Why is a curve one-dimensional

One-dimensional geometric objects:


Below are all known one-dimensional geometric objectsdiscussed.

1-D is an abbreviation for one-dimensional objects.

As a rule, these have a linear structure.

Geometric point:


A Point is one-dimensional (it has neither width, length nor depth).

But it designates a clear position (a place).

It is designated with a capital letter e.g. A

There are two main uses for the use of points:

a) Labeling of the corner points of geometric figures

b) for representations in the coordinate system defined by the "x / y" variables.

Route:


The route is the shortest connection between two points (e.g. as the crow flies between two locations).

In other words, the line is a one-dimensional structure, a straight line segment that has a starting point (e.g. A) and an end point (e.g. B).

A route is mathematically designated with [AB], the length of the route with | AB |.

Illustration:

Just:


A Just is a one-dimensional structure that is unlimited in both directions.

It therefore has no start point and end point.

Every straight line can be represented as a linear function.

Straight lines are designated with lower case letters e.g. g

Illustration:

Two straight lines in the plane can be parallel, intersecting or identical to each other

Two straight lines in space can be parallel, intersecting, or identical to one another

Beam:


A beamhas a starting point but no end point.

It is therefore infinitely long.

The ray is also called a half-line.

A ray has an orientation that is determined by its starting point.

A point divides a straight line into two half-straight lines.

The ray is thus closely related to the term interval:

An interval can be defined as the intersection of two half-lines.

Curve:


A Curve (Latin curvus = "bent") represents a one-dimensional object in mathematics, as one can only move on it in one direction or in the opposite direction.

Testing:


The geometric point test

The geometric half-line test

The geometric route test

The straight test

PDF sheets for printing:


Geometric objects 1-D leaflet

Geometric object 1-D exercise sheet

Geometrical object 1-D exercise sheet 2