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Generalization of a rectangle for higher dimensions
In geometry, a hyperrectangle (also called a box, hyperbox, k {\displaystyle k} -cell or orthotope), is the generalization of a rectangle (a plane figure)
Hyperrectangle
Convex polytope, the n-dimensional analogue of a square and a cube
hypercubes the γn polytopes. The hypercube is the special case of a hyperrectangle (also called an n-orthotope). A unit hypercube is a hypercube whose
Hypercube
Limiting case which is different from the rest of the class
opposite sides have length zero, the rectangle degenerates to a point. A hyperrectangle is the n-dimensional analog of a rectangle. If its sides along any of
Degeneracy_(mathematics)
Attribute of a geometric shape
same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest
Aspect_ratio
but implicitly by some recursive splitting-function defined on the hyperrectangles belonging to the tree's nodes. Each inner node's split plane is positioned
Implicit_k-d_tree
Fundamental space of geometry
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Euclidean_space
Quadrilateral with four right angles
RECTANGLE U+25AF ▯ WHITE VERTICAL RECTANGLE Cuboid Golden rectangle Hyperrectangle Superellipse (includes a rectangle with rounded corners) Tapson, Frank
Rectangle
Manifold or algebraic variety of dimension n in a space of dimension n+1
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Hypersurface
Property of a mathematical space
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Dimension
Cuboid with all right angles and equal opposite faces
to at least 54 for a rectangular cuboid of three different lengths. Hyperrectangle — generalization of a rectangle; Minimum bounding box — a measurement
Rectangular_cuboid
Type of polynomial
coordinates for the hyperrectangle. Geometrically, the point divides the domain into 2 n {\displaystyle 2^{n}} smaller hyperrectangles, and the weight of
Multilinear_polynomial
Generalized sphere of dimension n (mathematics)
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
N-sphere
Geometric space with five dimensions
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Five-dimensional_space
Four-dimensional number system
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Quaternion
Number of independent parameters of a system
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Degrees_of_freedom
Number of vectors in any basis of the vector space
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Dimension_(vector_space)
Probability that random variable X is less than or equal to x
1\right)=-1} as explained below. The probability that a point belongs to a hyperrectangle is analogous to the 1-dimensional case: F X 1 , X 2 ( a , c ) + F X
Cumulative distribution function
Cumulative_distribution_function
All numbers between two given numbers
1-dimensional hyperrectangle. Generalized to real coordinate space R n , {\displaystyle \mathbb {R} ^{n},} an axis-aligned hyperrectangle (or box) is the
Interval_(mathematics)
Topologically invariant definition of the dimension of a space
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Lebesgue_covering_dimension
Multi-dimensional generalization of triangle
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Simplex
Invariant measure of fractal dimension
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Hausdorff_dimension
Algorithm
multivariate case by substituting a hyperrectangle for the one-dimensional w region used in the original. The hyperrectangle H is initialized to a random position
Slice_sampling
Mathematical space with two coordinates
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Two-dimensional_space
Thing in mathematics and theoretical physics
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Quasi-sphere
coordinate axes of the space. Examples are axis-aligned rectangles (or hyperrectangles), the ones with edges parallel to the coordinate axes. Minimum bounding
Axis-aligned_object
of the bounding hyperrectangle of point set X and let Li(R(X)) denote the size of the i-th dimension of the bounding hyperrectangle of point set X. We
Well-separated pair decomposition
Well-separated_pair_decomposition
Faster-than-light travel in science fiction
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Hyperspace
Topics referred to by the same term
Millie Bobby Brown, an English actress Minimum bounding box, the box or hyperrectangle of minimal dimensions that contains the set of interest Mobile broadband
MBB
Geometric space with four dimensions
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Four-dimensional_space
Element of a unital algebra over the field of real numbers
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Hypercomplex_number
Completion of the usual space with "points at infinity"
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Projective_space
Geometric object with flat sides
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Polytope
In mathematics, a module that has a basis
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Free_module
Mathematical model combining space and time
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Spacetime
Method for producing composition algebras
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Cayley–Dickson_construction
Geometric model of the planar projection of the physical universe
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Euclidean_plane
Geometric space with seven dimensions
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Seven-dimensional_space
Geometric space with six dimensions
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Six-dimensional_space
Geometric model of the physical space
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Three-dimensional_space
Subspace of n-space whose dimension is (n-1)
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Hyperplane
Hypercomplex number system
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Octonion
N-dimensional generalisation of a pyramid
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Hyperpyramid
Fundamental object of geometry
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Point_(geometry)
Measure of a mathematical object studied in the field of algebraic geometry
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Dimension of an algebraic variety
Dimension_of_an_algebraic_variety
Study of uncertainty in the output of a mathematical model or system
total parameter space. More generally, the convex hull of the axes of a hyperrectangle forms a hyperoctahedron which has a volume fraction of 1 / n ! {\displaystyle
Sensitivity_analysis
Generalizes sine function to polytopes
Ericksson. The parallelotope is like a "squashed hyperrectangle", so it has less hypervolume than the hyperrectangle, meaning (see image for the 3d case): | Ω
Polar_sine
Hypercomplex number system
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Sedenion
Real-valued number of spatial dimensions
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Fractal_dimension
Geometric space with eight dimensions
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Eight-dimensional_space
Mathematical construct
{\displaystyle X} is an operator C {\displaystyle C} which associates to a hyperrectangle [ x ] {\displaystyle [x]} in R n {\displaystyle {\mathbf {R}}^{n}} another
Interval_contractor
Method of determining fractal dimension
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Minkowski–Bouligand_dimension
In mathematics, dimension of a ring
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Krull_dimension
Mathematical transformation in physics
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Time-translation_symmetry
Hypercomplex number system
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Trigintaduonion
1994 book by Michio Kaku
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Hyperspace_(book)
Invariant of topological spaces
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Inductive_dimension
Multidimensional search tree for points in k dimensional space
average. Instead of points, a k-d tree can also contain rectangles or hyperrectangles. Thus range search becomes the problem of returning all rectangles
K-d_tree
Geometric object used to describe rotation in any number of dimensions
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Plane_of_rotation
Generalization of definite integrals to functions of multiple variables
total (n + 1)-dimensional volume bounded below by the n-dimensional hyperrectangle T and above by the n-dimensional graph of f with the following Riemann
Multiple_integral
Topological space of dimension zero
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Zero-dimensional_space
Statistical distribution for dependence between random variables
argument is u and all others 1, C is d-non-decreasing, i.e., for each hyperrectangle B = ∏ i = 1 d [ x i , y i ] ⊆ [ 0 , 1 ] d {\displaystyle B=\prod _{i=1}^{d}[x_{i}
Copula_(statistics)
Regular polytope dual to the hypercube in any number of dimensions
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Cross-polytope
Space with one dimension
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
One-dimensional_space
PSSP. The three algorithms adopt the notion of spatial partition (a hyperrectangle) for identifying similar instances and extract prototypes for each set
Instance_selection
Topics referred to by the same term
function D'Alembert operator Rectangular cuboid, a geometric figure Hyperrectangle, in geometry BOx (psychedelics), a group of psychedelics and other psychoactive
Box_(disambiguation)
6-dimensional hypercube
[33,1,1] Coxeter group. The lowest symmetry construction is based on hyperrectangles or proprisms, cartesian products of lower dimensional hypercubes. The
6-cube
Distance estimation problems in computational geometry
in 3D and higher dimensions. Bounding box, the minimal axis-aligned hyperrectangle that contains all geometric data Closest pair of points: Given N points
Proximity_problems
Simplex formed from a right-angled path
into the same number of orthoschemes applies more generally to every hyperrectangle but in this case the orthoschemes may not be congruent. Every regular
Schläfli_orthoscheme
Surface in 3D space defined by an implicit function of three variables
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Implicit_surface
orthoschemes. A similar result applies more generally: every hypercube or hyperrectangle in d {\displaystyle d} dimensions can be dissected into d ! {\displaystyle
Dissection_into_orthoschemes
Property of a space in which the local dimensionality is the same everywhere
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Equidimensionality
Set of points touching all convex bodies of unit volume
bounded density that intersects all ellipsoids of unit volume, or all hyperrectangles of unit volume. For instance, in the plane, the shapes of these intersecting
Danzer_set
Polytope constructed from alternation of a hypercube
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid Number
Demihypercube
Geometrical object
X⁻ ⊂ X ⊂ X⁺. In R¹ the boxes are line segments, in R² rectangles and in Rⁿ hyperrectangles. A R² subpaving can be also a "non-regular tiling by rectangles", when
Subpaving
2D geometric minimization problem
studied in three or even more dimensions. In this case, the objects are hyperrectangles, and the strip is open-ended in one dimension and bounded in the residual
Strip_packing_problem
"Binary space partitions for axis-parallel segments, rectangles, and hyperrectangles". Discrete & Computational Geometry. 31 (2): 207–227. doi:10.1007/s00454-003-0729-3
Geometric_separator
Smallest dimension where a graph can be represented as an intersection graph of boxes
boxicity but with axis-parallel unit hypercubes instead of axis-parallel hyperrectangles. Boxicity is a generalization of cubicity. Sphericity is defined in
Boxicity
Family of regular honeycombs in geometry
three axial directions may have different edge lengths. The facets are hyperrectangles, also called orthotopes; in 2 and 3 dimensions the orthotopes are rectangles
Hypercubic_honeycomb
Y {\displaystyle Y} , Y ′ ⊂ X {\displaystyle Y'\subset X} be some hyperrectangles. That is, there exist some vectors a {\displaystyle a} , b {\displaystyle
Monotone_comparative_statics
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HYPERRECTANGLE
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HYPERRECTANGLE
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