Adjacent Words

modulus definitions

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WordNet (r) 3.0 (2005)

n
1: an integer that can be divided without remainder into the difference between two other integers; "2 is a modulus of 5 and 9"
2: the absolute value of a complex number
3: (physics) a coefficient that expresses how much of a specified property is possessed by a specified substance

Merriam Webster's

noun (plural moduli) Etymology: New Latin, from Latin, small measure Date: 1753 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)

Oxford Reference Dictionary

n. (pl. moduli) Math. 1 a the magnitude of a real number without regard to its sign. b the positive square root of the sum of the squares of the real and imaginary parts of a complex number. 2 a constant factor or ratio. 3 (in number theory) a number used as a divisor for considering numbers in sets giving the same remainder when divided by it. 4 a constant indicating the relation between a physical effect and the force producing it. Etymology: L, = measure, dimin. of modus

Webster's 1913 Dictionary

Modulus Mod"u*lus, n.; pl. Moduli. [L., a small measure. See Module, n.] (Math., Mech., & Physics) A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength, efficiency, etc.; a parameter. Modulus of a machine, a formula expressing the work which a given machine can perform under the conditions involved in its construction; the relation between the work done upon a machine by the moving power, and that yielded at the working points, either constantly, if its motion be uniform, or in the interval of time which it occupies in passing from any given velocity to the same velocity again, if its motion be variable; -- called also the efficiency of the machine. --Mosley. --Rankine. Modulus of a system of logarithms (Math.), a number by which all the Napierian logarithms must be multiplied to obtain the logarithms in another system. Modulus of elasticity. (a) The measure of the elastic force of any substance, expressed by the ratio of a stress on a given unit of the substance to the accompanying distortion, or strain. (b) An expression of the force (usually in terms of the height in feet or weight in pounds of a column of the same body) which would be necessary to elongate a prismatic body of a transverse section equal to a given unit, as a square inch or foot, to double, or to compress it to half, its original length, were that degree of elongation or compression possible, or within the limits of elasticity; -- called also Young's modulus. Modulus of rupture, the measure of the force necessary to break a given substance across, as a beam, expressed by eighteen times the load which is required to break a bar of one inch square, supported flatwise at two points one foot apart, and loaded in the middle between the points of support. --Rankine.