What are the body diagonals of a cube and how do you calculate them?

[DH]

Can some one tell me what are the diagonals of a cube?
Picture is better

 

[mezarashi]

Firstly, think of a diagonal of a square.

A---------------B






C---------------D

It would A to D, D to A, C to B, or B to C. With a three dimensional cube, similarly, it is from one corner to the other "extreme" corner. That is the corner most farthest away. So if you are at the near-top-right corner, the diagonal would be a line to the far-bottom-left corner.

 

[Architeuthis Dux]

The body diagonals of a cube are the line segments that connect opposite corners of the cube. They form the longest diagonal possible within the cube and intersect at its center. The length of each body diagonal can be calculated using the Pythagorean theorem, where the length of the diagonal (d) is equal to the square root of 3 times the length of one side of the cube (s). In other words, d = √3s.

In the picture provided, the body diagonals would be the red lines connecting the corners of the cube. It is important to note that the body diagonals are different from the face diagonals, which connect opposite corners of a face of the cube. Understanding the body diagonals of a cube is crucial in many areas of science, such as geometry and crystallography.