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In geometry, a Lambert quadrilateral (also known as Ibn al-Haytham–Lambert quadrilateral), [1] [2] is a quadrilateral in which three of its angles are right angles. Historically, the fourth angle of a Lambert quadrilateral was of considerable interest since if it could be shown to be a right angle, then the Euclidean parallel postulate could ...
A Saccheri quadrilateral is similar to a trapezoid in the hyperbolic plane, with two adjacent right angles, while it is a rectangle in the Euclidean plane. A Lambert quadrilateral in the hyperbolic plane has 3 right angles.
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The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
Ibn al-Haytham (Alhazen) (965–1039), an Arab mathematician, made an attempt at proving the parallel postulate using a proof by contradiction, [12] in the course of which he introduced the concept of motion and transformation into geometry. [13] He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham ...
Its fundamental domain is a Lambert quadrilateral, with 3 right angles. The dual tiling, called a deltoidal tetraoctagonal tiling , represents the fundamental domains of the *4222 orbifold. With edge-colorings there is a half symmetry form (4*4) orbifold notation .
The inscribed square problem, also known as the square peg problem or the Toeplitz' conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some square? This is true if the curve is convex or piecewise smooth and in other special cases. The problem was proposed by Otto Toeplitz in 1911. [1]
A square is a special case of a rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a trapezoid (one pair of opposite sides parallel), a parallelogram (all opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles), and therefore has all ...