Construct · 1 fields · 1 citations

plane: a standalone construct

One name. One construct. A landmark on the map.

● anchor · a standalone construct Nearest construct by meaningwingcompare the meanings
How to read this

Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to plane is wing.

Hold this as a prompt, not a verdict. Two constructs sitting close in meaning is a reason to read them side by side and decide for yourself whether they are one idea under two names. It is not proof that they are. Compare the meanings in the Collider.

plane1 CONSTRUCTEuclidean planeCOXETER · FLAT SURFACE

A single standalone construct; nearby constructs are located against it in the Collider. Tap a field for its definition, unit, and measures.

Mathematics and geometry

A flat two-dimensional surface

In geometry a plane is a flat, two-dimensional surface that extends without limit in every direction, so that any two of its points can be joined by a straight line lying wholly within it. It is fixed by three points that do not lie on one line, or by a single point together with a direction at right angles to the surface, and it carries the whole of two-dimensional coordinate geometry, including the complex plane. Coxeter's 1969 Introduction to Geometry sets out the Euclidean plane and the coordinate and transformation rules built on it. The referent is an abstract, infinite mathematical surface with no thickness, not a section drawn through a body, a tool that smooths wood, or a machine that flies.[1]

Unit
An infinite flat surface with no thickness, fixed by three points or by a point and a normal
Recovery means
Not applicable
Measured by
Specified by a linear equation in coordinates, or by a point together with a normal vector

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Nearby constructs

manifold2 fields · 2 citationsjingle · one word, two constructsvector3 fields · 3 citationsjingle · one word, three constructsprojection4 fields · 5 citationsjingle · one word, four constructs

References

  1. Coxeter, H. S. M. (1969). Introduction to geometry (2nd ed.). John Wiley & Sons.

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