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Measurement Of The Circle
''Measurement of a Circle'' or ''Dimension of the Circle'' (Greek: , ''Kuklou metrēsis'') is a treatise that consists of three propositions by Archimedes, ca. 250 BCE. The treatise is only a fraction of what was a longer work. Propositions Proposition one Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference ''c'' and a radius ''r'' is equal in area with a right triangle with the two legs being ''c'' and ''r''. This proposition is proved by the method of exhaustion. Proposition two Proposition two states: The area of a circle is to the square on its diameter as 11 to 14. This proposition could not have been placed by Archimedes, for it relies on the outcome of the third proposition. Proposition three Proposition three states: The ratio of the circumference of any circle to its diameter is great ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Page From Archimedes' Measurement Of A Circle
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, " a", and its variant " an", are indefinite articles. History The earliest certain ancestor of "A" is aleph (also written 'aleph), the first letter of the Phoenician alphabet, which consisted entirely of consonants (for that reason, it is also called an abjad to distinguish it fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other. For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other. If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Correspon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stomachion
''Ostomachion'', also known as ''loculus Archimedius'' (Archimedes' box in Latin) and also as ''syntomachion'', is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in an Arabic version and a copy, the ''Archimedes Palimpsest'', of the original ancient Greek text made in Byzantine times.Darling, David (2004). ''The universal book of mathematics: from Abracadabra to Zeno's paradoxes''. John Wiley and Sons, p. 188. The word Ostomachion has as its roots in the Greek Ὀστομάχιον, which means "bone-fight", from ὀστέον (''osteon''), "bone" and μάχη (''mache''), "fight, battle, combat". Note that the manuscripts refer to the word as "Stomachion", an apparent corruption of the original Greek. Ausonius gives us the correct name "Ostomachion" (''quod Graeci ostomachion vocavere,'' "which the Greeks called ostomachion"). The Ostomachion which he describes was a puzzle similar to tangrams and was played perhaps by several persons w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Little Heath
Sir Thomas Little Heath (; 5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English. Life Heath was born in Barnetby-le-Wold, Lincolnshire, England,being the third son of a farmer, Samuel Heath. He was educated at Caistor Grammar School and Clifton College before entering Trinity College, Cambridge, where he was awarded an ScD in 1896 and became an Honorary Fellow in 1920.He got first class honours in both the classical tripos and mathematical tripos and was the twelfth wrangler in 1882. In 1884 he took the Civil Service examination and became an Assistant Secretary to the Treasury, finally becoming Joint Permanent Secretary to the Treasury and auditor of the Civil List in 1913. He held the position til ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Heinrich Hunrath
Karl may refer to: People * Karl (given name), including a list of people and characters with the name * Karl der Große, commonly known in English as Charlemagne * Karl Marx, German philosopher and political writer * Karl of Austria, last Austrian Emperor * Karl (footballer) (born 1993), Karl Cachoeira Della Vedova Júnior, Brazilian footballer In myth * Karl (mythology), in Norse mythology, a son of Rig and considered the progenitor of peasants (churl) * ''Karl'', giant in Icelandic myth, associated with Drangey island Vehicles * Opel Karl, a car * ST ''Karl'', Swedish tugboat requisitioned during the Second World War as ST ''Empire Henchman'' Other uses * Karl, Germany, municipality in Rhineland-Palatinate, Germany * '' Karl-Gerät'', AKA Mörser Karl, 600mm German mortar used in the Second World War * KARL project, an open source knowledge management system * Korean Amateur Radio League, a national non-profit organization for amateur radio enthusiasts in South Korea * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Otto Hultsch
Friedrich may refer to: Names *Friedrich (surname), people with the surname ''Friedrich'' *Friedrich (given name), people with the given name ''Friedrich'' Other *Friedrich (board game), a board game about Frederick the Great and the Seven Years' War * ''Friedrich'' (novel), a novel about anti-semitism written by Hans Peter Richter *Friedrich Air Conditioning, a company manufacturing air conditioning and purifying products *, a German cargo ship in service 1941-45 See also *Friedrichs (other) *Frederick (other) *Nikolaus Friedreich Nikolaus Friedreich (1 July 1825 in Würzburg – 6 July 1882 in Heidelberg) was a German pathologist and neurologist, and a third generation physician in the Friedreich family. His father was psychiatrist Johann Baptist Friedreich (1796–1862) ... {{disambig ja:フリードリヒ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hieronymus Georg Zeuthen
Hieronymus Georg Zeuthen (15 February 1839 – 6 January 1920) was a Danish mathematician. He is known for work on the enumerative geometry of conic sections, algebraic surfaces, and history of mathematics. Biography Zeuthen was born in Grimstrup near Varde where his father was a minister. In 1849, his father moved to a church in Sorø where Zeuthen began his secondary schooling. In 1857 he entered the University of Copenhagen to study mathematics and graduated with a master's degree in 1862. Following this he earned a scholarship to study abroad, and decided to visit Paris where he studied geometry with Michel Chasles. After returning to Copenhagen, Zeuthen submitted his doctoral dissertation on a new method to determine the characteristics of conic systems in 1865. Enumerative geometry remained his focus up until 1875. In 1871 he was appointed as an extraordinary professor at the University of Copenhagen, as well as becoming an editor of ''Matematisk Tidsskrift'', a pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chronology Of Computation Of π
The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (). For more detailed explanations for some of these calculations, see Approximations of . The last 100 decimal digits of the latest 2022 world record computation are: 4658718895 1242883556 4671544483 9873493812 1206904813 2656719174 5255431487 2142102057 7077336434 3095295560 Before 1400 1400–1949 1949–2009 2009–present See also * History of pi *Approximations of π Approximations for the mathematical constant pi () in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era. In Chinese mathematics, this was improved to approximations correct ... References External links * Borwein, Jonathan,The Life of Pi {{DEFAULTSORT:Chronology Of Computation Of Pi Pi History of mathematics Pi Pi algorithms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Fantet De Lagny
Thomas Fantet de Lagny (7 November 1660 – 11 April 1734) was a French mathematician, well known for his contributions to computational mathematics, and for calculating π to 112 correct decimal places. Biography Thomas Fantet de Lagny was son of Pierre Fantet, a royal official in Grenoble, and Jeanne d'Azy, the daughter of a physician from Montpellier. He entered a Jesuit College in Lyon, where he became passionate about mathematics, as he studied some mathematical texts such as ''Euclid'' by Georges Fournier and an algebra text by Jacques Pelletier du Mans. Then he studied three years in the Faculty of Law in Toulouse. In 1686, he went to Paris and became a mathematics tutor to the Noailles family. He collaborated with de l'Hospital under the name of ''de Lagny'', and at that time he started publishing his first mathematical papers. He came back to Lyon when, on 11 December 1695, he was named an associate of the Académie Royale des Sciences. Then, in 1697, he became p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continued Fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression. In either case, all integers in the sequence, other than the first, must be positive. The integers a_i are called the coefficients or terms of the continued fraction. It is generally assumed that the numerator of all of the fractions is 1. If arbitrary values and/or functions are used in place of one or more of the numerators or the integers in the denominators, the resulting expression is a generalized continued fraction. When it is nece ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell's Equation
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x^2 - ny^2 = 1, where ''n'' is a given positive nonsquare integer, and integer solutions are sought for ''x'' and ''y''. In Cartesian coordinates, the equation is represented by a hyperbola; solutions occur wherever the curve passes through a point whose ''x'' and ''y'' coordinates are both integers, such as the trivial solution with ''x'' = 1 and ''y'' = 0. Joseph Louis Lagrange proved that, as long as ''n'' is not a perfect square, Pell's equation has infinitely many distinct integer solutions. These solutions may be used to accurately approximate the square root of ''n'' by rational numbers of the form ''x''/''y''. This equation was first studied extensively in India starting with Brahmagupta, who found an integer solution to 92x^2 + 1 = y^2 in his ''Brāhmasphuṭasiddhānta'' circa 628. Bhaskara II in the 12th century and Narayana Pandit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because . Every nonnegative real number has a unique nonnegative square root, called the ''principal square root'', which is denoted by \sqrt, where the symbol \sqrt is called the '' radical sign'' or ''radix''. For example, to express the fact that the principal square root of 9 is 3, we write \sqrt = 3. The term (or number) whose square root is being considered is known as the ''radicand''. The radicand is the number or expression underneath the radical sign, in this case 9. For nonnegative , the principal square root can also be written in exponent notation, as . Every positive number has two square roots: \sqrt, which is positive, and -\sqrt, which is negative. The two roots can be written more concisely using the ± sign as \plusmn\sq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
