About this Course

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Learner Career Outcomes

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started a new career after completing these courses

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Shareable Certificate
Earn a Certificate upon completion
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Flexible deadlines
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Beginner Level

High school mathematics

Approx. 9 hours to complete
English
Subtitles: English, Arabic

What you will learn

  • Fibonacci numbers

  • Golden ratio

  • Fibonacci identities and sums

  • Continued fractions

Skills you will gain

Recreational MathematicsDiscrete MathematicsElementary Mathematics

Learner Career Outcomes

50%

started a new career after completing these courses

14%

got a tangible career benefit from this course
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. 9 hours to complete
English
Subtitles: English, Arabic

Offered by

The Hong Kong University of Science and Technology logo

The Hong Kong University of Science and Technology

Syllabus - What you will learn from this course

Content RatingThumbs Up96%(1,842 ratings)Info
Week
1

Week 1

3 hours to complete

Fibonacci: It's as easy as 1, 1, 2, 3

3 hours to complete
7 videos (Total 55 min), 8 readings, 4 quizzes
7 videos
The Fibonacci Sequence | Lecture 18m
The Fibonacci Sequence Redux | Lecture 27m
The Golden Ratio | Lecture 38m
Fibonacci Numbers and the Golden Ratio | Lecture 46m
Binet's Formula | Lecture 510m
Mathematical Induction7m
8 readings
Welcome and Course Information1m
Fibonacci Numbers with Negative Indices5m
The Lucas Numbers5m
Neighbour Swapping10m
Some Algebra Practice10m
Linearization of Powers of the Golden Ratio10m
Another Derivation of Binet's formula10m
Binet's Formula for the Lucas Numbers10m
4 practice exercises
Diagnostic Quiz5m
The Fibonacci Numbers15m
The Golden Ratio15m
Week 1 Assessment30m
Week
2

Week 2

3 hours to complete

Identities, sums and rectangles

3 hours to complete
9 videos (Total 65 min), 10 readings, 3 quizzes
9 videos
Cassini's Identity | Lecture 78m
The Fibonacci Bamboozlement | Lecture 86m
Sum of Fibonacci Numbers | Lecture 98m
Sum of Fibonacci Numbers Squared | Lecture 107m
The Golden Rectangle | Lecture 115m
Spiraling Squares | Lecture 123m
Matrix Algebra: Addition and Multiplication5m
Matrix Algebra: Determinants7m
10 readings
Do You Know Matrices?
The Fibonacci Addition Formula10m
The Fibonacci Double Index Formula10m
Do You Know Determinants?
Proof of Cassini's Identity10m
Catalan's Identity10m
Sum of Lucas Numbers5m
Sums of Even and Odd Fibonacci Numbers5m
Sum of Lucas Numbers Squared5m
Area of the Spiraling Squares10m
3 practice exercises
The Fibonacci Bamboozlement15m
Fibonacci Sums15m
Week 2 Assessment30m
Week
3

Week 3

3 hours to complete

The most irrational number

3 hours to complete
8 videos (Total 61 min), 8 readings, 3 quizzes
8 videos
An Inner Golden Rectangle | Lecture 145m
The Fibonacci Spiral | Lecture 156m
Fibonacci Numbers in Nature | Lecture 164m
Continued Fractions | Lecture 1715m
The Golden Angle | Lecture 187m
A Simple Model for the Growth of a Sunflower | Lecture 198m
Concluding remarks4m
8 readings
The Eye of God10m
Area of the Inner Golden Rectangle10m
Continued Fractions for Square Roots10m
Continued Fraction for e10m
The Golden Ratio and the Ratio of Fibonacci Numbers10m
The Golden Angle and the Ratio of Fibonacci Numbers10m
Please Rate this Course1m
Acknowledgments
3 practice exercises
Spirals15m
Fibonacci Numbers in Nature15m
Week 3 Assessment30m

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