Pi Can Be Expressed Only Using The Numbers 1 and 2

Proving a beautiful and pleasing mathematical result

Today I am going to prove a beautiful and somewhat surprising result — that it is possible to find a mathematical expression for π that only uses the numbers 1 and 2 in the expression. The expression that I will prove is the following:

where the denominator is an infinite product of nested surds.

Step 1 of my proof will establish an important trigonometric identity, which we will use in Step 2 by taking…