modulus

Thân thiện

A student calculates the modulus of two numbers on a whiteboard.

Definition

1. Noun (Mathematics):

   • The absolute value of a real or complex number. It represents the magnitude or distance of that number from zero on the complex plane, disregarding its direction or sign.
   • An integer that can divide the difference between two other integers without leaving a remainder.

2. Noun (Physics/Engineering):

   • A coefficient or constant that expresses the measure of a specific physical property possessed by a given material or substance.

Examples of Usage

• Noun (Mathematics):
  • The modulus of the complex number 3 + 4i is 5.
  • In the statement "2 is a modulus of 5 and 9," it means (9 - 5) is divisible by 2.
• Noun (Physics):
  • The Young's modulus quantifies a material's stiffness or resistance to elastic deformation.
  • The shear modulus describes a substance's response to shear stress.

Advanced Usage

• Modulus of Elasticity: A comprehensive term for constants like Young's modulus, shear modulus, and bulk modulus, which describe a material's elastic properties.
• Congruence Modulo n: In modular arithmetic, two numbers are congruent modulo n if they have the same remainder when divided by the integer . Here, is the modulus. Example: 17 ≡ 5 (mod 6), meaning 6 is the modulus.

Variants and Related Words

• Modular (adjective): 1. Relating to a modulus or constructed using modules. 2. (Mathematics) Relating to congruence with respect to a specified modulus.
  • Modular arithmetic is fundamental to computer science.
• Modulo (preposition): A word used in mathematics to indicate the modulus being used for a congruence calculation.
  • "Calculate 17 modulo 5."

Synonyms

• Absolute Value (for the magnitude of a number).
• Coefficient or Constant (in a physics/engineering context).

Related Phrases

• Modulus of Rupture: A measure of the strength of a material in bending.
• Modulus of Resilience: The energy absorbed per unit volume without permanent deformation.

Học thuật

Noun

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