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ADDITIONAL FIBONACCI AND LUCAS OCCURRENCES

A thing of beauty is a joy forever:

Its loveliness increases; it will never

Pass into nothingness.

–John Keats (1795–1821)

Fibonacci and Lucas numbers appear in many other unexpected places. For example, index cards come in size c04-math-001 or c04-math-002; most rugs come in five different sizes: c04-math-003, c04-math-004, c04-math-005, c04-math-006, or c04-math-007. In the first two cases, the dimensions are adjacent Fibonacci numbers; in the third and fourth cases, the ratio 4:6 = 6:9 = 2:3, a Fibonacci ratio; and in the last case, 9:12 = 3:4, the ratio of two adjacent Lucas numbers. We will study such ratios in Chapter 16.

4.1 FIBONACCI OCCURRENCES

Before turning to our first example, we will make a few formal definitions. ...

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