|
John Leech (mathematician)
John Leech (21 July 1926 in Weybridge, Surrey – 28 September 1992 in Scotland) was a British mathematician working in number theory, geometry and combinatorial group theory. He is best known for his discovery of the Leech lattice In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by . It may also have been discovered (but not published) by ... in 1965. He also discovered Ta(3) in 1957. Leech was married to Jenifer Haselgrove, a British radio scientist. References External links MacTutor History of Mathematics biography 20th-century British mathematicians 1926 births 1992 deaths {{UK-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brackets
A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. Typically deployed in symmetric pairs, an individual bracket may be identified as a 'left' or 'right' bracket or, alternatively, an "opening bracket" or "closing bracket", respectively, depending on the Writing system#Directionality, directionality of the context. Specific forms of the mark include parentheses (also called "rounded brackets"), square brackets, curly brackets (also called 'braces'), and angle brackets (also called 'chevrons'), as well as various less common pairs of symbols. As well as signifying the overall class of punctuation, the word "bracket" is commonly used to refer to a specific form of bracket, which varies from region to region. In most English-speaking countries, an unqualified word "bracket" refers to the parenthesis (round bracket); in the United States, the square bracket. Glossary of mathematical sym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weybridge
Weybridge () is a town in the Borough of Elmbridge in Surrey, England, around southwest of central London. The settlement is recorded as ''Waigebrugge'' and ''Weibrugge'' in the 7th century and the name derives from a crossing point of the River Wey, which flows into the River Thames to the north of the town centre. The earliest evidence of human activity is from the Bronze Age. During the Anglo-Saxon and medieval periods, Weybridge was held by Chertsey Abbey. In the 1530s, Henry VIII constructed Oatlands Palace to the north of the town centre, which he intended to be the residence of his fourth wife, Anne of Cleves. He married Catherine Howard there in July 1540 and the palace remained a royal residence until the Civil War. The buildings were demolished in the early 1650s and a new mansion, Oatlands House, was constructed to the east of Weybridge later the same century. Prince Frederick, Duke of York and Albany owned the mansion in the 18th century. The town began to ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surrey
Surrey () is a ceremonial and non-metropolitan county in South East England, bordering Greater London to the south west. Surrey has a large rural area, and several significant urban areas which form part of the Greater London Built-up Area. With a population of approximately 1.2 million people, Surrey is the 12th-most populous county in England. The most populated town in Surrey is Woking, followed by Guildford. The county is divided into eleven districts with borough status. Between 1893 and 2020, Surrey County Council was headquartered at County Hall, Kingston-upon-Thames (now part of Greater London) but is now based at Woodhatch Place, Reigate. In the 20th century several alterations were made to Surrey's borders, with territory ceded to Greater London upon its creation and some gained from the abolition of Middlesex. Surrey is bordered by Greater London to the north east, Kent to the east, Berkshire to the north west, West Sussex to the south, East Sussex to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scotland
Scotland (, ) is a country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a border with England to the southeast and is otherwise surrounded by the Atlantic Ocean to the north and west, the North Sea to the northeast and east, and the Irish Sea to the south. It also contains more than 790 islands, principally in the archipelagos of the Hebrides and the Northern Isles. Most of the population, including the capital Edinburgh, is concentrated in the Central Belt—the plain between the Scottish Highlands and the Southern Uplands—in the Scottish Lowlands. Scotland is divided into 32 administrative subdivisions or local authorities, known as council areas. Glasgow City is the largest council area in terms of population, with Highland being the largest in terms of area. Limited self-governing power, covering matters such as education, social services and roads and transportation, is devolved from the Scott ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales and Northern Ireland. The United Kingdom includes the island of Great Britain, the north-eastern part of the island of Ireland, and many smaller islands within the British Isles. Northern Ireland shares a land border with the Republic of Ireland; otherwise, the United Kingdom is surrounded by the Atlantic Ocean, the North Sea, the English Channel, the Celtic Sea and the Irish Sea. The total area of the United Kingdom is , with an estimated 2020 population of more than 67 million people. The United Kingdom has evolved from a series of annexations, unions and separations of constituent countries over several hundred years. The Treaty of Union between the Kingdom of England (which included Wales, annexed in 1542) and the Kingdom of Scotland in 170 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leech Lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by . It may also have been discovered (but not published) by Ernst Witt in 1940. Characterization The Leech lattice Λ24 is the unique lattice in 24-dimensional Euclidean space, E24, with the following list of properties: *It is unimodular; i.e., it can be generated by the columns of a certain 24×24 matrix with determinant 1. *It is even; i.e., the square of the length of each vector in Λ24 is an even integer. *The length of every non-zero vector in Λ24 is at least 2. The last condition is equivalent to the condition that unit balls centered at the points of Λ24 do not overlap. Each is tangent to 196,560 neighbors, and this is known to be the largest number of non-overlapping 24-dimensional unit balls that can simultaneously touch a single unit ball. This arrangement of 196,560 un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Group Theory
In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a natural and geometric way such a presentation. A very closely related topic is geometric group theory, which today largely subsumes combinatorial group theory, using techniques from outside combinatorics besides. It also comprises a number of algorithmically insoluble problems, most notably the word problem for groups; and the classical Burnside problem. History See for a detailed history of combinatorial group theory. A proto-form is found in the 1856 icosian calculus of William Rowan Hamilton, where he studied the icosahedral symmetry group via the edge graph of the dodecahedron. The foundations of combinatorial group theory were laid by Walther von Dyck, student of Felix Klein Christian Felix Klein (; 25 April 1849 – 22 Ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taxicab Numbers
In mathematics, the ''n''th taxicab number, typically denoted Ta(''n'') or Taxicab(''n''), also called the ''n''th Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two ''positive'' integer cubes in ''n'' distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103. The name is derived from a conversation in about 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan. As told by Hardy: History and definition The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, who published the Hardy–Ramanujan number Ta(2) = 1729. This particular example of 1729 was made famous in the early 20th century by a story involving Srinivasa Ramanujan. In 1938, G. H. Hardy and E. M. Wright proved that such numbers exist for all positive integers ''n'', and their proof is easily converted into a program to generate such numbers. However, the proof makes no claims at all about whether the thus-genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> United Kingdom")
