Difference of two squares, staple diet for GCSE maths students, is first proposition in Carr’s book of magic and has ancient geometric roots in Euclid Book II.

Carr’s 626, in his magical book for Edwardian mathematical autodidacts, provides summary of general solutions for trigonometrical equations useful to STEP and A level students.

Friendly triangles – good visual method for memorising trig ratios of 30, 45 and 60 degree angles. Known for thousands of years as per the Babylonian tablet