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Lill's Method
In mathematics, Lill's method is a visual method of finding the real number, real zero of a function, roots of a univariate polynomial of any degree of a polynomial, degree. It was developed by Austrian engineer Eduard Lill in 1867. A later paper by Lill dealt with the problem of complex numbers, complex roots. Lill's method involves drawing a path of straight line segments making Right angle, right angles, with lengths equal to the coefficients of the polynomial. The roots of the polynomial can then be found as the Slope, slopes of other right-angle paths, also connecting the start to the terminus, but with vertices on the lines of the first path. Description of the method To employ the method, a diagram is drawn starting at the origin. A line segment is drawn rightwards by the magnitude of the leading coefficient, so that with a negative coefficient, the segment will end left of the origin. From the end of the first segment, another segment is drawn upwards by the magnitude o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lill Method Quartic Example
Lill is a surname. When borne by Estonian individuals, it means "flower". People with the surname Lill include: * Alfred John Lill, Jr. (1880-1956), American former president of the Amateur Athletic Union and member of the United States Olympic Committee * Alick Lill (1904–1987), Australian rules footballer * Andreas Lill (born 1965), German drummer ( Vanden Plas) * Anne Lill (born 1946), Estonian classical philologist and translator * Darren Lill (born 1982), South African racing cyclist * David Lill (born 1947), English footballer * Denis Lill (born 1942), British actor * Eduard Lill (1830–1900), Austrian engineer and army officer * Erkki Lill (born 1968), Estonian curler and curling coach * Harri Lill (born 1991), Estonian curler * Heino Lill (born 1944), Estonian basketball coach and basketball player * Ivo Lill (1953–2019), Estonian glass artist * Jim Lill (born 19??), American country musician * John Lill (born 1933), Australian cricketer * John Lill (born ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monic Polynomial
In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1. That is to say, a monic polynomial is one that can be written as :x^n+c_x^+\cdots+c_2x^2+c_1x+c_0, with n \geq 0. Uses Monic polynomials are widely used in algebra and number theory, since they produce many simplifications and they avoid divisions and denominators. Here are some examples. Every polynomial is associated to a unique monic polynomial. In particular, the unique factorization property of polynomials can be stated as: ''Every polynomial can be uniquely factorized as the product of its leading coefficient and a product of monic irreducible polynomials.'' Vieta's formulas are simpler in the case of monic polynomials: ''The th elementary symmetric function of the roots of a monic polynomial of degree equals (-1)^ic_, where c_ is the coefficient of the th po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1867 In Science
The year 1867 in science and technology involved many significant events, listed below. Events * April – First clear recorded use of the word ''science'' in English with today's usage as restricted to the natural and physical sciences (by Catholic theologian and mathematician W. G. Ward writing in the London-published '' Dublin Review''). Botany * Gorse naturalises in New Zealand and soon becomes the worst invasive weed. * Swiss botanist Simon Schwendener proposes his dual theory of lichens. * Rosa 'La France', the first hybrid tea rose, is cultivated by Jean-Baptiste Guillot. * The Big Trees Ranch at Felton, California, is bought by San Francisco businessman Joseph Warren Welch to preserve the giant redwoods (''Sequoia sempervirens'') from logging. Chemistry * Alfred Nobel patents dynamite (in the United Kingdom on May 7, and in Sweden on October 19). * Henry Enfield Roscoe isolates vanadium. * Charles-Adolphe Wurtz synthesizes neurine. Economics * Publication of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1867 Introductions
There were only 354 days this year in the newly purchased territory of Alaska. When the territory transferred from the Russian Empire to the United States, the calendric transition from the Julian to the Gregorian Calendar was made with only 11 days instead of 12 during the 19th century. This change was made due to the territorial and geopolitical shift from the Asian to the American side of the International Date Line. Friday, 6 October 1867 ''(Julian Calendar)'' was followed by Friday again on 18 October 1867 (instead of Saturday, 19 October 1867 in the Gregorian Calendar). Events January * January 1 – The Covington–Cincinnati Suspension Bridge opens between Cincinnati, Ohio, and Covington, Kentucky, in the United States, becoming the longest single-span bridge in the world. It was renamed after its designer, John A. Roebling, in 1983. * January 8 – African-American men are granted the right to vote in the District of Columbia. * January 11 – Benito Juárez be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carlyle Circle
In mathematics, a Carlyle circle is a certain circle in a coordinate plane associated with a quadratic equation; it is named after Thomas Carlyle. The circle has the property that the equation solving, solutions of the quadratic equation are the horizontal coordinates of the intersections of the circle with the horizontal axis. Carlyle circles have been used to develop ruler-and-compass constructions of regular polygons. Definition Given the quadratic equation :''x''2 − ''sx'' + ''p'' = 0 the circle in the coordinate plane having the line segment joining the points ''A''(0, 1) and ''B''(''s'', ''p'') as a diameter is called the Carlyle circle of the quadratic equation.JSTOR Defining property The defining property of the Carlyle circle can be established thus: the equation of the circle having the line segment ''AB'' as diameter is :''x''(''x'' − ''s'') + (''y'' − 1)(''y'' − ''p'') =& ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paper Folding
) is the Japanese paper art, art of Paper folding (other), paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word ' to refer to designs which use cuts. In the detailed Japanese classification, origami is divided into stylized ceremonial origami (儀礼折り紙, ''girei origami'') and recreational origami (遊戯折り紙, ''yūgi origami''), and only recreational origami is generally recognized as origami. In Japan, ceremonial origami is generally called "origata" (:ja:折形) to distinguish it from recreational origami. The term "origata" is one of the old terms for origami. The small number of basic Origam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Margherita Piazzola Beloch
Margherita Beloch Piazzolla (12 July 1879 – 28 September 1976) was an Italian mathematician who worked in algebraic geometry, algebraic topology and photogrammetry. Biography Beloch, born in Frascati, was the daughter of the German historian Karl Julius Beloch, who taught ancient history for 50 years at Sapienza University of Rome, and American Bella Bailey (daughter of Gamaliel Bailey) . Beloch studied mathematics at the Sapienza University of Rome and wrote her undergraduate thesis under the supervision of Guido Castelnuovo. She received her degree in 1908 with Laude and , which means that her work was worthy of publication, and in fact her thesis (On Birational Transformations in Space) was published in the . Castelnuovo was very impressed with her talent and offered her the position of assistant which Beloch took and held until 1919, when she moved to Pavia. In 1920 she moved to Palermo to work under Michele De Franchis, an important figure of the Italian school of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lill Method Folding Example
Lill is a surname. When borne by Estonian individuals, it means "flower". People with the surname Lill include: * Alfred John Lill, Jr. (1880-1956), American former president of the Amateur Athletic Union and member of the United States Olympic Committee * Alick Lill (1904–1987), Australian rules footballer * Andreas Lill (born 1965), German drummer ( Vanden Plas) * Anne Lill (born 1946), Estonian classical philologist and translator * Darren Lill (born 1982), South African racing cyclist * David Lill (born 1947), English footballer * Denis Lill (born 1942), British actor * Eduard Lill (1830–1900), Austrian engineer and army officer * Erkki Lill (born 1968), Estonian curler and curling coach * Harri Lill (born 1991), Estonian curler * Heino Lill (born 1944), Estonian basketball coach and basketball player * Ivo Lill (1953–2019), Estonian glass artist * Jim Lill (born 19??), American country musician * John Lill (born 1933), Australian cricketer * John Lill (born ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Triangle
A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle ( turn or 90 degrees). The side opposite to the right angle is called the '' hypotenuse'' (side c in the figure). The sides adjacent to the right angle are called ''legs'' (or ''catheti'', singular: '' cathetus''). Side a may be identified as the side ''adjacent'' to angle B and ''opposite'' (or ''opposed to'') angle A, while side b is the side adjacent to angle A and opposite angle B. Every right triangle is half of a rectangle which has been divided along its diagonal. When the rectangle is a square, its right-triangular half is isosceles, with two congruent sides and two congruent angles. When the rectangle is not a square, its right-triangular half is scalene. Every triangle whose base is the diameter of a circle and whose apex lies on the circle is a right triangle, with the right angle at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thales's Theorem
In geometry, Thales's theorem states that if , , and are distinct points on a circle where the line is a diameter, the angle is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's '' Elements''. It is generally attributed to Thales of Miletus, but it is sometimes attributed to Pythagoras. History Babylonian mathematicians knew this for special cases before Greek mathematicians proved it. Thales of Miletus (early 6th century BC) is traditionally credited with proving the theorem; however, even by the 5th century BC there was nothing extant of Thales' writing, and inventions and ideas were attributed to men of wisdom such as Thales and Pythagoras by later doxographers based on hearsay and speculation. Reference to Thales was made by Proclus (5th century AD), and by Diogenes Laërtius (3rd century AD) documenting Pamphila's (1st century AD) statement that T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lill Method Quadratic Example
Lill is a surname. When borne by Estonian individuals, it means "flower". People with the surname Lill include: * Alfred John Lill, Jr. (1880-1956), American former president of the Amateur Athletic Union and member of the United States Olympic Committee * Alick Lill (1904–1987), Australian rules footballer * Andreas Lill (born 1965), German drummer ( Vanden Plas) * Anne Lill (born 1946), Estonian classical philologist and translator * Darren Lill (born 1982), South African racing cyclist * David Lill (born 1947), English footballer * Denis Lill (born 1942), British actor * Eduard Lill (1830–1900), Austrian engineer and army officer * Erkki Lill (born 1968), Estonian curler and curling coach * Harri Lill (born 1991), Estonian curler * Heino Lill (born 1944), Estonian basketball coach and basketball player * Ivo Lill (1953–2019), Estonian glass artist * Jim Lill (born 19??), American country musician * John Lill (born 1933), Australian cricketer * John Lill (born ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
