Book:Leonardo Fibonacci/Flos

Leonardo Fibonacci: Flos

Published $\text {1225}$

Subject Matter

• Three problems set by Johannes of Palermo for Fibonacci to solve.

Problem $1$

Find a rational number such that $5$ added to, or subtracted from, its square, is also a square.

Problem $2$

Solve the cubic:

$x^3 + 2 x^2 + 10 x = 20$

Problem $3$

$3$ men possess a pile of money, their shares being $\dfrac 1 2$, $\dfrac 1 3$ and $\dfrac 1 6$.

Each man takes some money from the pile until nothing is left.

The first man returns $\dfrac 1 2$ of what he took,

the second $\dfrac 1 3$

and the third $\dfrac 1 6$.

When the total so returned is divided equally among the men it is found that each then possess what he is entitled to.

How much money was in the original pile, and how much did each man take from the pile?

Historical Note

Leonardo Fibonacci relates in the prologue how he was invited to the court of Emperor Frederick $\text {II}$ of Sicily to compete in a mathematical tournament.

He solved all the problems presented to him by Johannes of Palermo.

The problems and their answers were published in Flos.

Some suggest that they were also published in Liber Quadratorum, but it has not been possible to corroborate this.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Liber Abaci