Rhombus

A rhombus is a square that has been leaned on.^[1] It has four equal sides and two pairs of equal angles, and it is what most people draw when asked to draw a diamond, a kite or a square in a hurry.

Identification

A rhombus is identified by elimination. It is not a square, because it is leaning. It is not a rectangle, because its sides are all the same length. It is not a diamond, because it is not worth anything. Whatever is left over after these deductions is a rhombus.

Geometry teachers warn that the leftover is sometimes a square standing at an angle, which is technically also a rhombus but should not be encouraged.

The square question

Geometers have long disagreed about whether a square is a rhombus. The Inclusive School holds that every square is a rhombus with good posture. The Exclusive School holds that a rhombus is a square that has let itself go.^[2]

A congress held in 1964 to settle the matter could not agree on a seating plan. The table was square, and the Inclusive delegates insisted on sitting at it diagonally.

In everyday life

Rhombuses appear on kites, on patterned socks and in tiled floors, where they are walked on without anyone noticing that they are leaning. A rhombus is the only shape that can be turned into a square by tidying it.

See also

• Square – a rhombus that stood up straight
• Diamond – worth more, same outline
• Playing card – where rhombuses go to be called diamonds

References

1. Oblique, O. (1964). Leaning Shapes. Angle Press.
2. Proceedings of the Quadrilateral Congress (1964). “Seating Plan (Disputed)”. Pp. 1–40.