When a young schoolchild was asked what a rhombus was, he replied: "It's a tilted square." He was probably misled by the usual depiction of the shape, with its acute angles pointing vertically, whereas a square's sides are generally drawn horizontally and vertically. Yet the definition of this quadrilateral has nothing to do with its position or orientation.
What is a rhombus?
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In Definition 22 of Book I of the Éléments (as translated by Bernard Vitrac), Euclid states: "Among quadrilateral figures, a square is one that is both equilateral and right-angled; an oblong is one that is right-angled but not equilateral; a rhombus is one that is equilateral but not right-angled…"
A rhombus is a plane figure with four equal sides. A square is a special case of a rhombus, one that we include today, unlike Euclid.
