Published online by Cambridge University Press: 01 August 2016
The defining property of a rectangle is that it is a quadrilateral whose angles are all equal (or are right angles, which amounts to the same thing).
The opposite sides of a rectangle are equal. If a and b are the lengths of adjacent sides of a rectangle, such a rectangle can be described as an abab rectangle (or an (ab)2 rectangle). The area of the rectangle is ab.
As far as I understand the latest version of the national curriculum and the new A level syllabuses, which make no serious reference to irrational numbers, students leaving school will not necessarily know that there are two sorts of rectangle: those coverable by a set of identical squares, which can therefore be drawn on squared paper; and those not, such as the golden rectangle. An (ab)2 rectangle is coverable by squares if, and only if, a/b is rational.
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