Rhombus

From Freepedia

In geometry, a rhombus (also known as a rhomb) is a quadrilateral in which all of the sides are of equal length. More colloquially it may be described as a diamond or lozenge shape.

In any rhombus, opposite sides will be parallel. Thus, the rhombus is a special case of the parallelogram. One suggestive analogy is that the rhombus is to the parallelogram as the square is to the rectangle. If all the angles of a rhombus are right angles, it is then a rectangle and a square.

The rhombus has the same symmetry as the rectangle (with symmetry group D_{2, the Klein four-group) and is its dual: the vertices of one correspond to the sides of the other.}

A rhombus in the plane has five degrees of freedom: one for the shape, one for the size, one for the orientation, and two for the position.

The diagonals of a rhombus are perpendicular to each other.

One of the five 2D lattice types is the rhombic lattice, also called centered rectangular lattice.

Area

The area of any rhombus is one half the product of the lengths of its diagonals:
<math>A=\frac{D_1 \times D_2}{2}</math>
The area also equals the length of a side multiplied by the perpendicular distance between two opposite sides; i.e D₂

Origin

The origin of the word rhombus is from the Greek word for something that spins. Euclid uses the word ρομβος and in his translation Heath says it is apparently drawn from the Greek word ρεμβω, to turn round and round. He also points out that Archimedes used the term solid rhombus for two right circular cones sharing a common base. For more on the origin of the word, see Rhombus at the MathWords web page, [1].