Despite the temptations of gold alluded to in Shakespeare’s verse above fromThe Merchant of Venice, the pursuit ofmathematical gold leads not to gilded tombs but to the paradise of the Elysian fields of ancient Greece. Our journey in this chapter takes us back to the days of Phidias (480–430 BC), a Greek sculptor and mathematician who is said to have helped with the design of the Parthenon. The approach in this chapter uses a simple artifice—the ratio of two line segments.

1. 1.

   The appearance of\(\sqrt {5}\) implies that𝜖^⋆ is irrational, see the proof on page 171.

2. 2.

   The Internet is replete with interesting historical facts dealing with this ratio.

3. 3.

   This sequence is termed the Lucas sequence and will be revisited later in the chapter, see equation (5.23).

4. 4.

   An alternative derivation is found in (10.14).

5. 5.

   Equation (5.11) also generated this sequence.

6. 6.

   Derivation of equation (5.27) is found in equation (10.13) and the values in the table found on page 137.

Authors and Affiliations

1. (Home address), Beverly, MA, USA

   Randolph Nelson

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