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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 rhombus, rhombi, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrilateral
In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), 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 polygon, simple (not self-intersecting), or complex polygon, complex (self-intersecting, or crossed). Simple quadrilaterals are either convex polygon, convex or concave polygon, concave. The Internal and external angle, interior angles of a simple (and Plane (geometry), planar) quadrilateral ''ABCD'' add up to 360 Degree (angle), degrees, that is :\angle A+\angle B+\angle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isohedral Figure
In geometry, a tessellation of dimension (a plane tiling) or higher, or a polytope of dimension (a polyhedron) or higher, is isohedral or face-transitive if all its Face (geometry), faces are the same. More specifically, all faces must be not merely Congruence (geometry), congruent but must be ''transitive'', i.e. must lie within the same ''symmetry orbit''. In other words, for any two faces and , there must be a symmetry of the ''entire'' figure by Translation (geometry), translations, Rotation (mathematics), rotations, and/or Reflection (mathematics), reflections that maps onto . For this reason, Convex polytope, convex isohedral polyhedra are the shapes that will make fair dice. Isohedral polyhedra are called isohedra. They can be described by their face configuration. An isohedron has an Parity (mathematics), even number of faces. The Dual polyhedron, dual of an isohedral polyhedron is vertex-transitive, i.e. isogonal. The Catalan solids, the bipyramids, and the trapezo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Olaus Henrici
Olaus Magnus Friedrich Erdmann Henrici, FRS (9 March 1840, Meldorf, Duchy of Holstein – 10 August 1918, Chandler's Ford, Hampshire, England) was a German mathematician who became a professor in London. After three years as an apprentice in engineering, Henrici entered Karlsruhe Polytechnium where he came under the influence of Alfred Clebsch who encouraged him in mathematics. He then went to Heidelberg where he studied with Otto Hesse. Henrici attained his Dr. phil. degree on 6 June 1863 at University of Heidelberg. He continued his studies in Berlin with Karl Weierstrass and Leopold Kronecker. He was briefly docent of mathematics and physics at the University of Kiel, but ran into financial difficulties. Henrici moved to London in 1865 where he worked as a private tutor. In 1869 Hesse introduced him to J. J. Sylvester who in turn brought him into contact with Arthur Cayley, William Kingdon Clifford, and Thomas Archer Hirst. It was Hirst that gave him some work at Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kite (bird)
Kite is the common name for certain birds of prey in the family Accipitridae, particularly in the subfamilies Elaninae and Perninae and certain genera within Buteoninae."kite". Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica Inc., 2014. Web. 24 Nov. 2014 . The term is derived from Old English , onomatopoeic from the call notes of the buzzard (''Buteo buteo'') and red kite (''Milvus milvus''). The name, having no cognate names in other European languages, is thought to have arisen in England; it apparently originally denoted the buzzard, as the red kite was then known by the widespread Germanic name 'glede' or 'glead', and was only later transferred to the red kite as "fork-tailed kite" by Christopher Merret in his 1667 ''Pinax Rerum Naturalium Britannicarum''. By the time of Thomas Pennant's 1768 ''British Zoology'', the name had become fixed on the red kite, other birds named 'kite' around the world being named from their then-percei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kite
A kite is a tethered heavier than air flight, heavier-than-air craft with wing surfaces that react against the air to create Lift (force), lift and Drag (physics), drag forces. A kite consists of wings, tethers and anchors. Kites often have a bridle and tail to guide the face of the kite so the wind can lift it. Some kite designs do not need a bridle; box kites can have a single attachment point. A kite may have fixed or moving anchors that can balance the kite. The name is derived from the kite (bird), kite, the hovering bird of prey. There are several shapes of kites. The Lift (force), lift that sustains the kite in flight is generated when air moves around the kite's surface, producing low pressure above and high pressure below the wings. The interaction with the wind also generates horizontal Drag (physics), drag along the direction of the wind. The resultant force vector from the lift and drag force components is opposed by the tension of one or more of the rope, lines ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle Bisector
In geometry, bisection is the division of something into two equal or congruent parts (having the same shape and size). Usually it involves a bisecting line, also called a ''bisector''. The most often considered types of bisectors are the ''segment bisector'', a line that passes through the midpoint of a given segment, and the ''angle bisector'', a line that passes through the apex of an angle (that divides it into two equal angles). In three-dimensional space, bisection is usually done by a bisecting plane, also called the ''bisector''. Perpendicular line segment bisector Definition *The perpendicular bisector of a line segment is a line which meets the segment at its midpoint perpendicularly. *The perpendicular bisector of a line segment AB also has the property that each of its points X is equidistant from segment AB's endpoints: (D)\quad , XA, = , XB, . The proof follows from , MA, =, MB, and Pythagoras' theorem: :, XA, ^2=, XM, ^2+, MA, ^2=, XM, ^2+, MB, ^2=, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concave Polygon
A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180° degrees and 360° degrees exclusive. Polygon Some lines containing interior points of a concave polygon intersect its boundary at more than two points. Some diagonals of a concave polygon lie partly or wholly outside the polygon. Some sidelines of a concave polygon fail to divide the plane into two half-planes one of which entirely contains the polygon. None of these three statements holds for a convex polygon. As with any simple polygon, the sum of the internal angles of a concave polygon is (''n'' − 2) radians, equivalently 180°(''n'' − 2) degrees, where ''n'' is the number of sides. It is always possible to partition a concave polygon into a set of convex polygons. A polynomial-time algorithm for finding a decomposition into as few convex pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Polygon
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). Equivalently, a polygon is convex if every line that does not contain any edge intersects the polygon in at most two points. Strictly convex polygon A convex polygon is ''strictly'' convex if no line contains more than two vertices of the polygon. In a convex polygon, all interior angles are less than ''or equal'' to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees. Properties The following properties of a simple polygon are all equivalent to convexity: *Every internal angle is less than or equal to 180 degrees. *Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the bou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a Disk (mathematics), disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Terminology * Annulus (mathematics), Annulus: a ring-shaped object, the region bounded by two concentric circles. * Circular arc, Arc: any Connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deltoid
Deltoid (delta-shaped) can refer to: * The deltoid muscle, a muscle in the shoulder * Kite (geometry), also known as a deltoid, a type of quadrilateral * A deltoid curve, a three-cusped hypocycloid * A leaf shape * The deltoid tuberosity, a part of the humerus * The deltoid ligament, a ligament in the ankle See also *Delta (other) Delta commonly refers to: * Delta (letter) (Δ or δ), the fourth letter of the Greek alphabet * D (NATO phonetic alphabet: "Delta"), the fourth letter in the Latin alphabet * River delta, at a river mouth * Delta Air Lines, a major US carrier ... *'' The Deltoid Pumpkin Seed'' (1973), a book by John McPhee {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
