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Using his formula, Viète calculated π to an accuracy of nine decimal digits. [4] However, this was not the most accurate approximation to π known at the time, as the Persian mathematician Jamshīd al-Kāshī had calculated π to an accuracy of nine sexagesimal digits and 16 decimal digits in 1424. [12]
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 ...
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If w 1, w 2 and w 3 are the three cube roots of W, then the roots of the original depressed cubic are w 1 − p / 3w 1 , w 2 − p / 3w 2 , and w 3 − p / 3w 3 . The other root of the quadratic equation is − p 3 27 W . {\displaystyle \textstyle -{\frac {p^{3}}{27W}}.}
Google Sheets is a spreadsheet application and part of the free, web-based Google Docs Editors suite offered by Google. Google Sheets is available as a web application; a mobile app for: Android, iOS, and as a desktop application on Google's ChromeOS. The app is compatible with Microsoft Excel file formats. [5]
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
In 2006 Google launched a beta release spreadsheet web application, this is currently known as Google Sheets and one of the applications provided in Google Drive. [16] A spreadsheet consists of a table of cells arranged into rows and columns and referred to by the X and Y locations. X locations, the columns, are normally represented by letters ...