In the words of the old song, ‘the knee bone’s connected to the thigh bone,
and the thigh bone’s connected to the hip bone’. So it is with Pascal’s triangle and
its intimate connections with so many parts of mathematics – modern geometry,
combinatorics and algebra to name but three. More than this it is an exemplar of
the mathematical trade – the constant search for pattern and harmony which
reinforces our understanding of the subject itself.

the condensed idea

The number fountain