Definition:Quadrilateral/Rhombus

Definition

A rhombus is a parallelogram whose sides are all the same length.

Its angles may or may not all be equal.

Also known as

A rhombus is also known as a rhomb.

Particularly when it is oriented so that the longer diagonal is a vertical line, a rhombus is often referred to as a diamond.

Also see

• A square is a rhombus all of whose angles are equal to a right angle.

• A rhombus is a kite all of whose sides are the same length.

Euclid's Definitions

In the words of Euclid:

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 equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

(The Elements: Book $\text{I}$: Definition $22$)

Linguistic Note

The plural of rhombus is properly rhombi, although you may occasionally see the technically incorrect rhombuses.

The adjectival form of rhombus is rhombic, meaning:

shaped like, or appertaining to, a rhombus.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): diamond
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): lozenge
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): parallelogram
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): rhomb
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): rhombus, rhomb, diamond or lozenge
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): rhombus (rhomb)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): rhombus (rhomb)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): diamond
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rhombus (rhombi)