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.
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Fibonacci Numbers and the Golden Ratio
The Hong Kong University of Science and TechnologyÜber diesen Kurs
6.561 kürzliche Aufrufe
Flexible Fristen
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Zertifikat zur Vorlage
Erhalten Sie nach Abschluss ein Zertifikat
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Stufe „Anfänger“
High school mathematics
Ca. 10 Stunden zum Abschließen
Englisch
Untertitel: Arabischer Raum, Französisch, Portugiesisch (europäisch), Italienisch, Vietnamesisch, Deutsch, Russisch, Englisch, Spanisch
Was Sie lernen werden
Fibonacci numbers
Golden ratio
Fibonacci identities and sums
Continued fractions
Kompetenzen, die Sie erwerben
- Recreational Mathematics
- Discrete Mathematics
- Elementary Mathematics
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
Zertifikat zur Vorlage
Erhalten Sie nach Abschluss ein Zertifikat
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Stufe „Anfänger“
High school mathematics
Ca. 10 Stunden zum Abschließen
Englisch
Untertitel: Arabischer Raum, Französisch, Portugiesisch (europäisch), Italienisch, Vietnamesisch, Deutsch, Russisch, Englisch, Spanisch
von
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.
Lehrplan - Was Sie in diesem Kurs lernen werden
3 Stunden zum Abschließen
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.
3 Stunden zum Abschließen
7 Videos (Gesamt 55 min), 8 Lektüren, 4 Quiz
3 Stunden zum Abschließen
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.
3 Stunden zum Abschließen
9 Videos (Gesamt 65 min), 10 Lektüren, 3 Quiz
3 Stunden zum Abschließen
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.
3 Stunden zum Abschließen
8 Videos (Gesamt 61 min), 8 Lektüren, 3 Quiz
Bewertungen
- 5 stars82,25 %
- 4 stars15,25 %
- 3 stars1,89 %
- 2 stars0,49 %
- 1 star0,09 %
Top-Bewertungen von FIBONACCI NUMBERS AND THE GOLDEN RATIO
von BS24. Juni 2020
The course is concise, to the point and very interesting. Though it looks easy at first sight, without practice, you cannot complete it. Thank you, it was great fun.
von AR13. Jan. 2021
Very interesting. Much more math heavy than I was expecting, and would very hard to follow if you don't have at least first year university maths.
von UB5. Juni 2018
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
von BS29. Aug. 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.
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