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Rhomboidal
Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. A parallelogram with sides of equal length ( equilateral) is a rhombus but not a rhomboid. A parallelogram with right angled corners is a rectangle but not a rhomboid. The term ''rhomboid'' is now more often used for a rhombohedron or a more general parallelepiped, a solid figure with six faces in which each face is a parallelogram and pairs of opposite faces lie in parallel planes. Some crystals are formed in three-dimensional rhomboids. This solid is also sometimes called a rhombic prism. The term occurs frequently in science terminology referring to both its two- and three-dimensional meaning. History Euclid introduced the term in his '' Elements'' in Book I, Definition 22, Euclid never used the definition of rhomboid again and introduced the word parallelogram in Proposition 34 of Book I; ''"In parallelogrammic areas t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhomboid
Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. A parallelogram with sides of equal length (equilateral) is a rhombus but not a rhomboid. A parallelogram with right angled corners is a rectangle but not a rhomboid. The term ''rhomboid'' is now more often used for a rhombohedron or a more general parallelepiped, a solid figure with six faces in which each face is a parallelogram and pairs of opposite faces lie in parallel planes. Some crystals are formed in three-dimensional rhomboids. This solid is also sometimes called a rhombic prism. The term occurs frequently in science terminology referring to both its two- and three-dimensional meaning. History Euclid introduced the term in his '' Elements'' in Book I, Definition 22, Euclid never used the definition of rhomboid again and introduced the word parallelogram in Proposition 34 of Book I; ''"In parallelogrammic ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombohedron
In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a three-dimensional figure with six faces which are rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. A cube is a special case of a rhombohedron with all sides square. In general a ''rhombohedron'' can have up to three types of rhombic faces in congruent opposite pairs, ''C''''i'' symmetry, order 2. Four points forming non-adjacent vertices of a rhombohedron necessarily form the four vertices of an orthocentric tetrahedron, and all orthocentric tetrahedra can be formed in this way. Rhombohedral lattice system The rhombohedral lattice system has rhombohedral cells, with 6 congruent rhombic faces forming a trigonal trapezohedron: : Special cases by symmetry * Cube: with Oh symmetry, order 48. All faces are squares. * Trigonal trapezohedron (also c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calcium Pyrophosphate
Calcium pyrophosphate (Ca2P2O7) is a chemical compound, an insoluble calcium salt containing the pyrophosphate anion. There are a number of forms reported: an anhydrous form, a dihydrate, Ca2P2O7·2H2O and a tetrahydrate, Ca2P2O7·4H2O. Deposition of dihydrate crystals in cartilage are responsible for the severe joint pain in cases of calcium pyrophosphate deposition disease (pseudo gout) whose symptoms are similar to those of gout. Ca2P2O7 is commonly used as a mild abrasive agent in toothpastes, because of its insolubility and nonreactivity toward fluoride. __TOC__ Preparation Crystals of the tetrahydrate can be prepared by reacting sodium pyrophosphate, Na4P2O7 with calcium nitrate, Ca(NO3)2, at carefully controlled pH and temperature: :Na4P2O7(aq)+2 Ca(NO3)2(aq)→ Ca2P2O7·4 H2O + 4 NaNO3 The dihydrate, sometimes termed CPPD, can be formed by the reaction of pyrophosphoric acid with calcium chloride: :CaCl2 + H4P2O7(aq) → Ca2P2O7·2 H2O + HCl. The anhydrous forms can be p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudogout
Calcium pyrophosphate dihydrate (CPPD) crystal deposition disease, also known as pseudogout and pyrophosphate arthropathy, is a rheumatologic disease which is thought to be secondary to abnormal accumulation of calcium pyrophosphate dihydrate crystals within joint soft tissues. The knee joint is most commonly affected. Signs and symptoms When symptomatic, the disease classically begins with symptoms that are similar to a gout attack (thus the moniker "pseudogout"). These include: * severe pain * warmth * swelling of one or more joints The symptoms can be monoarticular (involving a single joint) or polyarticular (involving several joints). Symptoms usually last for days to weeks, and often recur. Although any joint may be affected, the knees, wrists, and hips are most common. X-ray, CT, or other imaging usually shows accumulation of calcium within the joint cartilage, known as chondrocalcinosis. There can also be findings of osteoarthritis.Rothschild, Bruce M The white blood cel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cephalopod Fin
Cephalopod fins, sometimes known as wings,Young, R.E., M. Vecchione & K.M. Mangold (1999)Cephalopoda Glossary Tree of Life Web Project. are paired flap-like locomotory appendages. They are found in ten-limbed cephalopods (including squid, bobtail squid, cuttlefish, and '' Spirula'') as well as in the eight-limbed cirrate octopuses and vampire squid. Many extinct cephalopod groups also possessed fins. Nautiluses and the more familiar incirrate octopuses lack swimming fins. An extreme development of the cephalopod fin is seen in the bigfin squid of the family Magnapinnidae. Fins project from the mantle and are often positioned dorsally. In most cephalopods, the fins are restricted to the posterior end of the mantle, but in cuttlefish and some squid they span the mantle's entire length. Fin attachment varies greatly among cephalopods, though in all cases it involves specialised fin cartilage (which reaches its greatest development in Octopodiformes). A fin may be attached to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Leaf Morphology
The following is a list of terms which are used to describe leaf morphology in the description and taxonomy of plants. Leaves may be simple (a single leaf blade or lamina) or compound (with several leaflets). The edge of the leaf may be regular or irregular, may be smooth or bearing hair, bristles or spines. For more terms describing other aspects of leaves besides their overall morphology see the leaf article. The terms listed here all are supported by technical and professional usage, but they cannot be represented as mandatory or undebatable; readers must use their judgement. Authors often use terms arbitrarily, or coin them to taste, possibly in ignorance of established terms, and it is not always clear whether because of ignorance, or personal preference, or because usages change with time or context, or because of variation between specimens, even specimens from the same plant. For example, whether to call leaves on the same tree "acuminate", "lanceolate", or "linear" could ... [...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 tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotational Symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids. Formal treatment Formally the rotational symmetry is symmetry with respect to some or all rotations in ''m''-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore, a symmetry group of rotational symmetry is a subgroup of ''E''+(''m'') (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid's Elements
The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions ( theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. ''Elements'' is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century. Euclid's ''Elements'' has been referred to as the most successful and influential textbook ever written. It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first print ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the philosophers Proclus and Pappus of Alexandria many centuries later. Until the early Renaissance he was often mistaken for the earlier philosopher Euclid of Megara, causing his biogr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallelepiped
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term '' rhomboid'' is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. In Euclidean geometry, the four concepts—''parallelepiped'' and ''cube'' in three dimensions, ''parallelogram'' and ''square'' in two dimensions—are defined, but in the context of a more general affine geometry, in which angles are not differentiated, only ''parallelograms'' and ''parallelepipeds'' exist. Three equivalent definitions of ''parallelepiped'' are *a polyhedron with six faces ( hexahedron), each of which is a parallelogram, *a hexahedron with three pairs of parallel faces, and *a prism of which the base is a parallelogram. The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces) are all specific cases of parallelepiped. "Parallelepiped" is now usually pronounced ... [...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 hy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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