Informações sobre o curso
4.8
207 ratings
74 reviews
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...
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cursos 100% online

Comece imediatamente e aprenda em seu próprio cronograma.
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Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Beginner Level

Nível iniciante

Clock

Sugerido: 5 hours/week

Aprox. 8 horas restantes
Comment Dots

English

Legendas: English
Globe

cursos 100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Calendar

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Beginner Level

Nível iniciante

Clock

Sugerido: 5 hours/week

Aprox. 8 horas restantes
Comment Dots

English

Legendas: English

Programa - O que você aprenderá com este curso

1

Seção
Clock
3 horas para concluir

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

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; 4) derive Binet’s formula. ...
Reading
7 vídeos (Total de 55 min), 9 leituras, 4 testes
Video7 videos
The Fibonacci Sequence8min
The Fibonacci Sequence Redux7min
The Golden Ratio8min
Fibonacci Numbers and the Golden Ratio6min
Binet's Formula10min
Mathematical Induction7min
Reading9 leituras
Welcome and Course Information10min
Get to Know Your Classmates10min
Fibonacci Numbers with Negative Indices10min
The Lucas Numbers10min
Neighbour Swapping10min
Some Algebra Practice10min
Linearization of Powers of the Golden Ratio10min
Another Derivation of Binet's formula10min
Binet's Formula for the Lucas Numbers10min
Quiz4 exercícios práticos
Diagnostic Quiz10min
The Fibonacci Numbers6min
The Golden Ratio6min
Week 120min

2

Seção
Clock
3 horas para concluir

Identities, sums and rectangles

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 Fibonacci numbers; 4) construct a golden rectangle and 5) draw a figure with spiralling squares. ...
Reading
9 vídeos (Total de 65 min), 10 leituras, 3 testes
Video9 videos
Cassini's Identity8min
The Fibonacci Bamboozlement6min
Sum of Fibonacci Numbers8min
Sum of Fibonacci Numbers Squared7min
The Golden Rectangle5min
Spiraling Squares3min
Matrix Algebra: Addition and Multiplication5min
Matrix Algebra: Determinants7min
Reading10 leituras
Do You Know Matrices?10min
The Fibonacci Addition Formula10min
The Fibonacci Double Index Formula10min
Do You Know Determinants?10min
Proof of Cassini's Identity10min
Catalan's Identity10min
Sum of Lucas Numbers10min
Sums of Even and Odd Fibonacci Numbers10min
Sum of Lucas Numbers Squared10min
Area of the Spiraling Squares10min
Quiz3 exercícios práticos
The Fibonacci Bamboozlement6min
Fibonacci Sums6min
Week 220min

3

Seção
Clock
3 horas para concluir

The most irrational number

By the end of this week, you will be able to: 1) describe the golden spiral and its relationship to the spiralling squares; 2) construct an inner golden rectangle; 3) explain continued fractions and be able to compute them; 4) explain why the golden ratio is called the most irrational of the irrational numbers; 5) understand why the golden ratio and the Fibonacci numbers may show up unexpectedly in nature. ...
Reading
8 vídeos (Total de 61 min), 8 leituras, 3 testes
Video8 videos
An Inner Golden Rectangle5min
The Fibonacci Spiral6min
Fibonacci Numbers in Nature4min
Continued Fractions15min
The Golden Angle7min
A Simple Model for the Growth of a Sunflower8min
Concluding remarks4min
Reading8 leituras
The Eye of God10min
Area of the Inner Golden Rectangle10min
Continued Fractions for Square Roots10min
Continued Fraction for e10min
The Golden Ratio and the Ratio of Fibonacci Numbers10min
The Golden Angle and the Ratio of Fibonacci Numbers10min
Please Rate this Course10min
Acknowledgments10min
Quiz3 exercícios práticos
Spirals6min
Fibonacci Numbers in Nature6min
Week 320min
4.8

Melhores avaliações

por GMMar 16th 2017

Finally I studied the Fibonacci sequence and the golden spiral. I used to say: one day I will.\n\nVery interesting course and made simple by the teacher in spite of the challenging topics

por BSAug 30th 2017

Very well designed. It was a lot of fun taking this course. It's the kind of course that can get you excited about higher mathematics. Sincere thanks to Prof. Chasnov and HKUST.

Instrutores

Jeffrey R. Chasnov

Professor
Department of Mathematics

Sobre 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....

Perguntas Frequentes – FAQ

  • 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.

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