Feeling Lucky? – Total Probability Theory

Total Probability Screenshot

When Blaise Pascal and Pierre de Fermat studied a problem related to a gambling game they developed what is now widely known as the probability theory.

They were hired by two very rich man, that were interrupted in a middle of a gambling game, to determine in which proportion the stakes should be divided based on the current score.

The formula of total probability is widely used and is very significant in the probability theory. 

The fun fact is that the interest in probability was solely influenced by gambling games throughout the 17. 18.  and 19. century. Only way later was probability studied for theoretical reasons. :)

The Most Beautiful Formula

The famous Euler’s identity is  widely considered the most beautiful formula in all of maths.

For me It is because it binds all of the fundamental mathematical constants in a single,  short and sweet equality.

  • The number e, which is the base of the natural logarithm,
  • The number pi, which represents the ratio between the, circumference and the diameter of a circle
  • The constant i, or the famous imaginary unit, defined as the square root of -1,
  • The constant 0, which is the neutral element for the operation of addition,
  • The constant 1, which is the neutral element for the operation of multiplication.

Thank you, sir Euler! 🙂

The Famous Harmonic Series

The divergence of the harmonic series is the source of many counterintuitive conclusions, such as this one:

Given a collection of identical dominoes, it is clearly possible to stack them at the edge of a table so that they hang over the edge of the table without falling. The fun fact is that one can stack them in such a way to make the overhang arbitrarily large, provided there are enough dominoes. 🙂