Defining ModulusDate: 12/10/2002 at 11:43:15 From: Jeremy Stone Subject: The use of the term 'modulus' I understand when this term is used to describe the congruent b-c relation as mod (b,m) as I have Excel for years, but why when we apply it to graphs does it translate as 'absoluted/directed value of'? Date: 12/10/2002 at 13:38:11 From: Doctor Peterson Subject: Re: The use of the term 'modulus' Hi, Jeremy. The word "modulus" is just a very vague term. I looked it up in Merriam-Webster and found even more definitions than you mentioned: 1 a : the factor by which a logarithm of a number to one base is multiplied to obtain the logarithm of the number to a new base b : ABSOLUTE VALUE 2 c (1) : the number (as a positive integer) or other mathematical entity (as a polynomial) in a congruence that divides the difference of the two congruent members without leaving a remainder -- compare RESIDUE b (2) : the number of different numbers used in a system of modular arithmetic 2 : a constant or coefficient that expresses usually numerically the degree to which a body or substance possesses a particular property (as elasticity) It comes from a Latin word that just means "small measure" (the diminutive form of "modus"). The three parts of definition 1 above are the mathematical uses, which are just three kinds of size that can be measured; definition 2 is the scientific use, which similarly applies to several different fields. There is no specific connection among these uses except that they are all numbers that measure something. It's also worth noting that "mod" is used with different meanings in math and in computer programming, and that many people get the wrong impression that the remainder is the modulus, when (as the definition above implies) it is actually the divisor. According to Merriam- Webster, the definition of "modulo" (which is the ablative of "modulus" in Latin) is with respect to a modulus of (19 and 54 are congruent modulo 7) This page discusses these ideas: What is Modulus? http://mathforum.org/library/drmath/view/54363.html If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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