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Geometry › Dimensions
Dimensions
Climb the ladder: a point has 0 dimensions, a line has 1, a plane has 2, a solid has 3. Geometry begins right here.
Dimensions ladder
Climb from a single point all the way to a solid. Each step adds one direction.
2D
Plane
Two dimensions — length and width. A flat surface.
Example: A piece of paper. A computer screen.
Building up
- Point (0D) — a position with no size. Drawn as a dot, but a true mathematical point has no dimensions at all.
- Line (1D) — extends in one direction, both ways, forever. A segment is the bit between two points; a ray goes one way only.
- Plane (2D) — a flat surface that extends forever in two directions. A piece of paper is a finite slice of one.
- Solid (3D) — extends in three directions. The space we live in.
Going further
Math doesn't stop at 3. A tesseract is a 4D analogue of a cube — you can't draw one perfectly on paper, but you can study its properties algebraically and see projections of it.
Each dimension adds an axis
To label a point you need one number per dimension. On a line, just x. In a plane, (x, y). In space, (x, y, z). Add a fourth axis and you can describe spacetime — three space, one time.
Defining each from the last
- Two distinct points define a line.
- Three non-collinear points define a plane.
- Four non-coplanar points define a 3D space.