Search results
Results From The WOW.Com Content Network
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 = = +.
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 ...
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.
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.
A fact from Viète's formula appeared on Wikipedia's Main Page in the Did you know column on 23 July 2021 (check views).The text of the entry was as follows: Did you know... that in 1593, French amateur mathematician François Viète found the first formula in European mathematics to represent an infinite process, a product of square roots that he used to compute π?
Since , the factors of 5 are addressed by noticing that since the residues of modulo 5 follow the cycle ,,, and those of follow the cycle ,,,, the residues of modulo 5 cycle through the sequence ,,,. Thus, 5 ∣ 149 n − 2 n {\displaystyle 5\mid 149^{n}-2^{n}} iff n = 4 k {\displaystyle n=4k} for some positive integer k {\displaystyle k} .
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)