In geometry, a rhombus (from Ancient Greek ῥόμβος - rrhombos, “rhombus, spinning top”), (plural rhombi or rhombuses) or rhomb (plural rhombs) is an equilateral quadrilateral. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position The Ancient Greek language is the historical stage in the development of the Hellenic language family spanning the Archaic (c In Geometry, an equilateral polygon is a Polygon which has all sides of the same length In Geometry, a quadrilateral is a Polygon with four sides or edges and four vertices or corners. 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). Analogues in other suits German suits: Jingle bells small bells (Schellen Swiss German suits jingle bells Applications Modal logic In Modal logic, the lozenge expresses the possibility of the following expression
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Supersets
In any rhombus, opposite sides are parallel. Thus, the rhombus is a special case of the parallelogram. In Geometry, a parallelogram is a Quadrilateral with two sets of Parallel sides 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). In Geometry a kite, or deltoid, is a Quadrilateral with two disjoint pairs of Congruent Adjacent sides in contrast 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:
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)
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. Area is a Quantity expressing the two- Dimensional size of a defined part of a Surface, typically a region bounded by a closed Curve. A diagonal can refer to a line joining two nonconsecutive vertices of a Polygon or Polyhedron, or in contexts any upward or downward sloping line In Geometry, a parallelogram is a Quadrilateral with two sets of Parallel 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 R n is a Discrete subgroup of
If A, B, C and D were the vertices of the rhombus, named in agreement with the figure (higher on this page). In Geometry, a vertex (plural "vertices" is a special kind of point. 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,
- = 0
since the norms of AB and BC are equal and since the inner product is bilinear and symmetric. In Mathematics, an inner product space is a Vector space with the additional Structure of inner product. The inner product of the diagonals is zero if and only if they are perpendicular. ↔ In Geometry, two lines or planes (or a line and a plane are considered perpendicular (or orthogonal) to each other if they form congruent
Tilings
 Rhombic tiling |
Origin
The word rhombus is from the Greek word for something that spins. A tessellation or tiling of the plane is a collection of Plane figures that fills the plane with no overlaps and no gaps Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly Euclid used ρόμβος (rhombos), from the verb ρέμβω (rhembo), meaning "to turn round and round". Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry [1][2] Archimedes used the term "solid rhombus" for two right circular cones sharing a common base. Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer A cone is a three-dimensional Geometric shape that tapers smoothly from a flat round base to a point called the apex or vertex [3]
References
External links
- 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.
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