Learn the mathematics behind the Fibonacci numbers, the golden ratio, and how they are related. These topics are not usually taught in a typical math curriculum, yet contain many fascinating results that are still accessible to an advanced high school student.
Offert par
Fibonacci Numbers and the Golden Ratio
Université des sciences et technologies de Hong KongÀ propos de ce cours
12 453 consultations récentes
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Certificat partageable
Obtenez un Certificat lorsque vous terminez
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Niveau débutant
High school mathematics
Approx. 10Â heures pour terminer
Anglais
Sous-titres : Arabe, Français, Portugais (européen), Italien, Vietnamien, Allemand, Russe, Anglais, Espagnol
Ce que vous allez apprendre
Fibonacci numbers
Golden ratio
Fibonacci identities and sums
Continued fractions
Compétences que vous acquerrez
- Recreational Mathematics
- Discrete Mathematics
- Elementary Mathematics
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Certificat partageable
Obtenez un Certificat lorsque vous terminez
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Niveau débutant
High school mathematics
Approx. 10Â heures pour terminer
Anglais
Sous-titres : Arabe, Français, Portugais (européen), Italien, Vietnamien, Allemand, Russe, Anglais, Espagnol
Offert par
Université des sciences et technologies de Hong Kong
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.
Programme de cours : ce que vous apprendrez dans ce cours
3Â heures pour terminer
Fibonacci: It's as easy as 1, 1, 2, 3
We learn about the Fibonacci numbers, the golden ratio, and their relationship. We derive the celebrated Binet's formula, an explicit formula for the Fibonacci numbers in terms of powers of the golden ratio and its reciprical.
3Â heures pour terminer
7 vidéos (Total 55 min), 8 lectures, 4 quiz
3Â heures pour terminer
Identities, sums and rectangles
We learn about the Fibonacci Q-matrix and Cassini's identity. Cassini's identity is the basis for a famous dissection fallacy colourfully named the Fibonacci bamboozlement. A dissection fallacy is an apparent paradox arising from two arrangements of different area from one set of puzzle pieces. We also derive formulas for the sum of the first n Fibonacci numbers, and the sum of the first n Fibonacci numbers squared. Finally, we show how to construct a golden rectangle, and how this leads to the beautiful image of spiralling squares.
3Â heures pour terminer
9 vidéos (Total 65 min), 10 lectures, 3 quiz
3Â heures pour terminer
The most irrational number
We learn about the golden spiral and the Fibonacci spiral. Because of the relationship between the Fibonacci numbers and the golden ratio, the Fibonacci spiral eventually converges to the golden spiral. You will recognise the Fibonacci spiral because it is the icon of our course. We next learn about continued fractions. To construct a continued fraction is to construct a sequence of rational numbers that converges to a target irrational number. The golden ratio is the irrational number whose continued fraction converges the slowest. We say that the golden ratio is the irrational number that is the most difficult to approximate by a rational number, or that the golden ratio is the most irrational of the irrational numbers. We then define the golden angle, related to the golden ratio, and use it to model the growth of a sunflower head. Use of the golden angle in the model allows a fine packing of the florets, and results in the unexpected appearance of the Fibonacci numbers in the sunflower.
3Â heures pour terminer
8 vidéos (Total 61 min), 8 lectures, 3 quiz
Avis
- 5 stars82,48Â %
- 4 stars15,06Â %
- 3 stars1,85Â %
- 2 stars0,48Â %
- 1 star0,09Â %
Meilleurs avis pour FIBONACCI NUMBERS AND THE GOLDEN RATIO
par MH12 juil. 2020
It was a wonderful experience. I have learnt a lot more about Fibonacci numbers and the golden ratio during this course. I urge the professor to create more and more courses like this.
par JR12 juil. 2020
Someone has said that God created the integers; all the rest is the work of man. After seeing how the Fibonacci numbers play out in nature, I am not so sure about that. A very enjoyable course.
par DL28 sept. 2019
I really enjoyed this class. The video lectures were clear and fascinating, and the math assignments were well-chosen and reinforced learning of the material presented in the lectures.
par BS29 août 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.
Foire Aux Questions
Quand aurai-je accès aux vidéos de cours et aux devoirs ?
À quoi ai-je droit si j'achète le Certificat ?
Une aide financière est-elle possible ?
D'autres questions ? Visitez le Centre d'Aide pour les Étudiants.
