About this Course
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Flexible deadlines

Reset deadlines in accordance to your schedule.

Beginner Level

Approx. 11 hours to complete

Suggested: 7 hours/week...

English

Subtitles: English, Greek, Arabic
User
Learners taking this Course are
  • Artists
  • Technical Solutions Engineers
  • Medical Doctors
  • Entrepreneurs
  • Researchers

What you will learn

  • Check

    Fibonacci numbers

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    Golden ratio

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    Fibonacci identities and sums

  • Check

    Continued fractions

Skills you will gain

Elementary MathematicsDifference EquationsElementary AlgebraRecreational MathematicsDiscrete Mathematics
User
Learners taking this Course are
  • Artists
  • Technical Solutions Engineers
  • Medical Doctors
  • Entrepreneurs
  • Researchers

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Beginner Level

Approx. 11 hours to complete

Suggested: 7 hours/week...

English

Subtitles: English, Greek, Arabic

Syllabus - What you will learn from this course

Week
1
4 hours to complete

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

7 videos (Total 55 min), 9 readings, 4 quizzes
7 videos
The Fibonacci Sequence8m
The Fibonacci Sequence Redux7m
The Golden Ratio8m
Fibonacci Numbers and the Golden Ratio6m
Binet's Formula10m
Mathematical Induction7m
9 readings
Welcome and Course Information2m
Get to Know Your Classmates3m
Fibonacci Numbers with Negative Indices10m
The Lucas Numbers10m
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 Quiz10m
The Fibonacci Numbers15m
The Golden Ratio15m
Week 150m
Week
2
4 hours to complete

Identities, sums and rectangles

9 videos (Total 65 min), 10 readings, 3 quizzes
9 videos
Cassini's Identity8m
The Fibonacci Bamboozlement6m
Sum of Fibonacci Numbers8m
Sum of Fibonacci Numbers Squared7m
The Golden Rectangle5m
Spiraling Squares3m
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?10m
Proof of Cassini's Identity10m
Catalan's Identity10m
Sum of Lucas Numbers10m
Sums of Even and Odd Fibonacci Numbers10m
Sum of Lucas Numbers Squared10m
Area of the Spiraling Squares10m
3 practice exercises
The Fibonacci Bamboozlement15m
Fibonacci Sums15m
Week 250m
Week
3
4 hours to complete

The most irrational number

8 videos (Total 61 min), 8 readings, 3 quizzes
8 videos
An Inner Golden Rectangle5m
The Fibonacci Spiral6m
Fibonacci Numbers in Nature4m
Continued Fractions15m
The Golden Angle7m
A Simple Model for the Growth of a Sunflower8m
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 Course10m
Acknowledgments10m
3 practice exercises
Spirals15m
Fibonacci Numbers in Nature15m
Week 350m
4.8
103 ReviewsChevron Right

50%

started a new career after completing these courses

14%

got a tangible career benefit from this course

Top reviews from Fibonacci Numbers and the Golden Ratio

By NRAug 18th 2019

Excellent exposition of a fascinating subject.\n\nVery well organized, including a handout with the course material.\n\nMany thanks to Prof. Chasnov and the HKUST for this worthwhile opportunity!

By AKMar 23rd 2019

Absolutely loved the content discussed in this course! It was challenging but totally worth the effort. Seeing how numbers, patterns and functions pop up in nature was a real eye opener.

Instructor

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

About The Hong Kong University of Science and Technology

HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world....

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

More questions? Visit the Learner Help Center.