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48 (number)
48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens. In mathematics 48 is a highly composite number, and a Størmer number. By a classical result of Honsberger, the number of incongruent integer-sided triangles of perimeter m is given by the equations \tfrac for even m, and \tfrac for odd m. 48 is the order of full octahedral symmetry, which describes three-dimensional mirror symmetries associated with the regular octahedron and cube. There are 48 symmetries of a cube. In other fields Forty-eight may also refer to: * In Chinese numerology, 48 is an auspicious number meaning 'determined to prosper', or simply 'prosperity', which is good for business. * '48 is a slang term in Palestinian Arabic for parts of Israel or Palestine not under the control of the State of Palestine Palestine, officially the State of Palestine, is a country in West Asia. Recognized by International recognition of Pal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Order
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is ''infinite''. The ''order'' of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element of a group, is thus the smallest positive integer such that , where denotes the identity element of the group, and denotes the product of copies of . If no such exists, the order of is infinite. The order of a group is denoted by or , and the order of an element is denoted by or , instead of \operatorname(\langle a\rangle), where the brackets denote the generated group. Lagrange's theorem states that for any subgroup of a finite group , the order of the subgroup divides the order of the group; that is, is a divisor of . In particular, the order of any element is a divisor of . Example The symmetric group S3 has t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Of Palestine
Palestine, officially the State of Palestine, is a country in West Asia. Recognized by International recognition of Palestine, 147 of the UN's 193 member states, it encompasses the Israeli-occupied West Bank, including East Jerusalem, and the Gaza Strip, collectively known as the occupied Palestinian territories, within the broader geographic and historical Palestine (region), Palestine region. Palestine shares most of its borders with Israel, and it borders Jordan to the east and Egypt to the southwest. It has a total land area of while Demographics of the State of Palestine, its population exceeds five million people. Its Status of Jerusalem, proclaimed capital is Jerusalem, while Ramallah serves as its administrative center. Gaza City was its largest city prior to Gaza Strip evacuations, evacuations in 2023. Situated at a Levantine corridor, continental crossroad, the region of Palestine was ruled by various empires and experienced Demographic history of Palestine (region ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palestine (region)
The region of Palestine, also known as historic Palestine, is a geographical area in West Asia. It includes the modern states of Israel and Palestine, as well as parts of northwestern Jordan in some definitions. Other names for the region include Canaan, the Promised Land, the Land of Israel, or the Holy Land. The earliest written record Timeline of the name Palestine, referring to Palestine as a geographical region is in the ''Histories (Herodotus), Histories'' of Herodotus in the 5th century BCE, which calls the area ''Palaistine'', referring to the territory previously held by Philistia, a state that existed in that area from the 12th to the 7th century BCE. The Roman Empire conquered the region and in 6 CE established the province known as Judaea (Roman province), Judaea. In the aftermath of the Bar Kokhba revolt (132–136 CE), the province was renamed Syria Palaestina. In 390, during the Byzantine period, the region was split into the provinces of Palaestina Prima, Pal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel
Israel, officially the State of Israel, is a country in West Asia. It Borders of Israel, shares borders with Lebanon to the north, Syria to the north-east, Jordan to the east, Egypt to the south-west, and the Mediterranean Sea to the west. Israeli-occupied territories, It occupies the Occupied Palestinian territories, Palestinian territories of the West Bank in the east and the Gaza Strip in the south-west. Israel also has a small coastline on the Red Sea at its southernmost point, and part of the Dead Sea lies along its eastern border. Status of Jerusalem, Its proclaimed capital is Jerusalem, while Tel Aviv is the country's Gush Dan, largest urban area and Economy of Israel, economic center. Israel is located in a region known as the Land of Israel, synonymous with the Palestine (region), Palestine region, the Holy Land, and Canaan. In antiquity, it was home to the Canaanite civilisation followed by the History of ancient Israel and Judah, kingdoms of Israel and Judah. Situate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palestinian Arabic
Palestinian Arabic (also known as simply Palestinian) is part of a dialect continuum comprising various mutually intelligible varieties of Levantine Arabic spoken by Palestinians in Palestine, which includes the State of Palestine, Israel, and the Palestinian diaspora. The Arabic dialects spoken in the region of Palestine and Transjordan do not form a homogeneous linguistic unit; rather, they encompass a diverse range of dialects influenced by geographical, historical, and socioeconomic factors. Comparative studies of Arabic dialects indicate that Palestinian Arabic is among the closest dialects to Modern Standard Arabic, particularly the dialect spoken in the Gaza Strip. Additional distinctions can be made within Palestinian Arabic, such as the dialects spoken in the northern West Bank and the Hebron area, which exhibit similarities to those spoken by descendants of Palestinian refugees. Palestinian Arabic dialects reflect a historical layering of languages previously spoken ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerology
Numerology (known before the 20th century as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in words and names. When numerology is applied to a person's name, it is a form of onomancy. It is often associated with astrology and other divinatory arts. Number symbolism is an ancient and pervasive aspect of human thought, deeply intertwined with religion, philosophy, mysticism, and mathematics. Different cultures and traditions have assigned specific meanings to numbers, often linking them to divine principles, cosmic forces, or natural patterns. The term numerologist can be used for those who place faith in numerical patterns and draw inferences from them, even if those people do not practice traditional numerology. For example, in his 1997 book ''Numerology: Or What Pythagoras Wrought'' (), mathematician Underwo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is Invariant (mathematics), invariant under some Transformation (function), transformations, such as Translation (geometry), translation, Reflection (mathematics), reflection, Rotation (mathematics), rotation, or Scaling (geometry), scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a space, spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including scientific model, theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube
A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular cuboid, with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with 1, unit s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Platonic Solid
In geometry, a Platonic solid is a Convex polytope, convex, regular polyhedron in three-dimensional space, three-dimensional Euclidean space. Being a regular polyhedron means that the face (geometry), faces are congruence (geometry), congruent (identical in shape and size) regular polygons (all angles congruent and all edge (geometry), edges congruent), and the same number of faces meet at each Vertex (geometry), vertex. There are only five such polyhedra: Geometers have studied the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato, who hypothesized in one of his dialogues, the ''Timaeus (dialogue), Timaeus'', that the classical elements were made of these regular solids. History The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes; however, these balls have rounded knobs rather than being polyhedral, the num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Group
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object ''X'' is ''G'' = Sym(''X''). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types of geometric structure. Introduction We consider the "objects" possessing symmetry to be geometric figures, images, and patterns, such as a wallpaper pattern. For symmetry of physical objects, one may also take their physical composition as part of the pattern. (A pattern may be specified formally as a scalar field, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octahedral Symmetry
A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has the same set of symmetries, since it is the polyhedron that is dual polyhedron, dual to an octahedron. The group of orientation-preserving symmetries is S4, the symmetric group or the group of permutations of four objects, since there is exactly one such symmetry for each permutation of the four diagonals of the cube. Details Chiral and full (or achiral) octahedral symmetry are the Point groups in three dimensions, discrete point symmetries (or equivalently, List of spherical symmetry groups, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. They are among the Crystal system#Overview of point groups by crystal system, crystallographic point groups of the cubic crystal system. As the hyperoctahedral group of dimension 3 the full octah ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
