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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 ...
A rectangular cuboid (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "cuboid" means "like a cube ", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the angles between its adjacent faces).
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]
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
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 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 ...