Об этом курсе: 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
Для кого этот курс: This course is suitable for anyone who loves mathematics, and should be accessible to those that remember their high school algebra.
Автор: The Hong Kong University of Science and Technology
Преподаватели: Jeffrey R. Chasnov, Professor
Department of Mathematics
| Уровень | Начинающий |
| Язык | English |
| Требования к аппаратным средствам | Pen, paper and the power of your brain. |
| Как пройти курс | Чтобы пройти курс, выполните все оцениваемые задания. |
| Оценки пользователей |
Программа курса
НЕДЕЛЯ 1
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.
7 видео, 9 материала для самостоятельного изучения, 3 тренировочных теста
- Reading: Welcome and Course Information
- Practice Quiz: Diagnostic Quiz
- Reading: Get to Know Your Classmates
- Видео: The Fibonacci Sequence
- Reading: Fibonacci Numbers with Negative Indices
- Reading: The Lucas Numbers
- Видео: The Fibonacci Sequence Redux
- Reading: Neighbour Swapping
- Practice Quiz: The Fibonacci Numbers
- Видео: The Golden Ratio
- Reading: Some Algebra Practice
- Видео: Fibonacci Numbers and the Golden Ratio
- Reading: Linearization of Powers of the Golden Ratio
- Видео: Binet's Formula
- Reading: Another Derivation of Binet's formula
- Reading: Binet's Formula for the Lucas Numbers
- Practice Quiz: The Golden Ratio
- Видео: Mathematical Induction
Оцениваемый: Week 1
НЕДЕЛЯ 2
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.
9 видео, 10 материала для самостоятельного изучения, 2 тренировочных теста
- Reading: Do You Know Matrices?
- Reading: The Fibonacci Addition Formula
- Reading: The Fibonacci Double Index Formula
- Reading: Do You Know Determinants?
- Видео: Cassini's Identity
- Reading: Proof of Cassini's Identity
- Reading: Catalan's Identity
- Видео: The Fibonacci Bamboozlement
- Practice Quiz: The Fibonacci Bamboozlement
- Видео: Sum of Fibonacci Numbers
- Reading: Sum of Lucas Numbers
- Reading: Sums of Even and Odd Fibonacci Numbers
- Видео: Sum of Fibonacci Numbers Squared
- Reading: Sum of Lucas Numbers Squared
- Practice Quiz: Fibonacci Sums
- Видео: The Golden Rectangle
- Видео: Spiraling Squares
- Reading: Area of the Spiraling Squares
- Видео: Matrix Algebra: Addition and Multiplication
- Видео: Matrix Algebra: Determinants
Оцениваемый: Week 2
НЕДЕЛЯ 3
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.
8 видео, 8 материала для самостоятельного изучения, 2 тренировочных теста
- Reading: The Eye of God
- Видео: An Inner Golden Rectangle
- Reading: Area of the Inner Golden Rectangle
- Видео: The Fibonacci Spiral
- Practice Quiz: Spirals
- Видео: Fibonacci Numbers in Nature
- Видео: Continued Fractions
- Reading: Continued Fractions for Square Roots
- Reading: Continued Fraction for e
- Reading: The Golden Ratio and the Ratio of Fibonacci Numbers
- Видео: The Golden Angle
- Reading: The Golden Angle and the Ratio of Fibonacci Numbers
- Видео: A Simple Model for the Growth of a Sunflower
- Practice Quiz: Fibonacci Numbers in Nature
- Видео: Concluding remarks
- Reading: Please Rate this Course
- Reading: Acknowledgments
Оцениваемый: Week 3
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Авторы
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.
Рейтинги и отзывы
Very clear exposition, interesting and fun. Accessible to anyone interested in maths and patterns.
Good explanation, Good example
This course blends the rational thinking of mathematics and the aesthetics of art in nature. Enjoyed it. Thanks Coursera and Hong Kong University of Science and Technology
Coursera делает лучшее в мире образование доступным каждому, предлагая онлайн-курсы от ведущих университетов и организаций.
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C
It was very useful to enhance my knowledge of Golden ration. A very good delivery by Professor Jasnov.