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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
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 ...
The smaller numbers, for use when subtracting, are the nines' complement of the larger numbers, which are used when adding. In mathematics and computing , the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (or mechanism ) for addition throughout ...
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]
Google Charts is an online tool that is used to create charts and graphs. It uses HTML5 and SVG to function on multiple browsers and devices without extra plugins or software. It is known for its wide range of chart options and features, which are explained on the official Google Charts website. [1]
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