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Cube is a 1997 Canadian science fiction horror film directed and co-written by Vincenzo Natali. [8] A product of the Canadian Film Centre's First Feature Project, [9] Nicole de Boer, Nicky Guadagni, David Hewlett, Andrew Miller, Julian Richings, Wayne Robson, and Maurice Dean Wint star as seven individuals trapped in a bizarre and deadly labyrinth of cube-shaped rooms.
The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that maps a number to its cube. It is an odd function, as (−n) 3 = −(n 3). The volume of a geometric cube is the cube of its side length, giving rise to the
Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to volume ratio of 6:1. The larger (2 m sides) cube has a surface area to volume ratio of (24/8) 3:1. As the dimensions increase, the volume will continue to grow faster than the surface area. Thus the square–cube law.
The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m −1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus
The proportion of space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.
In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x 3 = 2; in other words, x = , the cube root of two. This is because a cube of side length 1 has a volume of 1 3 = 1 , and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2.
A unit cube with a hole cut through it, large enough to allow Prince Rupert's cube to pass. In geometry, Prince Rupert's cube is the largest cube that can pass through a hole cut through a unit cube without splitting it into separate pieces. Its side length is approximately 1.06, 6% larger than the side length 1 of the unit cube through which ...
[5] Euler brick with edges a, b, c and face diagonals d, e, f. Exhaustive computer searches show that, if a perfect cuboid exists, the odd edge must be greater than 2.5 × 10 13, [6] the smallest edge must be greater than 5 × 10 11, [6] and; the space diagonal must be greater than 9 × 10 15. [7]