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Pappus Hexagon
Pappus may refer to: * Pappus (botany), a structure within certain flowers * ''Pappus'' (bug), a genus of insects in the tribe Mirini * Pappus of Alexandria, Greek mathematician ** Pappus's hexagon theorem, often just called 'Pappus's theorem', a theorem named for Pappus of Alexandria ** Pappus's centroid theorem, another theorem named for Pappus of Alexandria ** Pappus configuration, a geometric configuration related to 'Pappus's theorem' ** Pappus graph, a graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ... related to the pappus configuration See also * Papus (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus (botany)
In Asteraceae, the pappus is the modified calyx, the part of an individual floret, that surrounds the base of the corolla tube in flower. It functions as a wind-dispersal mechanism for the seeds. The term is sometimes used for similar structures in other plant families e.g. in certain genera of the Apocynaceae, although the pappus in Apocynaceae is not derived from the calyx of the flower. In Asteraceae, the pappus may be composed of bristles (sometimes feathery), awns, scales, or may be absent, and in some species, is too small to see without magnification. In genera such as ''Taraxacum'' or ''Eupatorium'', feathery bristles of the pappus function as a "parachute" which enables the seed to be carried by the wind. The name derives from the Ancient Greek word ''pappos'', Latin ''pappus'', meaning "old man", so used for a plant (assumed to be an ''Erigeron'' species) having bristles and also for the woolly, hairy seed of certain plants. The pappus of the dandelion plays a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus (bug)
Pappus may refer to: * Pappus (botany), a structure within certain flowers * ''Pappus'' (bug), a genus of insects in the tribe Mirini * Pappus of Alexandria, Greek mathematician ** Pappus's hexagon theorem, often just called 'Pappus's theorem', a theorem named for Pappus of Alexandria ** Pappus's centroid theorem, another theorem named for Pappus of Alexandria ** Pappus configuration, a geometric configuration related to 'Pappus's theorem' ** Pappus graph, a graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ... related to the pappus configuration See also * Papus (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mirini
Mirini is a tribe of plant bugs belonging to the subfamily Mirinae. Genera '' Acanthocranella'' - '' Acanthopeplus'' - '' Actinonotus'' - '' Adelphocoridea'' - ''Adelphocoris'' - '' Adelphocorisella'' - '' Adnotholopus'' - '' Adphytocoris'' - '' Adpiasus'' - '' Adtaedia'' - ''Agnocoris'' - '' Alloeochrus'' - '' Alloeonotus'' - '' Allorhinocoris'' - '' Anexochus'' - '' Anosibea'' - '' Apantilius'' - '' Aphanosoma'' - '' Apolygopsis'' - ''Apolygus'' - '' Araucanomiris'' - ''Argenis'' - '' Aristopeplus'' - '' Atahualpacoris'' - '' Austrocapsus'' - '' Austropeplus'' - '' Azumamiris'' - ''Bertsa ''Bertsa'' is a genus of true bugs in the family Miridae. Characteristics Elongated oval shaped body, attenna with four segments. The white band on the dorsal of the insect marks the difference between this genus with others within the same trib ...'' - ''Bipuncticoris'' - ''Bispinocoris'' - ''Bolivarmiris'' - ''Boliviocapsus'' - ''Boliviocoris'' - ''Bolteria'' - ''Bowdenella'' - ''Bra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) ''Collection'', his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra. Context Pappus was active in the 4th century AD. In a period of general stagnation in mathematical studies, he stands out as a remarkable exception. "How far he was above his contemporaries, how lit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus's Hexagon Theorem
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that *given one set of collinear points A, B, C, and another set of collinear points a,b,c, then the intersection points X,Y,Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the ''Pappus line''. These three points are the points of intersection of the "opposite" sides of the hexagon AbCaBc. It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring. Projective planes in which the "theorem" is valid are called pappian planes. If one restricts the projective plane such that the Pappus line u is the line at infinity, one gets the ''affine version'' of Pappus's theorem shown in the second diagram. If the Pappus line u and the lines g,h have a point in common, one gets the so-called little version of Pappus's theorem. The dual of this incidence theorem states that given one set of concurrent lines A, B, C, and an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus's Centroid Theorem
In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. The theorems are attributed to Pappus of Alexandria and Paul Guldin. Pappus's statement of this theorem appears in print for the first time in 1659, but it was known before, by Kepler in 1615 and by Guldin in 1640. The first theorem The first theorem states that the surface area ''A'' of a surface of revolution generated by rotating a plane curve ''C'' about an axis external to ''C'' and on the same plane is equal to the product of the arc length ''s'' of ''C'' and the distance ''d'' traveled by the geometric centroid of ''C'': : A = sd. For example, the surface area of the torus with minor radius ''r'' and major radius ''R'' is : A = (2\pi r)(2\pi R) = 4\pi^2 R r. Proof A curve given by the positive function f(x) is bounded by two po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Configuration
In geometry, the Pappus configuration is a configuration of nine points and nine lines in the Euclidean plane, with three points per line and three lines through each point. History and construction This configuration is named after Pappus of Alexandria. Pappus's hexagon theorem states that every two triples of collinear points ''ABC'' and ''abc'' (none of which lie on the intersection of the two lines) can be completed to form a Pappus configuration, by adding the six lines ''Ab'', ''aB'', ''Ac'', ''aC'', ''Bc'', and ''bC'', and their three intersection points , , and . These three points are the intersection points of the "opposite" sides of the hexagon ''AbCaBc''. According to Pappus' theorem, the resulting system of nine points and eight lines always has a ninth line containing the three intersection points ''X'', ''Y'', and ''Z'', called the ''Pappus line''. The Pappus configuration can also be derived from two triangles ''XcC'' and ''YbB'' that are in perspective with e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Graph
In the mathematical field of graph theory, the Pappus graph is a bipartite 3- regular undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration. It is named after Pappus of Alexandria, an ancient Greek mathematician who is believed to have discovered the "hexagon theorem" describing the Pappus configuration. All the cubic distance-regular graphs are known; the Pappus graph is one of the 13 such graphs. The Pappus graph has rectilinear crossing number 5, and is the smallest cubic graph with that crossing number . It has girth 6, diameter 4, radius 4, chromatic number 2, chromatic index 3 and is both 3- vertex-connected and 3- edge-connected. It has book thickness 3 and queue number 2. The Pappus graph has a chromatic polynomial equal to: (x-1)x(x^-26x^+325x^-2600x^+14950x^-65762x^+229852x^-653966x^9+1537363x^8-3008720x^7+4904386x^6-6609926x^5+7238770x^4-6236975x^3+3989074x^2-1690406x+356509). The name "Pappus graph" has also been used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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