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Heptagram
A heptagram, septagram, septegram or septogram is a seven-point star polygon, star drawn with seven straight strokes. The name ''heptagram'' combines a numeral prefix, ''hepta-'', with the Greek language, Greek suffix ''wikt:-gram, -gram''. The ''-gram'' suffix derives from ''γραμμῆ'' (''grammē'') meaning a line. Geometry In general, a heptagram is any self-intersecting heptagon (7-sided polygon). There are two ''regular'' heptagrams, labeled as and , with the second number representing the vertex interval step from a regular heptagon, . This is the smallest star polygon that can be drawn in two forms, as irreducible fractions. The two heptagrams are sometimes called the ''heptagram'' (for ) and the ''great heptagram'' (for ). The previous one, the regular hexagram , is a compound of two triangles. The smallest star polygon is the pentagram. The next one is the octagram and its related star figure (a compound of two squares), followed by the regular enneag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antiprism 7-2
In geometry, an antiprism or is a polyhedron composed of two Parallel (geometry), parallel Euclidean group, direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway polyhedron notation, Conway notation . Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron. Antiprisms are similar to Prism (geometry), prisms, except that the bases are twisted relatively to each other, and that the side faces (connecting the bases) are triangles, rather than quadrilaterals. The dual polyhedron of an -gonal antiprism is an -gonal trapezohedron. History In his 1619 book ''Harmonices Mundi'', Johannes Kepler observed the existence of the infinite family of antiprisms. This has conventionally been thought of as the first discovery of these shapes, but they may have been known earlier: an unsigned printing block for the net (geometry), net of a hexagonal antiprism has been attributed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heptagon
In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using ''Wikt:septa-, septa-'' (an elision of ''Wikt:septua-, septua-''), a Latin-derived numerical prefix, rather than ''Wikt:hepta-, hepta-'', a Greek language, Greek-derived numerical prefix (both are cognate), together with the suffix ''-gon'' for , meaning angle. Regular heptagon A regular polygon, regular heptagon, in which all sides and all angles are equal, has internal angles of 5π/7 radians (128 degree (angle), degrees). Its Schläfli symbol is . Area The area (''A'') of a regular heptagon of side length ''a'' is given by: :A = \fraca^2 \cot \frac \simeq 3.634 a^2. This can be seen by subdividing the unit-sided heptagon into seven triangular "pie slices" with Vertex (geometry), vertices at the center and at the heptagon's vertices, and then halving each triangle using the apothem as the common side. The apothem is half the cotangent of \pi/7 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antiprism 7-3
In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation . Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron. Antiprisms are similar to prisms, except that the bases are twisted relatively to each other, and that the side faces (connecting the bases) are triangles, rather than quadrilaterals. The dual polyhedron of an -gonal antiprism is an -gonal trapezohedron. History In his 1619 book ''Harmonices Mundi'', Johannes Kepler observed the existence of the infinite family of antiprisms. This has conventionally been thought of as the first discovery of these shapes, but they may have been known earlier: an unsigned printing block for the net of a hexagonal antiprism has been attributed to Hieronymus Andreae, who died in 1556. The German form of the word "antiprism" was used for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star Polygon
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, Decagram (geometry)#Related figures, certain notable ones can arise through truncation operations on regular simple or star polygons. Branko Grünbaum identified two primary usages of this terminology by Johannes Kepler, one corresponding to the regular star polygons with List of self-intersecting polygons, intersecting edges that do not generate new vertices, and the other one to the isotoxal Concave polygon, concave simple polygons.Grünbaum & Shephard (1987). Tilings and Patterns. Section 2.5 Polygram (geometry), Polygrams include polygons like the pentagram, but also compound figures like the hexagram. One definition of a ''star polygon'', used in turtle graphics, is a polygon having ''q'' ≥ 2 Turn (geometry), turns (''q'' is called the turning number or Density (polygon), density), like in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagram
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle around the five points creates a similar symbol referred to as the pentacle, which is used widely by Wiccans and in paganism, or as a sign of life and connections. The word ''pentagram'' comes from the Greek language, Greek word πεντάγραμμον (''pentagrammon''), from πέντε (''pente''), "five" + γραμμή (''grammē''), "line". The word pentagram refers to just the star and the word pentacle refers to the star within a circle, although there is some overlap in usage. The word ''pentalpha'' is a 17th-century revival of a post-classical Greek name of the shape. History Early history Early pentagrams have been found on Sumerian pottery from Ur c. 3500 Common Era, BCE, and the five-pointed star was at various times the symbol of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagram
, can be seen as a compound polygon, compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green). A hexagram (Greek language, Greek) or sexagram (Latin language, Latin) is a six-pointed geometric star figure with the Schläfli symbol , 2, or . The term is used to refer to a compound figure of two equilateral triangles. The intersection is a regular hexagon. The hexagram is part of an infinite series of shapes which are compounds of two n-dimensional simplex, simplices. In three dimensions, Compound of two tetrahedra, the analogous compound is the stellated octahedron, and in four dimensions the compound of two 5-cells is obtained. It has been historically used in various religious and cultural contexts and as decorative motifs. The symbol was used as a decorative motif in medieval Christian churches and Jewish synagogues. In the medieval period, a Muslim mystical symbol known as the Seal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cook County
Cook County is the most populous county in the U.S. state of Illinois and the second-most-populous county in the United States, after Los Angeles County, California. More than 40 percent of all residents of Illinois live within Cook County. the population was 5,275,541. The county seat is Chicago, the most populous city in Illinois and the third most populous city in the United States. The county is at the center of the Chicago metropolitan area. Cook county is also the sixth largest county in Illinois by area. Cook County was incorporated in 1831 and named for Daniel Pope Cook, an early Illinois statesman. It achieved its present boundaries in 1839. Within a century, the county recorded explosive population growth, going from a trading post village with a little over six hundred residents to four million, rivaling Paris by the Great Depression. During the first half of the 20th century it had the absolute majority of Illinois's population. There are more than 800 local ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coat Of Arms Of Australia
The coat of arms of Australia, officially the Commonwealth Coat of Arms, is a formal symbol of the Commonwealth of Australia. It depicts a shield, containing symbols of Australia's six states, and is held up by native Australian animals, the kangaroo and the emu. The seven-pointed Commonwealth Star surmounting the crest also represents the states and territories, while golden wattle, the national floral emblem, appears below the shield. The first arms were authorised by Edward VII, King Edward VII on 7 May 1908, and the current version by George V, King George V on 19 September 1912, although the 1908 version continued to be used in some contexts, notably appearing on the obverse and reverse, reverse of the Sixpence (Australian), sixpenny coin. Design Escutcheon The Escutcheon (heraldry), escutcheon (central shield) is the focal point of the coat of arms, and contains six Quarter (heraldry), quarters, each containing a representation of the badge of an Australian state. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Samarkand
Samarkand ( ; Uzbek language, Uzbek and Tajik language, Tajik: Самарқанд / Samarqand, ) is a city in southeastern Uzbekistan and among the List of oldest continuously inhabited cities, oldest continuously inhabited cities in Central Asia. Samarkand is the capital of the Samarkand Region and a district-level city, that includes the urban-type settlements Kimyogarlar, Farxod, Farhod and Xishrav, Khishrav. With 551,700 inhabitants (2021), it is the List of cities in Uzbekistan, third-largest city in Uzbekistan. There is evidence of human activity in the area of the city dating from the late Paleolithic Era. Though there is no direct evidence of when Samarkand was founded, several theories propose that it was founded between the 8th and 7th centuries BC. Prospering from its location on the Silk Road between East Asia, China, Persia and Europe, at times Samarkand was one of the largest cities in Central Asia,Guidebook of history of Samarkand", and was an important city of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Graph
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction). Graph theory itself is typically dated as beginning with Leonhard Euler's 1736 work on the Seven Bridges of Königsberg. However, drawings of complete graphs, with their vertices placed on the points of a regular polygon, had already appeared in the 13th century, in the work of Ramon Llull. Such a drawing is sometimes referred to as a mystic rose. Properties The complete graph on vertices is denoted by . Some sources claim that the letter in this notation stands for the German word , but the German name for a complete graph, , does not contain the letter , and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory. has edg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hokkaido
is the list of islands of Japan by area, second-largest island of Japan and comprises the largest and northernmost prefectures of Japan, prefecture, making up its own list of regions of Japan, region. The Tsugaru Strait separates Hokkaidō from Honshu; the two islands are connected by railway via the Seikan Tunnel. The largest city on Hokkaido is its capital, Sapporo, which is also its only cities designated by government ordinance of Japan, ordinance-designated city. Sakhalin lies about to the north of Hokkaidō, and to the east and northeast are the Kuril Islands, which are administered by Russia, though the four most southerly are Kuril Islands dispute, claimed by Japan. The position of the island on the northern end of the archipelago results in a colder climate, with the island seeing significant snowfall each winter. Despite the harsher climate, it serves as an agricultural breadbasket for many crops. Hokkaido was formerly known as ''Ezo'', ''Yezo'', ''Yeso'', or ''Yes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
