Spaces {space, geometry} have elements. For example, space can be points. Elements combine to make space and figures in space. For example, points along one dimension form line, points along two dimensions form surface, and points along three dimensions form volume. Elements can be lines, surfaces, volumes, vectors, triangles, loops, colors, or objects. Points can represent vectors {vector space}. Phase-space elements can represent system states or dynamical equations.
Spaces have components {dimension}. Spaces can have zero-dimension points, one-dimension curves, two-dimension surfaces, and three-dimension solids. Spaces can have infinitely many dimensions and can have fractional dimensions.
component
Dimension can be infinite or finite. Finite dimensions can be circular.
continuous
Dimensions can be discrete or continuous.
elements
Space can have different elements, such as points or lines. Two-dimensional space can use three reference points. Three-dimensional space can use four reference points. Three-dimensional space can use three orthogonal lines or four non-orthogonal lines.
coordinates
In two-dimensional space, point position is (x,y) {ordered pair, space}, where x and y are distances to two reference lines. In three-dimensional space, point position is (x,y,z) {ordered triple}, where x, y, and z are distances to three reference lines.
From reference points, lines can go in directions {direction} {orientation}.
Non-Euclidean space can have no parallel to given line through external point {elliptic space}. Elliptic space can have spherical geometry.
Line segments {line segment, magnitude} can represent magnitudes, ratios, or proportions.
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Date Modified: 2022.0225