Traditionally, in two-dimensional

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, a rhomboid is a

parallelogram In Euclidean geometry, a parallelogram is a simple polygon, simple (non-list of self-intersecting polygons, self-intersecting) quadrilateral with two pairs of Parallel (geometry), parallel sides. The opposite or facing sides of a parallelogram a ...

in which adjacent sides are of unequal lengths and angles are non-right angled. The terms "rhomboid" and "parallelogram" are often erroneously conflated with each other (i.e, when most people refer to a "parallelogram" they almost always mean a rhomboid, a specific subtype of parallelogram); however, while all rhomboids are parallelograms, not all parallelograms are rhomboids. A parallelogram with sides of equal length ( equilateral) is called a ''

rhombus In plane Euclidean geometry, a rhombus (: 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 rhom ...

'' 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 geometry, Euclidean plane geometry, a rectangle is a Rectilinear polygon, rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that a ...

'' but not a rhomboid. A parallelogram is a rhomboid if it is neither a rhombus nor a rectangle.

History

Euclid Euclid (; ; 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 geometry that largely domina ...

introduced the term in his '' Elements'' in Book 1, Definition 22, Euclid never used the definition of rhomboid again and introduced the word

in Proposition 34 of Book 1; ''"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 (geometry), shape has when it looks the same after some rotation (mathematics), rotation by a partial turn (angle), turn. An object's degree of rotational s ...

of order 2.

Occurrence

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 (: leaves) is a principal appendage of the stem of a vascular plant, usually borne laterally above ground and specialized for photosynthesis. Leaves are collectively called foliage, as in "autumn foliage", while the leaves, stem, ...

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 fin, flap-like locomotory appendages. They are found in Decapodiformes, ten-limbed cephalopods (inclu ...

In medicine

In a type of arthritis called pseudogout, crystals of calcium pyrophosphate dihydrate accumulate in the joint, causing inflammation. Aspiration of the joint fluid reveals rhomboid-shaped crystals under a microscope. In anatomy, rhomboid-shaped muscles include the

rhomboid major muscle The rhomboid major is a skeletal muscle of the back that connects the scapula with the vertebrae of the spinal column. It originates from the spinous processes of the thoracic vertebrae T2–T5 and supraspinous ligament; it inserts onto the lower ...

and the

rhomboid minor muscle In human anatomy, the rhomboid minor is a small skeletal muscle of the back that connects the scapula to the vertebrae of the spinal column. It arises from the nuchal ligament, the 7th cervical and 1st thoracic vertebrae and intervening sup ...

References

External links

* {{Polygons Types of quadrilaterals