Search

We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the " ballot sequences ", variant to which Catalan numbers offer a solution. Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined. • Giovanni Rizzetti (1675–1751) probability scholar in the group of Jacopo Riccati. • The historical work of Igor Pak and the birth of Catalan numbers. • The denomination "Catalan numbers" (from Igor Pak). • Catalan numbers as a solution to a probability problem in a manuscript of Rizzetti. • Rizzetti's solution and the first calculation of Catalan numbers. [ABSTRACT FROM AUTHOR]

The article presents a study about cubic and quadratic formula. Knowledge of the quadratic formula is older than the Pythagorean Theorem. Solving a cubic equation, on the other hand, was the first major success story of Renaissance mathematics in Italy. The solution was first published by Girolamo Cardano in his book "Ars Magna." Like the quadratic formula, the cubic formula gives the exact number in closed form. Furthermore, the study gives a canonical form for the cubic formula that is relatively easy to remember.