Traditionally, in two-dimensional

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, a rhomboid is a

parallelogram In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equa ...

in which adjacent sides are of unequal lengths and angles are non-right angled. A parallelogram with sides of equal length (

equilateral In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each othe ...

) is a

rhombus In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...

but not a rhomboid. A parallelogram with

right angle In geometry and trigonometry, a right angle is an angle of exactly 90 Degree (angle), degrees or radians corresponding to a quarter turn (geometry), turn. If a Line (mathematics)#Ray, ray is placed so that its endpoint is on a line and the ad ...

d corners is a

rectangle In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containi ...

but not a rhomboid. The term ''rhomboid'' is now more often used for a

rhombohedron In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right ang ...

or a more general

parallelepiped In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term ''rhomboid'' is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. In Euclidea ...

, a solid figure with six faces in which each face is a parallelogram and pairs of opposite faces lie in parallel planes. Some crystals are formed in three-dimensional rhomboids. This solid is also sometimes called a rhombic prism. The term occurs frequently in science terminology referring to both its two- and three-dimensional meaning.

History

Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...

introduced the term in his '' Elements'' in Book I, Definition 22, Euclid never used the definition of rhomboid again and introduced the word

in Proposition 34 of Book I; ''"In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas."'' Heath suggests that rhomboid was an older term already in use.

Symmetries

The rhomboid has no line of symmetry, but it has

rotational symmetry Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which i ...

of order 2.

In biology

In biology, rhomboid may describe a geometric rhomboid (e.g. the rhomboid muscles) or a bilaterally-symmetrical kite-shaped or diamond-shaped outline, as in

leaves A leaf (plural, : leaves) is any of the principal appendages of a vascular plant plant stem, stem, usually borne laterally aboveground and specialized for photosynthesis. Leaves are collectively called foliage, as in "autumn foliage", wh ...

cephalopod fin Cephalopod fins, sometimes known as wings,Young, R.E., M. Vecchione & K.M. Mangold (1999)Cephalopoda Glossary Tree of Life Web Project. are paired flap-like locomotory appendages. They are found in ten-limbed cephalopods (including squid, bobtail ...

In medicine

In a type of arthritis called

pseudogout Calcium pyrophosphate dihydrate (CPPD) crystal deposition disease, also known as pseudogout and pyrophosphate arthropathy, is a rheumatologic disease which is thought to be secondary to abnormal accumulation of calcium pyrophosphate dihydrate crys ...

, crystals of

calcium pyrophosphate Calcium pyrophosphate (Ca2P2O7) is a chemical compound, an insoluble calcium salt containing the pyrophosphate anion. There are a number of forms reported: an anhydrous form, a dihydrate, Ca2P2O7·2H2O and a tetrahydrate, Ca2P2O7·4H2O. Deposition ...

dihydrate accumulate in the joint, causing inflammation. Aspiration of the joint fluid reveals rhomboid-shaped crystals under a microscope.

References

External links

*{{MathWorld , urlname=Rhomboid , title=Rhomboid Types of quadrilaterals