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A form of casting out nines known to ancient Greek mathematicians was described by the Roman bishop Hippolytus (170–235) in The Refutation of all Heresies, and more briefly by the Syrian Neoplatonist philosopher Iamblichus (c.245–c.325) in his commentary on the Introduction to Arithmetic of Nicomachus of Gerasa. [2]
Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers in decimal, a method known as long ago as the 12th century. [3] If an odd perfect number exists, it will have at least nine distinct prime factors. [4] Non-intersecting chords between four points on a circle
Sum the digits of the first operand; any 9s (or sets of digits that add to 9) can be counted as 0. If the resulting sum has two or more digits, sum those digits as in step one; repeat this step until the resulting sum has only one digit. Repeat steps one and two with the second operand.
For divisibility by 9, this test is called the rule of nines and is the basis of the casting out nines technique for checking calculations. Digit sums are also a common ingredient in checksum algorithms to check the arithmetic operations of early computers. [ 3 ]
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 ...
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]
MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables action=purge&mathpurge=true. Imagine for example there is a wrong rendered formula in the article Integral
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