Rhomboid
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| Rhomboid | |
|---|---|
 A rhomboid is a parallelogram with two edge lengths and no right angles | |
| Type | quadrilateral, trapezium |
| Edges and vertices | 4 |
| Symmetry group | C2, [2]+, |
| Area | b × h (base × height); ab sin θ (product of adjacent sides and sine of the vertex angle determined by them) |
| Properties | convex |
Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram 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 but not a rhomboid. A parallelogram with right angled corners is a rectangle but not a rhomboid.
History
[edit]Euclid introduced the term in his Elements in Book I, Definition 22,
Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.
— Translation from the page of D.E. Joyce, Dept. Math. & Comp. Sci., Clark University [1]
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
[edit]The rhomboid has no line of symmetry, but it has rotational symmetry of order 2.
Occurrence
[edit]In biology
[edit]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 fins.[1]
In medicine
[edit]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 and the rhomboid minor muscle.