13 Pascal’s triangle
The number 1 is important but what about 11? It is interesting too and so is 11 × 11 =
121, 11 × 11 × 11 = 1331 and 11 × 11 × 11 × 11 = 14,641. Setting these out we get
These are the first lines of Pascal’s triangle. But where do we find it?
Throwing in 11° = 1 for good measure, the first thing to do is forget the
commas, and then introduce spaces between the numbers. So 14,641 becomes
1 4 6 4 1.
Pascal’s triangle is famous in mathematics for its symmetry and hidden
relationships. In 1653 Blaise Pascal thought so and remarked that he could not
possibly cover them all in one paper. The many connections of Pascal’s triangle
with other branches of mathematics have made it into a venerable mathematical
object, but its origins can be traced back much further than this. In fact Pascal
didn’t invent the triangle named after him – it was known to Chinese scholars of
the 13th century.