Defining Modulus

Date: 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/