Acerca de este Curso
4.7
213 ratings
77 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 % en línea

Comienza de inmediato y aprende a tu propio ritmo.
Calendar

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.
Beginner Level

Nivel principiante

Clock

Sugerido: 5 hours/week

Aprox. 8 horas para completar
Comment Dots

English

Subtítulos: English
Globe

Cursos 100 % en línea

Comienza de inmediato y aprende a tu propio ritmo.
Calendar

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.
Beginner Level

Nivel principiante

Clock

Sugerido: 5 hours/week

Aprox. 8 horas para completar
Comment Dots

English

Subtítulos: English

Programa - Qué aprenderás en este curso

1

Sección
Clock
3 horas para completar

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 videos (Total: 55 min), 9 readings, 4 quizzes
Video7 videos
The Fibonacci Sequence8m
The Fibonacci Sequence Redux7m
The Golden Ratio8m
Fibonacci Numbers and the Golden Ratio6m
Binet's Formula10m
Mathematical Induction7m
Reading9 lecturas
Welcome and Course Information10m
Get to Know Your Classmates10m
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
Quiz4 ejercicios de práctica
Diagnostic Quiz10m
The Fibonacci Numbers6m
The Golden Ratio6m
Week 120m

2

Sección
Clock
3 horas para completar

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 videos (Total: 65 min), 10 readings, 3 quizzes
Video9 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
Reading10 lecturas
Do You Know Matrices?10m
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
Quiz3 ejercicios de práctica
The Fibonacci Bamboozlement6m
Fibonacci Sums6m
Week 220m

3

Sección
Clock
3 horas para completar

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 videos (Total: 61 min), 8 readings, 3 quizzes
Video8 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
Reading8 lecturas
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
Quiz3 ejercicios de práctica
Spirals6m
Fibonacci Numbers in Nature6m
Week 320m
4.7

Principales revisiones

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.

Instructor

Jeffrey R. Chasnov

Professor
Department of Mathematics

Acerca de 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....

Preguntas Frecuentes

  • 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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