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In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
A "simple" squared square is one where no subset of more than one of the squares forms a rectangle or square. When a squared square has a square or rectangular subset, it is "compound". In 1978, A. J. W. Duijvestijn [ de ] discovered a simple perfect squared square of side 112 with the smallest number of squares using a computer search.
However, there are three distinct ways of partitioning a square into three similar rectangles: [1] [2] The trivial solution given by three congruent rectangles with aspect ratio 3:1. The solution in which two of the three rectangles are congruent and the third one has twice the side length of the other two, where the rectangles have aspect ...
A crossed square is sometimes likened to a bow tie or butterfly. the crossed rectangle is related, as a faceting of the rectangle, both special cases of crossed quadrilaterals. [12] The interior of a crossed square can have a polygon density of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise.
A separator square in a polygon P is a square s in P such that P−s is not connected. Lemma: in a simple rectilinear polygon, a maximal square that does not contain a knob is a separator. [3] A square containing a knob may or may not be a separator. The number of different separator squares may be infinite and even uncountable.
IM 67118, also known as Db 2-146, is an Old Babylonian clay tablet in the collection of the Iraq Museum that contains the solution to a problem in plane geometry concerning a rectangle with given area and diagonal. In the last part of the text, the solution is proved correct using the Pythagorean theorem. The steps of the solution are believed ...
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 quadrilateral is a square if and only if it is both a rhombus and a rectangle (i.e., four equal sides and four equal angles). Oblong: longer than wide, or wider than long (i.e., a rectangle that is not a square). [5] Kite: two pairs of adjacent sides are of equal length.