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Square Root Algorithm A simple approximation method is used by calculators to find square roots. The basic steps to finding y ϭ ͙x are first to guess the value of y, calculate y2, and then find r ϭ x Ϫ y2. Then if the magnitude of r is small enough, return y as the answer. Otherwise, increase or decrease y (depending on whether r is positive or negative) and repeat the process. The number of intermediate calculations required can be reduced by avoiding finding y2 and x Ϫ y2 for each value of y.

For example, some advanced scientific calculators allow the user to input numbers using up to twelve decimal places, and return results in this same format, but fifteen-digit numbers are actually used during calculation. Reverse Polish Notation and Algebraic Logic System The Polish logician Jan Lukasiewicz demonstrated a way of writing mathematical expressions unambiguously without using parentheses in 1951. For example, given the expression (2 ϩ 3) ϫ (7 Ϫ 1), each operator can be written before the corresponding operands: ϫ ϩ 2 3 Ϫ 7 1.

K. Byrne, J. A. Donnelly, R. W. Jones, and F. Yuan, A graphic calculator for mathematics and science classes, Hewlett-Packard Journal, 47 (3): 45–58, June 1996. DIANA K. htm ● HOME ● ABOUT US // ● CONTACT US ● HELP Wiley Encyclopedia of Electrical and Electronics Engineering Facsimile Equipment Standard Article Alan R. , Maidenhead, United Kingdom Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved. htm Abstract The sections in this article are Document Facsimile Group 3 Facsimile Terminal Operation Coding Scheme Scanning Systems Recording Methods Group 3 Communication Protocols Group 3 Error Correction Mode Basic and Optional Features for Group 3 Group 4 Facsimile Terminals Basic and Optional Features for Group 4 Group 3 Terminals on the Integrated Services Digital Network (ISDN) Networks PC Facsimile | | | Copyright © 1999-2008 All Rights Reserved.

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