Formal Sciences

Trajectory

A trajectory or flight path is the path that a mass moving object follows through space as a function of time. In classical mechanics, it is generally a continuous, derivable curve in three-dimensional Euclidean space. It can be derived from the law of time by separating it into the parametric equations in time of the […]

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Exponentiation

Exponentiation is one of the mathematical operations that replace multiple multiplications between equal numbers or variables, simplifying both writing and processing. If the exponent is greater than 1, the power is the product of as many factors as are indicated by the number of the exponent, all equal to the base. From this statement it is

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Dispersion index

In statistics, a dispersion index (or dispersion indicator or variability index or variance index) is an index that briefly describes the variability of a quantitative statistical distribution. Specifically, it measures how far the values in the distribution are from a central value chosen as a reference. The central value is usually a position index. The

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Statistical dispersion

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For example, if the variance of the data in a set is large, the data is widely spread. On the

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Monomial

It is defined monomial as a literal algebraic expression, consisting of a numerical part (coefficient) and a literal part among which only multiplication and exponentiation operations appear; for example: \[\dfrac{1}{2}x;\;7x^2y;\;-9x^n\] The monomial degree is defined as the sum of all the exponents of the literal part. Monomes that have the same literal part (with identical exponent) are

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Isometry

In mathematics, an isometry (from the Greek ἴσος, isos, which means equal | called also congruence, or congruent transformation) is a notion that generalizes that of rigid movement of an object or a geometric figure. Formally, it is a function between two metric spaces that preserves distances. An isometry is any geometric transformation defined in the plane or space

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Mathematical physics

Mathematical physics deals with the “applications of mathematics to problems of physics and the development of mathematical methods suitable for the formulation of physical theories and their applications,” using a mathematical formalism and the tools provided by mathematics itself. So, in other words, natural phenomena are observed, measured, and then analyzed using various mathematical tools.

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Distance

Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between the two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions. Although displacement is described in terms of direction, distance is not. Distance has no direction and, thus,

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Polygon

In geometry, a polygon (/ˈpɒlɪɡɒn/ from the Greek πολύς, polys, “many“ and γωνία, gōnia, “angle“) is a plane figure that is described by a finite number of straight-line segments connected to form a closed polygonal chain.

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Polygonal chain

A polygonal (also called polygonal chain, polygonal curve, polygonal circuit, polygonal path or polyline) is a geometric figure consisting of a finite and ordered set of consecutive oriented segments (i.e. such that the second end of a segment coincides with the first end of the next segment and it is the only common point between the two segments) and not adjacent (i.e. such

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Quadratic equation

A quadratic equation (from the Latin quadratus for “square“) is any equation that can be rearranged in standard form as: \[ax^2+bx+c=0\] where \(x\) represents an unknown, and \(a\), \(b\), and \(c\) represent known numbers, where \(a\neq 0\). If \(a=0\), then the equation is linear, not quadratic, as there is no \(ax^2\) term. The numbers \(a\), \(b\), and

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Equation

In mathematics, equations are equalities between monomials or polynomials, for which the purpose is to search for the numerical value of one or more literal variables, called unknown (for example \(x\)), which make the equality true. This value is called the solution or root of the equation. An equation is written as two expressions, connected by an equals sign (“=“)

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Isogon [isogonic line]

In the study of the Earth’s magnetic field, the term isogon or isogonic line refers to a line that connect the points of the earth that have equal magnetic declination, the variation of magnetic north from geographic north. In other words, it is a line connecting all points on the Earth’s surface in which there is the same value

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Vector

Vectors are indicated in the scientific literature with a letter, generally lowercase, with an arrow above it: (vec{v}). Vectors are essential to physics and engineering. Many fundamental physical quantities are vectors, including displacement, velocity, force, and electric and magnetic vector fields. In this context, the following fundamental entities are assigned: Let us now explain specifically what

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Line segment

A line segment is defined as a portion (set of internal points) of a straight line between two points A and B (called extremes of the line segment). A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. A line segment divides the straight line on which it

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Scientific notation

Scientific notation (also referred to as exponential notation) is a concise way of expressing real numbers with many digits that would otherwise be inconvenient to represent in decimal notation. This is accomplished by using integer powers of the base used for the positional notation in use. A number \(\alpha\) is written in scientific notation if it

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Series

A series can be described as the sum of some set of terms of a sequence. The \(n\)th partial sum of a sequence is usually called \(S_n\). If the sequence being summed is \(s_n\) we can use sigma notation to define the series: \[S_n=\sum_{i=1}^ns_i\] which just says to sum up the first \(n\) terms of the sequence \(s\).

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Complex number

A complex number is a number that can be expressed in the form \(a+bi\), where \(a\) and \(b\) are real numbers, and \(i\) is a solution of the equation \(x^2 = −1\). Because no real number satisfies this equation, \(i\) is called an imaginary number. For the complex number \(a + bi\), \(a\) is called the real part, and

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Rational number

A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator. Negative denominators are allowed, but are commonly avoided, as every rational number is equal to a fraction with positive denominator. Fractions are written as two integers, the numerator and the denominator, with a dividing bar

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