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Fibonacci: It's as easy as 1, 1, 2, 3
By the end of this week, you will be able to: 1) describe the origin of the Fibonacci sequence; 2) describe the origin of the golden ratio; 3) find the relationship between the Fibonacci sequence and the golden ratio; 4) derive Binet’s formula.
Identities, sums and rectangles
By the end of this week, you will be able to: 1) identify the Fibonacci Q-matrix and derive Cassini’s identity; 2) explain the Fibonacci bamboozlement; 3) derive and prove the sum of the first n Fibonacci numbers, and the sum of the squares of the first n Fibonacci numbers; 4) construct a golden rectangle and 5) draw a figure with spiralling squares.
The most irrational number
By the end of this week, you will be able to: 1) describe the golden spiral and its relationship to the spiralling squares; 2) construct an inner golden rectangle; 3) explain continued fractions and be able to compute them; 4) explain why the golden ratio is called the most irrational of the irrational numbers; 5) understand why the golden ratio and the Fibonacci numbers may show up unexpectedly in nature.