A picture is worth a thousand words.

–A Chinese proverb

In the previous chapter, we encountered numerous Fibonacci and Lucas identities, and summation formulas. In this chapter, we add a geometric dimension to some of them, and to some new ones, by illustrating them pictorially.

To begin with, consider the identities

6.2

These can be confirmed easily; see Exercises 6.1 through 6.4. We can obtain their Lucas counterparts by changing to . The techniques work for any sequence that satisfies the Fibonacci recurrence, but always adjust the least value as required.

## 6.1 GEOMETRIC ILLUSTRATIONS

Interestingly, we can illustrate geometrically these Fibonacci identities (and hence their Lucas counterparts), as Br. A. Brousseau did, among others, ...

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