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Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
Geometry – mathematics concerned with questions of shape, size, the relative position of figures, and the properties of space. Geometry is used extensively in trigonometry. Angle – the angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays ...
In other words, the box definition is extrinsic – one assumes the fractal space S is contained in a Euclidean space, and defines boxes according to the external geometry of the containing space. However, the dimension of S should be intrinsic , independent of the environment into which S is placed, and the ball definition can be formulated ...
A four-dimensional orthotope is likely a hypercuboid. [7]The special case of an n-dimensional orthotope where all edges have equal length is the n-cube or hypercube. [2]By analogy, the term "hyperrectangle" can refer to Cartesian products of orthogonal intervals of other kinds, such as ranges of keys in database theory or ranges of integers, rather than real numbers.
In the former case, equivalence of two definitions means that a mathematical object (for example, geometric body) satisfies one definition if and only if it satisfies the other definition. In the latter case, the meaning of equivalence (between two definitions of a structure) is more complicated, since a structure is more abstract than an object.
It consists of terms that are either variables, function definitions (𝜆-terms), or applications of functions to terms. Terms are manipulated through some rules, (the α-equivalence, the β-reduction, and the η-conversion), which are the axioms of the theory and may be interpreted as rules of computation.
Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
The attendant parallel displacement operations also had natural algebraic interpretations in terms of the connection. Koszul's definition was subsequently adopted by most of the differential geometry community, since it effectively converted the analytic correspondence between covariant differentiation and parallel translation to an algebraic one.