In 1224, Leonardo of Pisa, better known as Fibonacci, answered a mathematical challenge...

In 1224, Leonardo of Pisa, better known as Fibonacci, answered a mathematical challenge of John of Palermo in the presence of Emperor Frederick II: find a root of the equation x³ +2x² +10x = 20. He first showed that the equation had no rational roots and no Euclidean irrational root—that is, no root in any of the forms where a and b are rational numbers. He then approximated the only real root, probably using an algebraic technique of Omar Khayyam involving the intersection of a circle and a parabola. His answer was given in the base-60 number system as