrow above it: $$\vec{v}$$. Vectors are essential to physics and engineering. Many fundamental physical quantities are vectors, …

## Volume

In geometry, the volume is defined as the measure of space occupied by a three-dimensional body. The volume of a three-dimensional body is a numerical characteristic of the body; in the simplest …

## Distance

Distance formula.

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