Rhomboid


Rhomboid

:"This article is about mathematics. For rhomboid muscles in anatomy, see Rhomboid major muscle and Rhomboid minor muscle. For rhomboid in botany see Leaf shape."

In geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are oblique.

A shape like a rhomboid with sides of equal length (equilateral) is a rhombus.

A shape like a rhomboid with right angled corners is a rectangle.

The word Rhomboid which means "rhomb"-like was commonly used in the 19th century for a parallelogram which was neither a rectangle nor a rhombus. Today it is more often used for a solid figure with six faces in which each face is a parallelogram and opposite faces in pairs lie in parallel planes. Some crystals are formed in 3D rhomboids. It is also sometimes called a rhombic prism. The term shows up frequently in science terminology referring to both its two and three dimensional meaning.

Euclid introduces 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 [http://aleph0.clarku.edu/~djoyce/java/elements/elements.html]

Euclid never uses the definition of rhomboid again and introduces the word parallelogram in Proposition 31 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 .

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Look at other dictionaries:

  • rhomboid — [räm′boid΄] n. [Fr rhomboïde < L rhomboides < Gr rhomboeidēs, rhomboid shaped: see RHOMBUS & OID] a parallelogram with oblique angles and only the opposite sides equal: see QUADRILATERAL adj. 1. shaped like a rhomboid 2. shaped somewhat… …   English World dictionary

  • Rhomboid — Rhom boid (r[o^]m boid), n. [Gr. ??? rhomboidal; ??? rhomb + e i^dos shape: cf. F. rhombo[ i]de.] (Geom.) An oblique angled parallelogram like a rhomb, but having only the opposite sides equal, the length and with being different. [1913 Webster] …   The Collaborative International Dictionary of English

  • Rhomboid — Rhom boid (r[o^]m boid), a. Same as {Rhomboidal}. [1913 Webster] …   The Collaborative International Dictionary of English

  • Rhomboïd — (griech.), ein Parallelogramm mit schiefen Winkeln, dessen Seiten nicht alle gleichlang sind …   Meyers Großes Konversations-Lexikon

  • rhomboid — 1560s (n.); 1690s (adj.), from Fr. rhomboide or directly from L.L. rhomboides, from Gk. rhomboeides; see RHOMBUS (Cf. rhombus) + OID (Cf. oid). Related: Rhomboidal …   Etymology dictionary

  • rhomboid — ► ADJECTIVE ▪ having or resembling the shape of a rhombus. ► NOUN ▪ a quadrilateral of which only the opposite sides and angles are equal. DERIVATIVES rhomboidal adjective …   English terms dictionary

  • rhomboid — I UK [ˈrɒmbɔɪd] / US [ˈrɑmˌbɔɪd] noun [countable] Word forms rhomboid : singular rhomboid plural rhomboids maths a parallelogram II UK [ˈrɒmbɔɪd] / US [ˈrɑmˌbɔɪd] adjective maths 1) in the shape of a rhomboid 2) relating to a rhombus …   English dictionary

  • rhomboid — rhomboidally, adv. /rom boyd/, n. 1. an oblique angled parallelogram with only the opposite sides equal. 2. Anat. rhomboideus. adj. 3. Also, rhomboidal. having a form like or similar to that of a rhombus; shaped like a rhomboid. [1560 70; < LL… …   Universalium

  • rhomboid — n. either of two muscles (rhomboid major and rhomboid minor) situated in the upper part of the back, between the backbone and shoulder blade. They help to move the shoulder blade backwards and upwards. * * * rhom·boid (romґboid) [Gr. rhombos… …   Medical dictionary

  • rhomboid — rhom|boid1 [ ram,bɔıd ] noun count TECHNICAL a PARALLELOGRAM rhomboid rhom|boid 2 [ ram,bɔıd ] adjective TECHNICAL 1. ) in the shape of a rhomboid 2. ) relating to a rhombus …   Usage of the words and phrases in modern English