Rhombus

	Email		Print
	Bookmark		Link

Rhombus

In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a rhombus (from Ancient Greek

Ancient Greek

Ancient Greek is the historical stage in the development of the Greek language spanning across the Archaic Greece , Classical Greece , and Hellenistic civilization periods of ancient Greece and the classical antiquity....
??µß?? - rhombos, “rhombus, spinning top”), (plural rhombi or rhombuses) or rhomb (plural rhombs) is an equilateral parallelogram

Parallelogram

In geometry, a parallelogram is a quadrilateral with two sets of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are of equal size....
. In other words, it is a four-sided polygon in which every side has the same length.

The rhombus is often called a diamond, after the diamonds

Diamonds (suit)

Diamonds is one of the four Suit s found in the Standard 52-card deck of playing cards. The standard "international" deck uses the French suit system....
suit in playing cards, or a lozenge

Lozenge

A lozenge , colloquially known as a diamond, is a form of rhombus. The definition of lozenge is not strictly fixed, and it is sometimes used simply as a synonym for rhombus....
, because those shapes are similar rhombi, although rhombi are not necessarily diamonds or lozenges.

A rhombus is a variety of quadrilateral

Quadrilateral

In geometry, a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on....
.

Discussion

Ask a question about 'Rhombus'

Start a new discussion about 'Rhombus'

Answer questions from other users

Full Discussion Forum

A proof that the diagonals are perpendicular

One of the five 2D lattice

Lattice (group)

In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which linear span the real number vector space Rn....
types is the rhombic lattice, also called centered rectangular lattice..

If A, B, C and D were the vertices

Vertex (geometry)

In geometry, a vertex is a special kind of point which describes the corners or intersections of geometric shapes. Vertices are commonly used in computer graphics to define the corners of surfaces in 3d models, where each such point is given as a vector....
of the rhombus, named in agreement with the figure (higher on this page). Using to represent the vector from A to B, one notices that

.
The last equality comes from the parallelism of CD and AB. Taking the inner product,

since the norms of AB and BC are equal and since the inner product is bilinear

Bilinear

Bilinear may refer to* Bilinear sampling, a method in computer graphics for choosing the color of a texture.* Bilinear form* Bilinear interpolation...
and symmetric. The inner product of the diagonals is zero if and only if

If and only if

If and only if, in logic and fields that rely on it such as mathematics and philosophy, is a biconditional logical connective between statements....
they are perpendicular

Perpendicular

In geometry, two line or plane , are considered perpendicular to each other if they form congruence adjacent angles angles . The term may be used as a noun or adjective....
.

Origin

The word rhombus is from the Greek

Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
word for something that spins. Euclid

Euclid

Euclid , floruit 300 BC, also known as Euclid of Alexandria, was a Greek mathematics and is often referred to as the Father of Geometry. He was active in Alexandria during the reign of Ptolemy I ....
used ??µß?? (rhombos), from the verb ??µß? (rhembo), meaning "to turn round and round". Archimedes

Archimedes

Archimedes of Syracuse was a Greek mathematics, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity....
used the term "solid rhombus" for two right circular cone

Cone (geometry)

A cone is a dimension geometric shape that tapers smoothly from a flat, round base to a point called the apex or vertex. More precisely, it is the solid figure bounded by a plane base and the surface formed by the locus of all straight line segments joining the apex to the perimeter of the base....
s sharing a common base.

External links

With interactive applet.
Shows three different ways to compute the area of a rhombus, with interactive applet.