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James Ivory (mathematician)
James Ivory, FRS FRSE KH LLD (17 February 1765 – 21 September 1842) was a British mathematician. He stated and proved Ivory's lemma. Life Ivory was born in Dundee, son of watchmaker James Ivory. The family lived and worked on the High Street in Dundee. He was educated at Dundee Grammar School. In 1779 he entered the University of St Andrews, distinguishing himself especially in mathematics. He then studied theology; but, after two sessions at St Andrews and one at Edinburgh University, he abandoned all idea of the church, and in 1786 he became an assistant-teacher of mathematics and natural philosophy in the newly established Dundee Academy. Three years later he became partner in, and manager of, a flax spinning company at Douglastown in Forfarshire, while continuing mathematical research as a hobby. He was essentially a self-trained mathematician, and was not only deeply versed in geometry, but also kept up with contemporary developments in mathematical analysis. He p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dundee, Scotland
Dundee (; ; or , ) is the List of towns and cities in Scotland by population, fourth-largest city in Scotland. The mid-year population estimate for the locality was . It lies within the eastern central Lowlands on the north bank of the Firth of Tay, which feeds into the North Sea. Under the name of Dundee City, it forms one of the 32 Council areas of Scotland, council areas used for local government in Scotland. Within the boundaries of the Shires of Scotland, historic county of Angus, Scotland, Angus, the city developed into a burgh in the late 12th century and established itself as an important east coast trading port. Rapid expansion was brought on by the Industrial Revolution, particularly in the 19th century when Dundee was the centre of the global jute industry. This, along with its other major industries, gave Dundee its epithet as the city of "jute, jam and journalism". With the decline of traditional industry, the city has adopted a plan to regenerate and reinvent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dundee Grammar School
The High School of Dundee is a private, co-educational, day school in Dundee, Scotland, which provides nursery, primary and secondary education to just over one thousand pupils. Its foundation has been dated to 1239, and it is the only private school in Dundee. The school's rector is a member of the Headmasters' and Headmistresses' Conference. The school has been registered as a charity in Scotland since July 1897. History The Grammar School The school has origins in the Grammar School of Dundee founded by the abbot and monks of Lindores Abbey after they were granted a charter by Gregory, Bishop of Brechin, in the early 1220s to "plant schools wherever they please in the burgh". Their rights were confirmed by a papal bull conferred by Pope Gregory IX on 14 February 1239. It is from this bull that the school's Latin motto "''Prestante Domino''", translated as "Under the Leadership of God", is taken. Little information survives about the early grammar school: it would have taug ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lemma (mathematics)
In mathematics and other fields, a lemma (: lemmas or lemmata) is a generally minor, proven Theorem#Terminology, proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to mathematical proof, prove; however, a lemma can also turn out to be more important than originally thought. Etymology From the Ancient Greek λῆμμα, (perfect passive εἴλημμαι) something received or taken. Thus something taken for granted in an argument. Comparison with theorem There is no formal distinction between a lemma and a theorem, only one of intention (see Theorem#Terminology, Theorem terminology). However, a lemma can be considered a minor result whose sole purpose is to help prove a more substantial theorem – a step in the direction of proof. Well-known lemmas Some powerful results in mathematics are known as lemmas, first named for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, including mathematics, engineering science, and medical science". Overview Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to :Fellows of the Royal Society, around 8,000 fellows, including eminent scientists Isaac Newton (1672), Benjamin Franklin (1756), Charles Babbage (1816), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Jagadish Chandra Bose (1920), Albert Einstein (1921), Paul Dirac (1930), Subrahmanyan Chandrasekhar (1944), Prasanta Chandra Mahalanobis (1945), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955), Satyendra Nath Bose (1958), and Francis Crick (1959). More recently, fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Transactions Of The Royal Society
''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the second journal in the world exclusively devoted to science, after the '' Journal des sçavans'', and therefore also the world's longest-running scientific journal. It became an official society publication in 1752. The use of the word ''philosophical'' in the title refers to natural philosophy, which was the equivalent of what would now be generally called ''science''. Current publication In 1887 the journal expanded and divided into two separate publications, one serving the physical sciences ('' Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences'') and the other focusing on the life sciences ('' Philosophical Transactions of the Royal Society B: Biological Sciences''). Both journals now publish theme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Military College, Great Marlow
The Royal Military College (RMC) was a British military academy for training infantry and cavalry officers of the British and Indian Armies. It was founded in 1801 at Great Marlow and High Wycombe in Buckinghamshire, but moved in October 1812 to Sandhurst, Berkshire. The RMC was reorganised at the outbreak of the Second World War, but some of its units remained operational at Sandhurst and Aldershot. In 1947, the Royal Military College was merged with the Royal Military Academy, Woolwich, to form the present-day all-purpose Royal Military Academy Sandhurst. History Pre-dating the college, the Royal Military Academy, Woolwich, had been established in 1741 to train artillery and engineer officers, but there was no such provision for training infantry and cavalry officers. The Royal Military College was conceived by Colonel John Le Marchant, whose scheme for establishing schools for the military instruction of officers at High Wycombe and Great Marlow first met strong res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kepler Problem
In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force that varies in strength as the inverse square of the distance between them. The force may be either attractive or repulsive. The problem is to find the position or speed of the two bodies over time given their masses, positions, and velocities. Using classical mechanics, the solution can be expressed as a Kepler orbit using six orbital elements. The Kepler problem is named after Johannes Kepler, who proposed Kepler's laws of planetary motion (which are part of classical mechanics and solved the problem for the orbits of the planets) and investigated the types of forces that would result in orbits obeying those laws (called ''Kepler's inverse problem''). For a discussion of the Kepler problem specific to radial orbits, see Radial trajectory. General relativity provides more accurate solutions to the two-body problem, especially in stron ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Equations
In algebra, a cubic equation in one variable is an equation of the form ax^3+bx^2+cx+d=0 in which is not zero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients , , , and of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by the following means: * algebraically: more precisely, they can be expressed by a ''cubic formula'' involving the four coefficients, the four basic arithmetic operations, square roots, and cube roots. (This is also true of quadratic (second-degree) and quartic (fourth-degree) equations, but not for higher-degree equations, by the Abel–Ruffini theorem.) * trigonometrically * numerical approximations of the roots can be found using root-finding algorithms such as Newton's method. The coefficients do not need to be real numbers. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transactions Of The Royal Society Of Edinburgh
Transaction or transactional may refer to: Commerce *Financial transaction, an agreement, communication, or movement carried out between a buyer and a seller to exchange an asset for payment *Debits and credits in a Double-entry bookkeeping system *Electronic funds transfer, the electronic exchange or transfer of money from one account to another *Real estate transaction, the process whereby rights in a unit of property is transferred between two or more parties *Transaction cost, a cost incurred in making an economic exchange *Transactional law, the practice of law concerning business and commerce Computing *Transaction processing, information processing that is divided into individual, indivisible operations *Database transaction, a unit of work performed within a database management system *Atomic transaction, a series of database operations such that either all occur, or nothing occurs Other uses *Transactions, the published proceedings of a learned society: ** *Transaction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity (mathematics), eccentricity e, a number ranging from e = 0 (the Limiting case (mathematics), limiting case of a circle) to e = 1 (the limiting case of infinite elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic solution for its area, but for Perimeter of an ellipse, its perimeter (also known as circumference), Integral, integration is required to obtain an exact solution. The largest and smallest diameters of an ellipse, also known as its width and height, are typically denoted and . An ellipse has four extreme points: two ''Vertex (geometry), vertices'' at the endpoints of the major axis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytical Expression
In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. Commonly, the basic functions that are allowed in closed forms are ''n''th root, exponential function, logarithm, and trigonometric functions. However, the set of basic functions depends on the context. For example, if one adds polynomial roots to the basic functions, the functions that have a closed form are called elementary functions. The ''closed-form problem'' arises when new ways are introduced for specifying mathematical objects, such as limits, series, and integrals: given an object specified with such tools, a natural problem is to find, if possible, a ''closed-form expression'' of this object; that is, an expression of this object in terms of previous ways of specifying it. Example: roots of polynomials The quadratic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
