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In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking) of the class of objects to which it belongs. Magnitude as a concept dates to Ancient ...
Square of −1. The square of −1, i.e. −1 multiplied by −1, equals 1. As a consequence, a product of two negative numbers is positive. For an algebraic proof of this result, start with the equation. 0 = −1 ⋅ 0 = −1 ⋅ [1 + (−1)]. The first equality follows from the above result, and the second follows from the definition of −1 ...
The most commonly used terms are V-shaped (with variations of square-root shaped, and Nike-swoosh shaped), U-shaped, W-shaped (also known as a double-dip recession), and L-shaped recessions, with the COVID-19 pandemic leading to the K-shaped recession (also known as a two-stage recession). The names derive from the shape the economic data ...
Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x 3 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of the main theorem, which states that if p and q are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence x 3 ≡ p (mod q) is solvable if and only if ...
Comparison of 1 square foot with some Imperial and metric units of area. The square foot (pl. square feet; abbreviated sq ft, sf, or ft 2; also denoted by ' 2) is an imperial unit and U.S. customary unit (non-SI, non-metric) of area, used mainly in the United States and partially in Canada, the United Kingdom, Bangladesh, India, Nepal, Pakistan, Ghana, Liberia, Malaysia, Myanmar, Singapore and ...
t. e. The number π ( / paɪ /; spelled out as " pi ") is a mathematical constant that is the ratio of a circle 's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics.
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces , the hypersurface of the tesseract consists of eight cubical cells , meeting at right angles .
The quadratic excess E ( p) is the number of quadratic residues on the range (0, p /2) minus the number in the range ( p /2, p) (sequence A178153 in the OEIS ). For p congruent to 1 mod 4, the excess is zero, since −1 is a quadratic residue and the residues are symmetric under r ↔ p − r.