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Rhombus
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Rhombus
In geometry, a rhombus (pl.: rhombi or rhombuses) is an equilateral quadrilateral, a quadrilateral whose four sides all have the same length. Other names for rhombus include diamond, lozenge, and calisson.
Every rhombus is a simple polygon (having no self-intersections). A rhimbus is a special case of a parallelogram and a kite. A rhombus with right angles is a square. A non-square rhombus has two opposite acute angles and two opposite obtuse angles.
The name rhombus comes from Greek ῥόμβος rhómbos, meaning something that spins, such as a bullroarer or an ancient precursor of the button whirligig. The word was used both by Euclid and Archimedes, who also used the term "solid rhombus" for a bicone, two right circular cones sharing a common base. A planar rhombus is a cross section of a bicone.
The name diamond comes from the shape of an octahedral diamond gemstone; the diamonds suit in playing cards is named after the shape – it was originally called carreaux (lit. "squares") in French. In the context of polyiamonds, shapes like polyominos but constructed from equilateral triangles, a diamond is a rhombus with a 60° angle.
The etymology of lozenge is uncertain. It might come from a shape of some lauzinaj almond pastries, or from the shape of tombstones. A lozenge is often specifically to a rhombus with a 45° angle.
A calisson is a type of rhombus-shaped French sweet.
A simple (non-self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following:
Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties:
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Rhombus
In geometry, a rhombus (pl.: rhombi or rhombuses) is an equilateral quadrilateral, a quadrilateral whose four sides all have the same length. Other names for rhombus include diamond, lozenge, and calisson.
Every rhombus is a simple polygon (having no self-intersections). A rhimbus is a special case of a parallelogram and a kite. A rhombus with right angles is a square. A non-square rhombus has two opposite acute angles and two opposite obtuse angles.
The name rhombus comes from Greek ῥόμβος rhómbos, meaning something that spins, such as a bullroarer or an ancient precursor of the button whirligig. The word was used both by Euclid and Archimedes, who also used the term "solid rhombus" for a bicone, two right circular cones sharing a common base. A planar rhombus is a cross section of a bicone.
The name diamond comes from the shape of an octahedral diamond gemstone; the diamonds suit in playing cards is named after the shape – it was originally called carreaux (lit. "squares") in French. In the context of polyiamonds, shapes like polyominos but constructed from equilateral triangles, a diamond is a rhombus with a 60° angle.
The etymology of lozenge is uncertain. It might come from a shape of some lauzinaj almond pastries, or from the shape of tombstones. A lozenge is often specifically to a rhombus with a 45° angle.
A calisson is a type of rhombus-shaped French sweet.
A simple (non-self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following:
Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties:
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