 Two rhombi. 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. Rhombus may refer to: Rhombus, a geometric shape (often colloquially described as a diamond) Port Rhombus EP, an electronic music EP by Squarepusher Rhombus (band), a band from New Zealand Category: ...
Image File history File links Rhombus. ...
For other uses, see Geometry (disambiguation). ...
Beginning of Homers Odyssey The Ancient Greek language is the historical stage of the Greek language[1] as it existed during the Archaic (9th–6th centuries BC) and Classical (5th–4th centuries BC) periods in Ancient Greece. ...
A polygon whose sides are equal (Williams 1979, pp. ...
This article is about the geometric shape. ...
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). Diamonds () is one of the four suits found in playing cards. ...
A lozenge (â—Š) is a form of rhombus. ...
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. Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ...
A parallelogram. ...
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. A kite showing its equal sides and its inscribed circle. ...
Area The area of any rhombus is the product of the lengths of its diagonals divided by two:
This article is about the physical quantity. ...
A diagonal can refer to a line joining two nonadjacent vertices of a polygon or polyhedron, or in contexts any upward or downward sloping line. ...
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) A parallelogram. ...
The area also equals the square of the side multiplied by the sine of any of the interior angles:
Area = a2sinθ
where a is the length of the side and θ 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. In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. ...
If A, B, C and D were the vertices of the rhombus, named in agreement with the figure (higher on this page). Using to represent the vector from A to B, one notices that
 .
The last equality comes from the parallelism of CD and AB. Taking the inner product, In geometry, a vertex (plural vertices) is a special kind of point, usually a corner of a polygon, polyhedron, or higher dimensional polytope. ...
This article is about vectors that have a particular relation to the spatial coordinates. ...
In mathematics, an inner product space is a vector space with additional structure, an inner product (also called a scalar product), which allows us to introduce geometrical notions such as angles and lengths of vectors. ...
  - = 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. In mathematics, a bilinear operator is a generalized multiplication which satisfies the distributive law. ...
↔ ⇔ ≡ logical symbols representing iff. ...
Fig. ...
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".[1][2] Archimedes used the term "solid rhombus" for two right circular cones sharing a common base.[3] For other uses, see Euclid (disambiguation). ...
For other uses, see Archimedes (disambiguation). ...
This article is about the geometric object, for other uses see Cone. ...
References - ^ Rhombos, "A Greek-English Lexicon", Liddel and Scott, at Perseus
- ^ Rhembo, "A Greek-English Lexicon", Liddel and Scott, at Perseus
- ^ http://www.pballew.net/rhomb.html MathWords web page for Rhombus
External links Look up Rhombus in Wiktionary, the free dictionary. Wikimedia Commons has media related to: Rhombus - Parallelogram and Rhombus - Animated course (Construction, Circumference, Area)
- Rhombus definition. Math Open Reference With interactive applet.
- Rhombus area. Math Open Reference Shows three different ways to compute the area of a rhombus, with interactive applet.
Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 151 languages. ...
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