Math 2.0

Geometry Definition

Lambert quadrilateral

Builds on Absolute geometryAngle at a point

Definition

Let ABCDABCD be a convex quadrilateral in an absolute plane. It is a Lambert quadrilateral if three of its angles, say ∠DAB\angle DAB, ∠ABC\angle ABC and ∠BCD\angle BCD, are right angles.

Remarks

Example: in ℝ2\R^2, the rectangle with vertices (0,0)(0,0), (3,0)(3,0), (3,1)(3,1), (0,1)(0,1) is a Lambert quadrilateral, since all four of its angles are right. Non-example: the quadrilateral with vertices (0,0)(0,0), (2,0)(2,0), (2,1)(2,1), (0,3)(0,3) has right angles at (0,0)(0,0) and (2,0)(2,0) only, so it is not a Lambert quadrilateral. The fourth angle ∠CDA\angle CDA is right in the Euclidean plane and acute in the hyperbolic plane.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Absolute geometry, concept, no evidence levelAbsolute geometryconceptAngle at a point, concept, no evidence levelAngle at a pointconceptLambert quadrilateral, definition, no evidence levelLambert quadrilateraldefinition
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  1. Absolute geometry concept
  2. Angle at a point concept
  3. Lambert quadrilateral definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Lambert_quadrilateral
About this page
TagJM98RN8HVF
URIm2://JM98RN8HVF
Kinddefinition
WritingW0 stub
MSC51F05, 51M09
DefinesLambert quadrilateral
UsesAbsolute geometry, Angle at a point

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