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According to the characterization of these quadrilaterals, the two red squares on two opposite sides of the quadrilateral have the same total area as the two blue squares on the other pair of opposite sides. In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles.
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four straight sides of equal length and four equal angles (90-degree angles, π /2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adjacent sides.
Right kite: a kite with two opposite right angles. It is a type of cyclic quadrilateral. Harmonic quadrilateral: a cyclic quadrilateral such that the products of the lengths of the opposing sides are equal. Bicentric quadrilateral: it is both tangential and cyclic. Orthodiagonal quadrilateral: the diagonals cross at right angles.
Geometric Shapes; Range: U+25A0..U+25FF (96 code points) Plane: BMP: Scripts: Common: Symbol sets: Control code graphics Geometric shapes: Assigned: 96 code points
The apparent paradox is explained by the fact that the side of the new large square is a little smaller than the original one. If θ is the angle between two opposing sides in each quadrilateral, then the ratio of the two areas is given by sec 2 θ. For θ = 5°, this is approximately 1.00765, which corresponds to a difference of about 0.8%.
A rhombus. Each angle marked with a black dot is a right angle. The height h is the perpendicular distance between any two non-adjacent sides, which equals the diameter of the circle inscribed. The diagonals of lengths p and q are the red dotted line segments.
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.