Fibonacci Numbers and the Golden Ratio
- Offered byCoursera
- Public/Government Institute
Fibonacci Numbers and the Golden Ratio at Coursera Overview
Duration | 10 hours |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Beginner |
Official Website | Explore Free Course  |
Credential | Certificate |
Fibonacci Numbers and the Golden Ratio at Coursera Highlights
- Shareable Certificate Earn a Certificate upon completion
- 100% online Start instantly and learn at your own schedule.
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Beginner Level High school mathematics
- Approx. 10 hours to complete
- English Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish
Fibonacci Numbers and the Golden Ratio at Coursera Course details
- Learn the mathematics behind the Fibonacci numbers, the golden ratio, and how they are related. These topics are not usually taught in a typical math curriculum, yet contain many fascinating results that are still accessible to an advanced high school student.
- The course culminates in an explanation of why the Fibonacci numbers appear unexpectedly in nature, such as the number of spirals in the head of a sunflower.
- Download the lecture notes:
- https://www.math.ust.hk/~machas/fibonacci.pdf
- Watch the promotional video:
- https://youtu.be/VWXeDFyB1hc
Fibonacci Numbers and the Golden Ratio at Coursera Curriculum
Fibonacci: It's as easy as 1, 1, 2, 3
Promotional Video
The Fibonacci Sequence
Lecture 1
The Fibonacci Sequence Redux
Lecture 2
The Golden Ratio
Lecture 3
Fibonacci Numbers and the Golden Ratio
Lecture 4
Binet's Formula
Lecture 5
Mathematical Induction
Welcome and Course Information
Fibonacci Numbers with Negative Indices
The Lucas Numbers
Neighbour Swapping
Some Algebra Practice
Linearization of Powers of the Golden Ratio
Another Derivation of Binet's formula
Binet's Formula for the Lucas Numbers
Diagnostic Quiz
The Fibonacci Numbers
The Golden Ratio
Week 1 Assessment
Identities, sums and rectangles
The Fibonacci Q-matrix
Lecture 6
Cassini's Identity
Lecture 7
The Fibonacci Bamboozlement
Lecture 8
Sum of Fibonacci Numbers
Lecture 9
Sum of Fibonacci Numbers Squared
Lecture 10
The Golden Rectangle
Lecture 11
Spiraling Squares
Lecture 12
Matrix Algebra: Addition and Multiplication
Matrix Algebra: Determinants
Do You Know Matrices?
The Fibonacci Addition Formula
The Fibonacci Double Index Formula
Do You Know Determinants?
Proof of Cassini's Identity
Catalan's Identity
Sum of Lucas Numbers
Sums of Even and Odd Fibonacci Numbers
Sum of Lucas Numbers Squared
Area of the Spiraling Squares
The Fibonacci Bamboozlement
Fibonacci Sums
Week 2 Assessment
The most irrational number
The Golden Spiral
Lecture 13
An Inner Golden Rectangle
Lecture 14
The Fibonacci Spiral
Lecture 15
Fibonacci Numbers in Nature
Lecture 16
Continued Fractions
Lecture 17
The Golden Angle
Lecture 18
A Simple Model for the Growth of a Sunflower
Lecture 19
Concluding remarks
The Eye of God
Area of the Inner Golden Rectangle
Continued Fractions for Square Roots
Continued Fraction for e
The Golden Ratio and the Ratio of Fibonacci Numbers
The Golden Angle and the Ratio of Fibonacci Numbers
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Acknowledgments
Spirals
Fibonacci Numbers in Nature
Week 3 Assessment
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