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In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
The slope of the initial, linear portion of this curve gives Young's modulus. Mathematically, Young's modulus E is calculated using the formula E=σ/ϵ, where σ is the stress and ϵ is the strain. Shear modulus (G) Initial structure: Start with a relaxed structure of the material. All atoms should be in a state of minimum energy with no ...
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for ...
Young's modulus (or Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the ...
Modular equation. In mathematics, a modular equation is an algebraic equation satisfied by moduli, [1] in the sense of moduli problems. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli. The most frequent use of the term modular equation is in ...
Strictly speaking, the bulk modulus is a thermodynamic quantity, and in order to specify a bulk modulus it is necessary to specify how the pressure varies during compression: constant- temperature (isothermal ), constant- entropy (isentropic ), and other variations are possible. Such distinctions are especially relevant for gases.