# Book:Leonardo Fibonacci/Flos

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## Leonardo Fibonacci:

## Leonardo Fibonacci: *Flos*

Published $\text {1225}$.

### Subject Matter

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

### Contents

### 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