Q&A #6073

Teachers' Lounge Discussion: Mathematical terminology

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From: pat ballew

To: Teacher2Teacher Public Discussion
Date: 2005082813:30:14
Subject: Re: terminology

A single source for this and most of the other questions that have been asked in this string is http://www.pballew.net/etyindex.html For example, if you click on repeating decimal, you will find, "vinculum, fraction bar, "repeat bar" As a "Math Doctor", one of the most common questions asked by elementary school students is, "What is the name for the bar over repeating decimal fractions?" I always answer that "repeat bar" seems the best name to communicate what it does, but I know they want the classic Latin name for the bar, vinculum. The word is from the diminutive of vincere, to tie. vinculum referred to a small cord for binding the hands or feet. The meaning in math is mostly unchanged from that original meaning, as the purpose of the repeat bar is to bind together the sequence of repeating digits. The term repeating decimal has sometimes been replaced with "recurrent" or "Circulating". The sequence of digits which repeat have also been called the "circulants" and "repetends" (and sometimes "repetents"). The vinculum notation was once used in much the same way we now use parenthesis and brackets to "bind together" a group of numbers or symbols. Originally the line was placed under the items to be grouped although a bar over the grouping became the more lasting usage (and still is in the symbols for roots and the one for division). It is in the expression for repeating decimals that students are most familiar with the use of the overbar as a symbol, yet it seems to have been the last application of the bar, and seems not to have occured until after 1930 in the US. In F. Cajori's A History of Mathematical Notations (1929) he points out two forms of marking repeating sequences in decimals but does not mention the vincula or overbar. Cajori credits John Marsh [Decimal Arithmetic Made Perfect, (London, 1742)] with being the first to use a symbol to indicate the repeat sequence. Marsh sometimes placed a single dot over the first number in the repeat sequence, and sometimes placed one on the first and last. " and much more... hope this is a help.. Pat

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