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'Three by One' printed from http://nrich.maths.org/
The solutions produced here by school
students show eight different methods. Reflection on these methods
will help other students to see something of the 'bigger picture'
in a way they will not experience from ploughing through the
syllabus and working from textbooks (although that is also
Eight distinct proofs were given to this
problem by two students, Alex and Neil (Madras College) using
respectively sines, cosines, tangents, vectors, matrices,
coordinate geometry, complex numbers and pure geometry.
Alex and Neil went on to generalise this
problem to rectangles with dimensions $n$ by 1.