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 ...
, a rhomboid is a
parallelogram 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 oth ...
) 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 angled corners is a
rectangle 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) is a three-dimensional figure with six faces which are rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be us ...
or a more general
parallelepiped, 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, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
introduced the term in his ''
Elements'' in Book I, Definition 22,
Euclid never used the definition of rhomboid again and introduced the word
parallelogram 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 or
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, bobtai ...
s.
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 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