AskDefine | Define rhombus

Dictionary Definition

rhombus n : a parallelogram with four equal sides; an oblique-angled equilateral parallelogram [syn: rhomb] [also: rhombi (pl)]

User Contributed Dictionary

English

Etymology

First coined 1567, from rhombus < ῥόμβος < ῥέμβομαι

Pronunciation

  • (UK) /ˈɹɒmbəs/, /"rQmb@s/
  • (US) /ˈɹɑːmbəs/, /"rA:mb@s/

Noun

  1. A parallelogram having all sides of equal length.

Synonyms

Translations

A parallelogram having all sides of equal length

Related terms

Latin

Etymology

From ῥόμβος < ῥέμβομαι

Noun

rhombus

Extensive Definition

In geometry, a rhombus (from Ancient Greek ῥόμβος - rrhombos, “rhombus, spinning top”), (plural rhombi or rhombuses) or rhomb (plural rhombs) is an equilateral quadrilateral. In other words, it is a four-sided polygon in which every side has the same length.
The rhombus is often casually called a diamond, after the diamonds suit in playing cards, or a lozenge, because those shapes are rhombi (though not all rhombi are actually diamonds or lozenges).

Supersets

In any rhombus, opposite sides are parallel. Thus, the rhombus is a special case of the parallelogram. One analogy holds that the rhombus is to the parallelogram as the square is to the rectangle. In its turn, the square is a special case of the rhombus, being most readily defined as a rhombus with one right angle.
A rhombus is also a special case of a kite (a quadrilateral with two distinct pairs of adjacent sides of equal lengths). The opposite sides of a kite are not parallel unless the kite is also a rhombus.

Area

The area of any rhombus is the product of the lengths of its diagonals divided by two:
Area=() /2
Because the rhombus is a parallelogram, the area also equals the length of a side (B) multiplied by the perpendicular distance between two opposite sides(H)
Area=B \times H
The area also equals the square of the side multiplied by the sine of any of the interior angles:
Area=
where a is the length of the side and \theta is the angle between two sides.

A proof that the diagonals are perpendicular

One of the five 2D lattice types is the rhombic lattice, also called centered rectangular lattice.
If A, B, C and D were the vertices of the rhombus, named in agreement with the figure (higher on this page). Using \overrightarrow to represent the vector from A to B, one notices that \overrightarrow = \overrightarrow + \overrightarrow \overrightarrow = \overrightarrow+ \overrightarrow= \overrightarrow- \overrightarrow. The last equality comes from the parallelism of CD and AB. Taking the inner product, =
= - + -
= 0
since the norms of AB and BC are equal and since the inner product is bilinear and symmetric. The inner product of the diagonals is zero if and only if they are perpendicular.

Tilings

Origin

The word rhombus is from the Greek word for something that spins. Euclid used ρόμβος (rhombos), from the verb ρέμβω (rhembo), meaning "to turn round and round". Archimedes used the term "solid rhombus" for two right circular cones sharing a common base.

References

External links

rhombus in Arabic: دالتون(رياضيات)
rhombus in Asturian: Rombu
rhombus in Azerbaijani: Romb
rhombus in Bosnian: Romb
rhombus in Bulgarian: Ромб
rhombus in Catalan: Rombe
rhombus in Czech: Kosočtverec
rhombus in Danish: Rombe
rhombus in German: Raute
rhombus in Estonian: Romb
rhombus in Modern Greek (1453-): Ρόμβος
rhombus in Spanish: Rombo
rhombus in Esperanto: Rombo
rhombus in French: Losange
rhombus in Galician: Rombo
rhombus in Korean: 마름모
rhombus in Croatian: Romb
rhombus in Italian: Rombo (geometria)
rhombus in Hebrew: מעוין
rhombus in Georgian: რომბი
rhombus in Haitian: Lozanj
rhombus in Latvian: Rombs
rhombus in Lithuanian: Rombas
rhombus in Limburgan: Roet
rhombus in Hungarian: Rombusz
rhombus in Mongolian: Ромб
rhombus in Dutch: Ruit (meetkunde)
rhombus in Japanese: 菱形
rhombus in Norwegian: Rombe
rhombus in Central Khmer: ចតុកោណស្មើ
rhombus in Low German: Ruut
rhombus in Polish: Romb
rhombus in Portuguese: Losango
rhombus in Romanian: Romb
rhombus in Quechua: Puytu
rhombus in Russian: Ромб
rhombus in Sicilian: Rummu
rhombus in Simple English: Rhombus
rhombus in Slovenian: Romb
rhombus in Serbian: Ромб
rhombus in Finnish: Neljäkäs
rhombus in Swedish: Romb
rhombus in Vietnamese: Hình thoi
rhombus in Ukrainian: Ромб
rhombus in Vlaams: Rute
rhombus in Chinese: 菱形
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