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An a × b rectangle can be packed with 1 × n strips if and only if n divides a or n divides b. [15] [16] de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) [15]
A rectangular cuboid with integer edges, as well as integer face diagonals, is called an Euler brick; for example with sides 44, 117, and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists. [6] The number of different nets for a simple cube is 11 ...
For a room of length l, width w and height h, the spider a distance b below the ceiling, and the fly a distance a above the floor, length of the spiral path is (+) + (+ +) while the naive solution has length + | |. [1] Depending on the dimensions of the cuboid, and on the initial positions of the spider and fly, one or another of these paths ...
[1] [3] Along with the rectangular cuboids, parallelepiped is a cuboid with six parallelogram. Rhombohedron is a cuboid with six rhombus faces. A square frustum is a frustum with a square base, but the rest of its faces are quadrilaterals; the square frustum is formed by truncating the apex of a square pyramid .
Each new cuboid added has a length and width that matches the length and width of the face being added to. The height of the nth added cuboid is the nth Padovan number. [1] [3] Connecting alternate points where the spiral bends creates a series of triangles, where each triangle has two sides that are successive Padovan numbers and that has an ...
The minimal enclosing box of the regular tetrahedron is a cube, with side length 1/ √ 2 that of the tetrahedron; for instance, a regular tetrahedron with side length √ 2 fits into a unit cube, with the tetrahedron's vertices lying at the vertices (0,0,0), (0,1,1), (1,0,1) and (1,1,0) of the unit cube. [7]
The cuboid's space diagonals all have the same length. If the edge lengths of a cuboid are a , b , and c , then the distinct rectangular faces have edges ( a , b ), ( a , c ), and ( b , c ); so the respective face diagonals have lengths a 2 + b 2 , {\displaystyle {\sqrt {a^{2}+b^{2}}},} a 2 + c 2 , {\displaystyle {\sqrt {a^{2}+c^{2}}},} and b 2 ...
1 2-D Centroids. 2 3-D Centroids. 3 See also. 4 References. ... Cuboid: a, b = the sides of the cuboid's base ... h = the height of the prism's triangular base