térátló

térátló is the Hungarian geometric term for the space diagonal of a rectangular prism or cube. It denotes the straight line segment that connects two opposite vertices and runs through the solid’s interior, as opposed to a face diagonal that lies on a face.

Etymology: the word combines tér meaning space with átlo (diagonal).

In a rectangular prism with side lengths a, b, c, the length L of the térátló is given by L = sqrt(a^2 + b^2 + c^2). A prism has four space diagonals, each connecting opposite vertices.

In a cube with side length s, the térátló length simplifies to L = s√3. All four space diagonals of a cube have the same length and intersect at the prism’s center.

Angles and orientation: The space diagonals that meet at the center form an angle of arccos(-1/3), approximately 109.47 degrees, often associated with the tetrahedral angle. This reflects the symmetric orientation of the diagonals in a cube.

Applications: The concept is used in 3D distance measurements, computer graphics, architectural design, and crystallography. It also appears in vector geometry when determining distances between opposite corners in three-dimensional figures.

See also: diagonal (general), face diagonal, body diagonal (alternate English term for the same concept).