Pascal’s Triangle: A Secret Unveiled
For 1500 years, a secret lay buried in the rows of Pascal’s triangle
“All of humanity’s problems stem from man’s inability to sit quietly in a room alone.” ― Blaise Pascal (1623–1662)
(Note: Friend and fellow science writer Cole Frederick and I have started a new publication called “Science Spectrum” here on Medium where we will now be publishing our content. Please consider following our new pub to support our efforts!)
Background
For 1500 years, mathematicians from many cultures have explored the patterns and relationships found in what we now, in the West, refer to as Pascal’s triangle. Named posthumously for the French mathematician, physicist, philosopher, and monk Blaise Pascal, this table of binomial coefficients was the subject of his Traité du Triangle Arithmétique (1665).
While Pascal was primarily concerned with its links to probability theory, the triangle also has many wonderful connections to combinatorics, Euclidean geometry, fractal geometry (in the form of the Sierpinski gasket), and numerous number sequences including the Fibonacci series. Beyond these many interesting properties, there is one remarkable aspect that has remained hidden until recently — the base of the natural logarithm, e.
