AskDefine | Define rhombic

Dictionary Definition

rhombic adj : resembling a rhombus

User Contributed Dictionary

English

Adjective

rhombic
  1. having the characteristics of a rhombus.

Derived terms

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

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