Studio Brief 3 - Research - Geometry

The Geometry of Three Dimensional Space 

Three dimensional space

Three dimensional space is a geometric setting. Three values (parameters (in diagram they would be the x,y and z coordinates)) are needed to determine the position of a point within a space. It is the informal meaning of the term dimension.

   

A sequence of numbers can be known as a position in a dimensional space, this is also known as three dimensional Euclidean space.

This acts as a three parameter model of the physical universe.

The three values refer to measurements in different directions (coordinates) with any directions being used as long as the vectors are not be in the same plane.

The values can be labelled in any combination of, width, height , depth and breadth.

Coordinate Systems

The coordinates system describes every point in three dimensional space with the use of three coordinates.

This system uses three axes (x,y,z) perpendicular to the origin, with the origin the point at which they cross.

 Lines and Planes

Two distinct points show a straight line.

Three distinct points are either collinear (in a row) or create a unique plane.

Four distinct points can be either collinear (in a straight line), coplanar (being or operating in the same plane) or determine a unique plane.

A plane is a flat two dimensional surface which extends infinitely far.

Geometry and visualising space

Looking at preexisting diagrams and drawings could help to better understand ways of interpreting space. Venn diagrams show interlocking or overlapping space. Cube drawings can be see through, closed or open reflecting different types of space. Flat shapes can be combined to create three dimensional shapes through the addition of lines.