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Vieta Relations
Vieta may refer to: *François Viète (1540–1603), commonly known by the Latin form of his name Franciscus Vieta, a French mathematician *Vieta (crater), a crater on the Moon, named after him *Vieta's formulas, expressing the coefficients of a polynomial In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ... as signed sums and products of its roots. * Artūras Vieta (born 1961), Lithuanian sprint canoer * Eduard Vieta, a Spanish psychiatrist * Vieta (beetle), a genus of beetles {{disambiguation, surname ...
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François Viète
François Viète (; 1540 – 23 February 1603), known in Latin as Franciscus Vieta, was a French people, French mathematician whose work on new algebra was an important step towards modern algebra, due to his innovative use of letters as parameters in equations. He was a lawyer by trade, and served as a Conseil du Roi, privy councillor to both Henry III of France, Henry III and Henry IV of France, Henry IV of France. Biography Early life and education Viète was born at Fontenay-le-Comte in present-day Vendée. His grandfather was a merchant from La Rochelle. His father, Etienne Viète, was an attorney in Fontenay-le-Comte and a notary in Le Busseau. His mother was the aunt of Barnabé Brisson, a magistrate and the first president of parliament during the ascendancy of the Ligue, Catholic League of France. Viète went to a Franciscan school and in 1558 studied law at Poitiers, graduating as a Bachelor of Laws in 1559. A year later, he began his career as an attorney in ...
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Vieta (crater)
Vieta is a lunar impact crater that lies due north of the walled plain Schickard, in the southwestern part of the Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar .... About half a crater diameter to the southeast is the smaller Fourier, and to the north-northeast lies Cavendish. The outer rim of this crater has undergone some impact erosion, and small craters lie along the northeast, south, and north-northwestern sides. The inner walls are irregular, with incised bases in some locations. A chain of small craters lies across the northern half of the interior floor, following a line towards the east-northeast. The floor is nearly level, but with some uneven areas in the south and by the crater chain. Satellite craters By convention these features are identified on lunar map ...
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Vieta's Formulas
In mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named after François Viète (1540-1603), more commonly referred to by the Latinised form of his name, "Franciscus Vieta." Basic formulas Any general polynomial of degree ''n'' P(x) = a_n x^n + a_x^ + \cdots + a_1 x + a_0 (with the coefficients being real or complex numbers and ) has (not necessarily distinct) complex roots by the fundamental theorem of algebra. Vieta's formulas relate the polynomial coefficients to signed sums of products of the roots as follows: Vieta's formulas can equivalently be written as \sum_ \left(\prod_^k r_\right)=(-1)^k\frac for (the indices are sorted in increasing order to ensure each product of roots is used exactly once). The left-hand sides of Vieta's formulas are the elementary symmetric polynomials of the roots. Vieta's system can be solved by Newton's method through an explicit simple iterative formula, the Dura ...
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Polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problem (mathematics education), word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are ...
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Artūras Vieta
Artūras Vieta (born May 31, 1961) is a Lithuanian sprint canoeist, born in Šiauliai. He won ten medals at the ICF Canoe Sprint World Championships with three golds (K-4 500 m: 1987, K-4 10000 m: 1989, 1990), three silvers (K-1 1000 m: 1983, K-2 1000 m: 1989, 1990; K-4 500 m: 1983, K-4 1000 m: 1985), and two bronzes (K-4 1000 m: 1985, 1987). At the 1992 Summer Olympics in Barcelona Barcelona ( ; ; ) is a city on the northeastern coast of Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second-most populous municipality of Spain. With a population of 1.6 million within c ..., he competed for Lithuania and finished ninth in both the K-1 500 m and the K-1 1000 m events. References * 1961 births Canoeists at the 1992 Summer Olympics Lithuanian male canoeists Soviet male canoeists Living people Olympic canoeists for Lithuania ICF Canoe Sprint World Championships medalists in kayak Sportspeople from ...
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Eduard Vieta
Eduard Vieta Pascual is a Catalan psychiatrist from Spain known for his work in the field of mood disorders. His unit is a world reference in clinical care, research and teaching of bipolar disorder and depression. Education Eduard Vieta was born in Barcelona, Spain. He studied medicine at the Autonomous University of Barcelona and graduated in 1987. He did his residency training at the Hospital Clinic of Barcelona and became a specialist in Psychiatry in 1991. He subsequently received his PhD with honors at the University of Barcelona in 1994. Career Research focus/interests Dr. Vieta has focused his research activity on the study of the causes and the pharmacological and psychological treatment of bipolar disorder and depression, as well as in Precision Psychiatry. His contributions stand out for identifying neurocognitive dysfunctions and promoting the clinical development of new pharmacological treatments to address this condition. Additionally, his research has concent ...
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