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Doubling the cube, also known as the Delian problem, is an ancient [a][1]: 9 geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be ...
Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
The dual of a cube is an octahedron.Vertices of one correspond to faces of the other, and edges correspond to each other. In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. [1]
If a player accepts a double, the cube is placed on their side of the board with the corresponding power of two facing upward, to indicate that the right to re-double belongs exclusively to the player who last accepted a double; this player is then said to "own" the cube. A player who drops a double loses the game at the current value of the ...
A facetting of a rectangular cuboid, creating compounds of two tetragonal or two rhombic disphenoids, with a bipyramid or rhombic fusil cores. This is first in a set of uniform compound of two antiprisms. A facetting of a trigonal trapezohedron creates a compound of two right triangular pyramids with a triangular antiprism core.
Menaechmus is remembered by mathematicians for his discovery of the conic sections and his solution to the problem of doubling the cube. [2] Menaechmus likely discovered the conic sections, that is, the ellipse, the parabola, and the hyperbola, as a by-product of his search for the solution to the Delian problem. [3]
Superflip. The superflip or 12-flip is a special configuration on a Rubik's Cube, in which all the edge and corner pieces are in the correct permutation, and the eight corners are correctly oriented, but all twelve edges are oriented incorrectly ("flipped"). The term superflip is also used to refer to any algorithm that transforms the Rubik's ...
The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases. It was first [dubious – discuss] described ...
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