About this course: This is a course about the Fibonacci numbers, the golden ratio, and their intimate relationship. In this course, we learn the origin of the Fibonacci numbers and the golden ratio, and derive a formula to compute any Fibonacci number from powers of the golden ratio. We learn how to add a series of Fibonacci numbers and their squares, and unveil the mathematics behind a famous paradox called the Fibonacci bamboozlement. We construct a beautiful golden spiral and an even more beautiful Fibonacci spiral, and we learn why the Fibonacci numbers may appear unexpectedly in nature. The course lecture notes, problems, and professor's suggested solutions can be downloaded for free from http://bookboon.com/en/fibonacci-numbers-and-the-golden-ratio-ebook Course Overview video: https://youtu.be/GRthNC0_mrU

Who is this class for: This course is suitable for anyone who loves mathematics, and should be accessible to those that remember their high school algebra.

Created by: The Hong Kong University of Science and Technology

Taught by: Jeffrey R. Chasnov, Professor
Department of Mathematics

Level	Beginner
Language	English
Hardware Req	Pen, paper and the power of your brain.
How To Pass	Pass all graded assignments to complete the course.
User Ratings	4.8 stars Average User Rating 4.8See what learners said

Syllabus

WEEK 1

Dip your toes in the water

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, including derive Binet’s formula. Downlo...

7 videos, 1 reading, 1 practice quiz

Graded: Week 1

WEEK 2

Dive deeper

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 Fibo...

9 videos

Graded: Week 2

WEEK 3

Swim with the big fish

By the end of this week, you will be able to: 1) describe the golden spiral and its relationship to the spiraling squares; 2) construct an inner golden rectangle; 3) explain the continued fraction and be able to compute them; 4) explain why the golden ratio is...

8 videos, 1 practice quiz

Graded: Week 3

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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.

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Rated 4.8 out of 5 of 97 ratings