Fibonacci: It's as easy as 1, 1, 2, 3-Welcome
Welcome and Course Information
Fibonacci: It's as easy as 1, 1, 2, 3-The Fibonacci Numbers
The Fibonacci Sequence | Lecture 1
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Fibonacci Numbers with Negative Indices
The Lucas Numbers
The Fibonacci Sequence Redux | Lecture 2
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Neighbour Swapping
Fibonacci: It's as easy as 1, 1, 2, 3-The Golden Ratio
The Golden Ratio | Lecture 3
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Some Algebra Practice
Fibonacci Numbers and the Golden Ratio | Lecture 4
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Linearization of Powers of the Golden Ratio
Binet's Formula | Lecture 5
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Another Derivation of Binet's formula
Binet's Formula for the Lucas Numbers
Fibonacci: It's as easy as 1, 1, 2, 3-Supplemental Videos
Mathematical Induction
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Identities, sums and rectangles-The Fibonacci Bamboozlement
Do You Know Matrices?
The Fibonacci Q-matrix | Lecture 6
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The Fibonacci Addition Formula
The Fibonacci Double Index Formula
Do You Know Determinants?
Cassini's Identity | Lecture 7
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Proof of Cassini's Identity
Catalan's Identity
The Fibonacci Bamboozlement | Lecture 8
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Identities, sums and rectangles-Fibonacci Sums
Sum of Fibonacci Numbers | Lecture 9
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Sum of Lucas Numbers
Sums of Even and Odd Fibonacci Numbers
Sum of Fibonacci Numbers Squared | Lecture 10
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Sum of Lucas Numbers Squared
Identities, sums and rectangles-The Golden Rectangle
The Golden Rectangle | Lecture 11
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Spiraling Squares | Lecture 12
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Area of the Spiraling Squares
Identities, sums and rectangles-Supplemental Videos
Matrix Algebra: Addition and Multiplication
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Matrix Algebra: Determinants
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The most irrational number-Spirals
The Golden Spiral | Lecture 13
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The Eye of God
An Inner Golden Rectangle | Lecture 14
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Area of the Inner Golden Rectangle
The Fibonacci Spiral | Lecture 15
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The most irrational number-Fibonacci Numbers in Nature
Fibonacci Numbers in Nature | Lecture 16
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Continued Fractions | Lecture 17
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Continued Fractions for Square Roots
Continued Fraction for e
The Golden Ratio and the Ratio of Fibonacci Numbers
The Golden Angle | Lecture 18
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The Golden Angle and the Ratio of Fibonacci Numbers
A Simple Model for the Growth of a Sunflower | Lecture 19
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The most irrational number-Farewell
Concluding remarks
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Please Rate this Course
Acknowledgments