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.
ofrecido por
Fibonacci Numbers and the Golden Ratio
Universidad Científica y Tecnológica de Hong KongAcerca de este Curso
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Fechas límite flexibles
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Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
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Nivel principiante
High school mathematics
Aprox. 10 horas para completar
Inglés (English)
Subtítulos: Árabe (Arabic), Francés (French), Portugués (europeo), Italiano, Vietnamita, Alemán (German), Ruso (Russian), Inglés (English), Español (Spanish)
Qué aprenderás
Fibonacci numbers
Golden ratio
Fibonacci identities and sums
Continued fractions
Habilidades que obtendrás
- Recreational Mathematics
- Discrete Mathematics
- Elementary Mathematics
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Nivel principiante
High school mathematics
Aprox. 10 horas para completar
Inglés (English)
Subtítulos: Árabe (Arabic), Francés (French), Portugués (europeo), Italiano, Vietnamita, Alemán (German), Ruso (Russian), Inglés (English), Español (Spanish)
ofrecido por
Universidad Científica y Tecnológica 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.
Programa - Qué aprenderás en este curso
3 horas para completar
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 horas para completar
7 videos (Total 55 minutos), 8 lecturas, 4 cuestionarios
3 horas para completar
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 horas para completar
9 videos (Total 65 minutos), 10 lecturas, 3 cuestionarios
3 horas para completar
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 horas para completar
8 videos (Total 61 minutos), 8 lecturas, 3 cuestionarios
Reseñas
- 5 stars82,52 %
- 4 stars15,05 %
- 3 stars1,83 %
- 2 stars0,48 %
- 1 star0,09 %
Principales reseñas sobre FIBONACCI NUMBERS AND THE GOLDEN RATIO
por TP24 de jul. de 2020
These kind of courses are always interesting, where the world is full of mathematical calculations and hope to see more videos on nature and maths
por JR12 de jul. de 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.
por UB5 de jun. de 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
por CN13 de feb. de 2021
Very neat and well organized, all material at hand. I liked the skipped math bits that the others mentioned, so that I could myself engage in figuring out.
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