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A method similar to Vieta's formula can be found in the work of the 12th century Arabic mathematician Sharaf al-Din al-Tusi. It is plausible that the algebraic advancements made by Arabic mathematicians such as al-Khayyam, al-Tusi, and al-Kashi influenced 16th-century algebraists, with Vieta being the most prominent among them. [2] [3]
For any (a, b) satisfying the given condition, let k = a 2 + b 2 + 1 / ab and rearrange and substitute to get x 2 − (kb) x + (b 2 + 1) = 0. One root to this quadratic is a, so by Vieta's formulas the other root may be written as follows: x 2 = kb − a = b 2 + 1 / a . The first equation shows that x 2 is an integer and the ...
Viète obtained his formula by comparing the areas of regular polygons with 2 n and 2 n + 1 sides inscribed in a circle. [1] [2] The first term in the product, /, is the ratio of areas of a square and an octagon, the second term is the ratio of areas of an octagon and a hexadecagon, etc.
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 as signed sums and products of its roots. Artūras Vieta (born 1961), Lithuanian sprint canoer
Vieta's substitution is a method introduced by François Viète (Vieta is his Latin name) in a text published posthumously in 1615, which provides directly the second formula of § Cardano's method, and avoids the problem of computing two different cube roots. [35]
Another example. Dickson, Elementary Theory of Equations, does not give the formula for the non-normalized case. He states the monic Vieta formulas, and then that in the general case one can normalize the polynomial and adjust the formula accordingly. See chapter VI pp.55-56. 73.89.25.252 15:22, 13 June 2020 (UTC)
François Viète (French: [fʁɑ̃swa vjɛt]; 1540 – 23 February 1603), known in Latin as Franciscus Vieta, was a 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.
where A 1 and A 2 are the centers of the two circles and r 1 and r 2 are their radii. The power of a point arises in the special case that one of the radii is zero. If the two circles are orthogonal, the Darboux product vanishes. If the two circles intersect, then their Darboux product is