|
Braikenridge–Maclaurin Theorem
In geometry, the , named for 18th century British mathematicians William Braikenridge and Colin Maclaurin, is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line ''L'', then the six vertices of the hexagon lie on a conic ''C''; the conic may be degenerate, as in Pappus's theorem. The Braikenridge–Maclaurin theorem may be applied in the Braikenridge–Maclaurin construction, which is a synthetic Synthetic things are composed of multiple parts, often with the implication that they are artificial. In particular, 'synthetic' may refer to: Science * Synthetic chemical or compound, produced by the process of chemical synthesis * Synthetic ... construction of the conic defined by five points, by varying the sixth point. Namely, Pascal's theorem states that given six points on a conic (the vertices of a hexagon), the lines defined by opposite sides intersect in three col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Braikenridge–Maclaurin Theorem
In geometry, the , named for 18th century British mathematicians William Braikenridge and Colin Maclaurin, is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line ''L'', then the six vertices of the hexagon lie on a conic ''C''; the conic may be degenerate, as in Pappus's theorem. The Braikenridge–Maclaurin theorem may be applied in the Braikenridge–Maclaurin construction, which is a synthetic Synthetic things are composed of multiple parts, often with the implication that they are artificial. In particular, 'synthetic' may refer to: Science * Synthetic chemical or compound, produced by the process of chemical synthesis * Synthetic ... construction of the conic defined by five points, by varying the sixth point. Namely, Pascal's theorem states that given six points on a conic (the vertices of a hexagon), the lines defined by opposite sides intersect in three col ... [...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 geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Braikenridge
William Braikenridge (also Brakenridge) (c.1700–1762) was a Scottish mathematician and cleric, a Fellow of the Royal Society from 1752. Life He was son of John Braikenridge of Glasgow. s:Page:Alumni Oxoniensis (1715–1886) volume 1.djvu/169 In the 1720s he taught mathematics in Edinburgh. Braikenridge was Honorary A.M. in 1735, and D.D. in 1739, of Marischal College, when he was vicar of New Church, Isle of Wight. He was incorporated at The Queen's College, Oxford, in 1741. He became rector of St Michael Bassishaw, and from 1745 librarian of Sion College, in London. Works In geometry the Braikenridge–Maclaurin theorem was independently discovered by Colin Maclaurin. It occasioned a priority dispute after Braikenridge published it in 1733; Stella Mills writes that, while Braikenridge may have wished to establish priority, Maclaurin rather felt slighted by the implication that he did not know theorems in the ''Exercitatio'' that he had taught for a number of years. *''Exerc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colin Maclaurin
Colin Maclaurin (; gd, Cailean MacLabhruinn; February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. He is also known for being a child prodigy and holding the record for being the youngest professor. The Maclaurin series, a special case of the Taylor series, is named after him. Owing to changes in orthography since that time (his name was originally rendered as M'Laurine), his surname is alternatively written MacLaurin. Early life Maclaurin was born in Kilmodan, Argyll. His father, John Maclaurin, minister of Glendaruel, died when Maclaurin was in infancy, and his mother died before he reached nine years of age. He was then educated under the care of his uncle, Daniel Maclaurin, minister of Kilfinan. A child prodigy, he entered university at age 11. Academic career At eleven, Maclaurin, a child prodigy at the time, entered the University of Glasgow. He graduated Master of Arts three years later by defendin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pascal's Theorem
In projective geometry, Pascal's theorem (also known as the ''hexagrammum mysticum theorem'') states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet at three points which lie on a straight line, called the Pascal line of the hexagon. It is named after Blaise Pascal. The theorem is also valid in the Euclidean plane, but the statement needs to be adjusted to deal with the special cases when opposite sides are parallel. This theorem is a generalization of Pappus's (hexagon) theorem, which is the special case of a degenerate conic of two lines with three points on each line. Euclidean variants The most natural setting for Pascal's theorem is in a projective plane since any two lines meet and no exceptions need to be made for parallel lines. However, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Braikenridge–Maclaurin Construction
In Euclidean and projective geometry, just as two (distinct) points determine a line (a degree-1 plane curve), five points determine a conic (a degree-2 plane curve). There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines. Formally, given any five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non- degenerate; this is true over both the Euclidean plane and any pappian projective plane. Indeed, given any five points there is a conic passing through them, but if three of the points are collinear the conic will be degenerate (reducible, because it contains a line), and may not be unique; see further discussion. Proofs This result can be proven numerous different ways; the dimension counting argument is most direct, and generalizes to higher degree, while other proofs are special to conic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synthetic Geometry
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates or formulae. It relies on the axiomatic method and the tools directly related to them, that is, compass and straightedge, to draw conclusions and solve problems. Only after the introduction of coordinate methods was there a reason to introduce the term "synthetic geometry" to distinguish this approach to geometry from other approaches. Other approaches to geometry are embodied in analytic and algebraic geometries, where one would use analysis and algebraic techniques to obtain geometric results. According to Felix Klein Synthetic geometry is that which studies figures as such, without recourse to formulae, whereas analytic geometry consistently makes use of such formulae as can be written down after the adoption of an appropriate system of coordinates. Geometry as presented by Euclid in the ''Elements'' is the quintessential example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 1529 18th Street, Northwest in the Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the ''American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to records on JSTOR. Mission and Vision The mission of the MAA is to advance the understanding of mathematics and its impact on our world. We envision a society that values the power and beauty of mathematics and fully realizes its potential to promote human flourishi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorems About Polygons
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In the mainstream of mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Colin Maclaurin")
.PNG "Click for more on -> Theorems About Polygons")