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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's formula, as printed in Viète's Variorum de rebus mathematicis responsorum, liber VIII (1593). In mathematics, Viète's formula is the following infinite product of nested radicals representing twice the reciprocal of the mathematical constant π: = + + + It can also be represented as = = +.
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.
The characteristic polynomial of a square matrix is an example of application of Vieta's formulas. The roots of this polynomial are the eigenvalues of the matrix . When we substitute these eigenvalues into the elementary symmetric polynomials, we obtain – up to their sign – the coefficients of the characteristic polynomial, which are ...
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.
I think the last sentence summarizes it well. In English at least, the tradition has been to use Vieta, and Viete is an overcorrection (outside historical or biographic contexts), like saying "Hero's formula" with Greek pronunciation, instead than Heron's formula. 73.89.25.252 04:52, 13 June 2020 (UTC)
The value of 5 1 ⁄ 8 · 35 1 ⁄ 3 is very close to 4, which is why a 7-limit interval 6144 : 6125 (which is the difference between the 5-limit diesis 128 : 125 and the septimal diesis 49 : 48), equal to 5.362 cents, appears very close to the quarter-comma ( 81 / 80 ) 1 ⁄ 4 of 5.377 cents.