In geometry, a rhombus (pl.: rhombi or rhombuses) is an equilateral quadrilateral, a quadrilateral whose four sides all have the same length. Other names for rhombus include diamond, lozenge, and calisson.
Every rhombus is a simple polygon (having no self-intersections). A rhombus is a special case of a parallelogram and a kite. A rhombus with right angles is a square. A non-square rhombus has two opposite acute angles and two opposite obtuse angles.
In geometry, a square is a regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal sides. As with all rectangles, a square's angles are right angles (90 degrees, or π/2 radians), making adjacent sides perpendicular. The area of a square is the side length multiplied by itself, and so in algebra, multiplying a number by itself is called squaring.
Equal squares can tile the plane edge-to-edge in the square tiling. Square tilings are ubiquitous in tiled floors and walls, graph paper, image pixels, and game boards. Square shapes are also often seen in building floor plans, origami paper, food servings, in graphic design and heraldry, and in instant photos and fine art.
In geology, a basin is a region where subsidence generates accommodation space for the deposition of sediments. A pull-apart basin is a structural basin where two overlapping (en echelon) strike-slip faults or a fault bend create an area of crustal extension undergoing tension, which causes the basin to sink down. Frequently, the basins are rhombic or sigmoidal in shape. Dimensionally, basins are limited to the distance between the faults and the length of overlap.
In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word diagonal derives from the ancient Greek διαγώνιος diagonios, "from corner to corner" (from διά- dia-, "through", "across" and γωνία gonia, "corner", related to gony "knee"); it was used by both Strabo and Euclid to refer to a line connecting two vertices of a rhombus or cuboid, and later adopted into Latin as diagonus ("slanting line").
A Klemperer rosette is a gravitational system of (optionally) alternating heavier and lighter bodies orbiting in a symmetrical pattern around a common barycenter. It was first described by W.B. Klemperer in 1962, and is a special case of a central configuration.
Klemperer described rosette systems as follows:
In mathematics, a transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X.Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations.
A lozenge (/ˈlɒzɪndʒ/ LOZ-inj; symbol: ◊), often referred to as a diamond, is a form of rhombus. The definition of lozenge is not strictly fixed, and the word is sometimes used simply as a synonym (from Old French losenge) for rhombus. Most often, though, lozenge refers specifically to a thin rhombus, especially one with two acute angles of 45° and two obtuse angles of 135°.
The lozenge shape is often used in parquetry (with acute angles that are 360°/n with n being an integer higher than 4, because they can be used to form a set of tiles of the same shape and size, reusable to cover the plane in various geometric patterns as the result of a tiling process called tessellation in mathematics) and as decoration on ceramics, silverware and textiles. It also features in heraldry and playing cards.
The hindbrain, rhombencephalon (shaped like a rhombus) is a developmental categorization of portions of the central nervous system in vertebrates. It includes the medulla, pons, and cerebellum. Together they support vital bodily processes.