Search results
Results from the WOW.Com Content Network
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 +, +, and +. Thus each face diagonal of a cube with side length a is . [3] A regular dodecahedron has 60 face diagonals ...
A magic square is an arrangement of numbers in a square grid so that the sum of the numbers along every row, column, and diagonal is the same. Similarly, one may define a magic cube to be an arrangement of numbers in a cubical grid so that the sum of the numbers on the four space diagonals must be the same as the sum of the numbers in each row, each column, and each pillar.
An almost-perfect cuboid has 6 out of the 7 lengths as rational. Such cuboids can be sorted into three types, called body, edge, and face cuboids. [14] In the case of the body cuboid, the body (space) diagonal g is irrational. For the edge cuboid, one of the edges a, b, c is irrational. The face cuboid has one of the face diagonals d, e, f ...
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 ...
Both formulas can be determined by using Pythagorean theorem. The surface area of a cube is six times the area of a square: [4] =. The volume of a cuboid is the product of its length, width, and height. Because all the edges of a cube are equal in length, it is: [4] =.
A perfect parallelepiped is a parallelepiped with integer-length edges, face diagonals, and space diagonals. In 2009, dozens of perfect parallelepipeds were shown to exist, [3] answering an open question of Richard Guy. One example has edges 271, 106, and 103, minor face diagonals 101, 266, and 255, major face diagonals 183, 312, and 323, and ...
The diagonals of a cube with side length 1. AC' (shown in blue) is a space diagonal with length , while AC (shown in red) is a face diagonal and has length .. In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.
The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere.