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Rhombus
In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a "diamond", after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (which some authors call a calisson after the French sweet – also see Polyiamond), and the latter sometimes refers specifically to a rhombus with a 45° angle. Every rhombus is simple (non-self-intersecting), and is a special case of a parallelogram and a kite. A rhombus with right angles is a square. Etymology The word "rhombus" comes from grc, ῥόμβος, rhombos, meaning something that spins, which derives from the verb , romanized: , meaning "to turn round and round." The word was used both by Eucl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides 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. It is the only regular polygon whose internal angle, central angle, and external angle are all equal (90°), and whose diagonals are all equal in length. A square with vertices ''ABCD'' would be denoted . Characterizations A convex quadrilateral is a square if and only if it is any one of the following: * A rectangle with two adjacent equal sides * A rhombus with a right vertex angle * A rhombus with all angles equal * A parallelogram with one right vertex angle and two adjacent equal sides * A quadrilateral with four equal sides and four right angles * A quadrilateral where the diagonals are equal, and are the perpendicular bisectors of each other (i.e., a rhombus with equal diagonals) * A convex quadrilateral with successiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kite (geometry)
In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, but the word ''deltoid'' may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals.See H. S. M. Coxeter's review of in : "It is unfortunate that the author uses, instead of 'kite', the name 'deltoid', which belongs more properly to a curve, the three-cusped hypocycloid." A kite may also be called a dart, particularly if it is not convex. Every kite is an orthodiagonal quadrilateral (its diagonals are at right angles) and, when convex, a tangential quadrilateral (its sides are tangent to an inscribed circle). The convex kites are exactly the quadrilaterals that are both orthodiagonal and tangential. They include as special cases the right kites, with two opposite right angles; the rhombi, with two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotoxal Figure
In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal () or edge-transitive if its symmetries act transitively on its edges. Informally, this means that there is only one type of edge to the object: given two edges, there is a translation, rotation, and/or reflection that will move one edge to the other, while leaving the region occupied by the object unchanged. Isotoxal polygons An isotoxal polygon is an even-sided i.e. equilateral polygon, but not all equilateral polygons are isotoxal. The duals of isotoxal polygons are isogonal polygons. Isotoxal 4n-gons are centrally symmetric, so are also zonogons. In general, an isotoxal 2n-gon has \mathrm_n, (^*nn) dihedral symmetry. For example, a rhombus is an isotoxal "2×2-gon" (quadrilateral) with \mathrm_2, (^*22) symmetry. All regular polygons (equilateral triangle, square, etc.) are isotoxal, having double the minimum symmetry order: a regular n-gon has \mathrm_n, (^*nn) dihedral symmetry. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapezoid
A quadrilateral with at least one pair of parallel sides is called a trapezoid () in American and Canadian English. In British and other forms of English, it is called a trapezium (). A trapezoid is necessarily a Convex polygon, convex quadrilateral in Euclidean geometry. The parallel sides are called the ''bases'' of the trapezoid. The other two sides are called the ''legs'' (or the ''lateral sides'') if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases). A ''scalene trapezoid'' is a trapezoid with no sides of equal measure, in contrast with the #Special cases, special cases below. Etymology and ''trapezium'' versus ''trapezoid'' Ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια (''trapezia'' literally "a table", itself fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kite (geometry)
In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, but the word ''deltoid'' may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals.See H. S. M. Coxeter's review of in : "It is unfortunate that the author uses, instead of 'kite', the name 'deltoid', which belongs more properly to a curve, the three-cusped hypocycloid." A kite may also be called a dart, particularly if it is not convex. Every kite is an orthodiagonal quadrilateral (its diagonals are at right angles) and, when convex, a tangential quadrilateral (its sides are tangent to an inscribed circle). The convex kites are exactly the quadrilaterals that are both orthodiagonal and tangential. They include as special cases the right kites, with two opposite right angles; the rhombi, with two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lozenge (shape)
A lozenge ( ; 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 () for ''rhombus''. Most often, though, lozenge refers to a thin rhombus—a rhombus with two acute and two obtuse angles, especially one with acute angles of 45°. 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. Symbolism The lozenge motif dates from the Neolithic and Paleolithic period in Eastern Europe and represents a sown field and female fertility. The ancient lozenge pattern often shows up in Diamond vault ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectangle
In Euclidean plane geometry, a rectangle is 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''. The term "oblong" is occasionally used to refer to a non-square rectangle. A rectangle with vertices ''ABCD'' would be denoted as . The word rectangle comes from the Latin ''rectangulus'', which is a combination of ''rectus'' (as an adjective, right, proper) and ''angulus'' (angle). A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperboli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, derived from greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices A, B, C and D is sometimes denoted as \square ABCD. Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ''ABCD'' add up to 360 degrees of arc, that is :\angle A+\angle B+\angle C+\angle D=360^. This is a special case of the ''n''-gon interior angle sum formula: ''S'' = (''n'' − 2) × 180°. All non-self-crossing quadrilaterals tile the plane, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallelogram
In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The three-dimensional counterpart of a parallelogram is a parallelepiped. The etymology (in Greek παραλληλ-όγραμμον, ''parallēl-ógrammon'', a shape "of parallel lines") reflects the definition. Special cases *Rectangle – A parallelogram with four angles of equal size (right angles). *Rhombus – A parallelogram with four sides of eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bicone
In geometry, a bicone or dicone (from la, bi-, and Greek: ''di-'', both meaning "two") is the three-dimensional surface of revolution of a rhombus around one of its axes of symmetry. Equivalently, a bicone is the surface created by joining two congruent, right, circular cones at their bases. A bicone has circular symmetry and orthogonal bilateral symmetry. Geometry For a circular bicone with radius ''R'' and height center-to-top ''H'', the formula for volume becomes :V = \frac \pi R^2 H. For a right circular cone, the surface area is :SA =2\pi R S\, where S = \sqrt is the slant height. See also * Sphericon * Biconical antenna In radio systems, a biconical antenna is a broad-bandwidth antenna made of two roughly conical conductive objects, nearly touching at their points.Zhuohui Zhang,''Analysis and design of a broadband antenna for software defined radio'', ProQuest, 2 ... References External links * Elementary geometry Surfaces {{ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagonal
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 angle to angle" (from διά- ''dia-'', "through", "across" and γωνία ''gonia'', "angle", 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"). In matrix algebra, the diagonal of a square matrix consists of the entries on the line from the top left corner to the bottom right corner. There are also other, non-mathematical uses. Non-mathematical uses In engineering, a diagonal brace is a beam used to brace a rectangular structure (such as scaffolding) to withstand strong forces pushing into it; although called a diagonal, due to practical consideration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyiamond
A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino) is a polyform whose base form is an equilateral triangle. The word ''polyiamond'' is a back-formation from ''diamond'', because this word is often used to describe the shape of a pair of equilateral triangles placed base to base, and the initial 'di-' looks like a Greek prefix meaning 'two-' (though ''diamond'' actually derives from Greek '' ἀδάμας'' - also the basis for the word "adamant"). The name was suggested by recreational mathematics writer Thomas H. O'Beirne in ''New Scientist'' 1961 number 1, page 164. Counting The basic combinatorial question is, How many different polyiamonds exist with a given number of cells? Like polyominoes, polyiamonds may be either free or one-sided. Free polyiamonds are invariant under reflection as well as translation and rotation. One-sided polyiamonds distinguish reflections. The number of free ''n''-iamonds for ''n'' = 1, 2, 3, ... is: :1, 1, 1, 3, 4, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
