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Modulus Meaning: Definition, Examples, and Translations

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modulus

[ˈmɒdʒʊləs ]

Definitions

Context #1 | Noun

mathematics

The remainder after division of one number by another. It is represented by the symbol '%'.

Synonyms

remainder, residue.

Which Synonym Should You Choose?

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Word Description / Examples
modulus

This appears to be a duplication in your input. Refer to the previous entry for usage.

  • The modulus of the complex number 3 + 4i is 5
  • In the equation 13 mod 5, the modulus is 5
remainder

Typically used in arithmetic to refer to what is left after dividing one number by another. It is also used in everyday situations to denote what is left over from something.

  • When you divide 10 by 3, the remainder is 1
  • She ate most of her sandwich and gave the remainder to her friend
residue

This term is often used in chemistry to refer to the substance remaining after a process such as evaporation or combustion. It can also be used more generally to denote what is left over, especially in a negative sense.

  • After boiling the solution, we were left with a white residue
  • There was a sticky residue on the table after the glue dried

Examples of usage

  • 12 % 5 = 2
  • The modulus of 15 divided by 4 is 3.
Context #2 | Noun

physics

A physical property that remains constant for a particular substance regardless of the amount or form of the substance.

Synonyms

coefficient, constant.

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Word Description / Examples
modulus

Commonly used in mathematics and engineering to refer to the absolute value of a complex number or the remainder in modular arithmetic.

  • The modulus of a complex number 3 + 4i is 5.
  • In modular arithmetic, 17 mod 3 equals 2.
constant

Used in mathematics and science to refer to a value that does not change.

  • In the equation y = mx + b, b is a constant.
  • The speed of light is a constant in physics.
coefficient

Typically used in algebra and statistics to describe a numerical factor that multiplies a variable.

  • In the equation 3x + 4, 3 is the coefficient of x.
  • The correlation coefficient measures the relationship between two variables.

Examples of usage

  • The modulus of elasticity of a material determines its stiffness.
Context #3 | Noun

computing

A mathematical operation that returns the remainder of a division between two numbers.

Synonyms

modulo, remainder.

Which Synonym Should You Choose?

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Word Description / Examples
modulus

This term is commonly used in mathematics and can refer to several different contexts such as the 'absolute value' of a complex number or the 'remainder operation' in modular arithmetic.

  • In modular arithmetic, the modulus determines the range of possible values.
  • The modulus of a complex number gives the distance from the origin on the complex plane.
remainder

Used in general arithmetic and everyday language to refer to the amount left over after division. It is more commonly understood by the general public compared to the technical term 'modulo'.

  • When you divide 13 by 5, the remainder is 3.
  • The remainder of the cake was divided among the children.
modulo

Primarily used in computational contexts or computer programming languages to refer to the operation of finding the remainder when one number is divided by another.

  • In Python, the '%' operator is used for the modulo operation.
  • Calculating 10 modulo 3 gives a result of 1.

Examples of usage

  • In programming, the modulus operator is often denoted by '%'.

Translations

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Interesting Facts

Mathematics

  • In modular arithmetic, numbers wrap around after reaching a certain value, known as the modulus. For example, under modulus 5, both 7 and 2 are equivalent to 2.
  • The concept is crucial in various fields like computer science, cryptography, and number theory.
  • Famous for its use in calculating checksums, registration numbers, and error detection in data transmission.

Historical Origins

  • The term 'modulus' originates from Latin, where 'modulus' means 'a small measure'.
  • It gained prominence in mathematics during the 19th century with the work of mathematicians like Carl Friedrich Gauss.
  • Early applications of modulus were found in ancient number systems, such as the Chinese and Indian mathematics.

Pop Culture

  • The idea of modular arithmetic can be seen in video games, where positions on a grid reset after a certain point, like in games with wrap-around maps.
  • Mathematical concepts including modulus often appear in puzzles and brain teasers, making them a fun way to engage with numbers.
  • Modular systems are commonly used in coding challenges and competitions, showing how math can be both competitive and entertaining.

Science

  • Modulus is used in physics to define properties like elastic modulus, measuring material stiffness.
  • In computer science, modulus operations are performed using algorithms essential for hashing functions and managing data structures.
  • Understanding modulus helps in algorithms for ensuring secure communications and safeguarding against unauthorized access.

Origin of 'modulus'

The word 'modulus' originates from the Latin word 'modulus', meaning 'small measure' or 'standard of measurement'. It was first used in the field of mathematics to refer to the remainder after division. Over time, the term has been adopted in physics and computing to denote various concepts related to proportionality and division. The concept of modulus has played a significant role in the development of mathematical and computational theories.

Word Frequency Rank

Position #8,849 indicates this is an advanced-level word. While not essential for basic communication, it will enhance your ability to understand and create more nuanced content.