Rhomboid: Difference between revisions
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{{Short description|Geometrical concept}} | {{Short description|Geometrical concept}} | ||
{{about|the two-dimensional figure|the three-dimensional shape|Rhombohedron|the human back muscles|Rhomboid muscles}} | |||
{{more citations needed|date=September 2012}} | {{more citations needed|date=September 2012}} | ||
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{{Infobox polygon | {{Infobox polygon | ||
| name = Rhomboid | | name = Rhomboid | ||
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==History== | ==History== | ||
[[Euclid]] introduced the term in his ''[[Euclid's Elements|Elements]]'' in Book | [[Euclid]] introduced the term in his ''[[Euclid's Elements|Elements]]'' in Book 1, Definition 22, | ||
{{blockquote|text=''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.''|sign=Translation from the page of [[David E. Joyce (mathematician)|D.E. Joyce]], Dept. Math. & Comp. Sci., Clark University [http://aleph0.clarku.edu/~djoyce/java/elements/bookI/defI22.html]}} | {{blockquote|text=''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.'' |sign=Translation from the page of [[David E. Joyce (mathematician)|D.E. Joyce]], Dept. Math. & Comp. Sci., Clark University [http://aleph0.clarku.edu/~djoyce/java/elements/bookI/defI22.html]}} | ||
Euclid never used the definition of rhomboid again and introduced the word [[parallelogram]] in Proposition 34 of Book | Euclid never used the definition of rhomboid again and introduced the word [[parallelogram]] 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== | ==Symmetries== | ||
Latest revision as of 01:31, 13 June 2025
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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. A parallelogram is a rhomboid if it is neither a rhombus nor a rectangle.
History
Euclid introduced the term in his Elements in Book 1, Definition 22,
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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.
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Euclid never used the definition of rhomboid again and introduced the word parallelogram 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 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 or cephalopod fins.[1]
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 and the rhomboid minor muscle.
References
External links
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