Acerca de este Curso
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Nivel principiante

Aprox. 11 horas para completar

Sugerido: 7 hours/week...

Inglés (English)

Subtítulos: Inglés (English)

100 % en línea

Comienza de inmediato y aprende a tu propio ritmo.

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.

Nivel principiante

Aprox. 11 horas para completar

Sugerido: 7 hours/week...

Inglés (English)

Subtítulos: Inglés (English)

Programa - Qué aprenderás en este curso

Semana
1
4 horas para completar

Fibonacci: It's as easy as 1, 1, 2, 3

In this week's lectures, we learn about the Fibonacci numbers, the golden ratio, and their relationship. We conclude the week by deriving the celebrated Binet's formula, an explicit formula for the Fibonacci numbers in terms of powers of the golden ratio and its reciprical.

...
7 videos (Total 55 minutos), 9 readings, 4 quizzes
7 videos
The Fibonacci Sequence8m
The Fibonacci Sequence Redux7m
The Golden Ratio8m
Fibonacci Numbers and the Golden Ratio6m
Binet's Formula10m
Mathematical Induction7m
9 lecturas
Welcome and Course Information2m
Get to Know Your Classmates3m
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
4 ejercicios de práctica
Diagnostic Quiz10m
The Fibonacci Numbers15m
The Golden Ratio15m
Week 150m
Semana
2
4 horas para completar

Identities, sums and rectangles

In this week's lectures, 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.

...
9 videos (Total 65 minutos), 10 readings, 3 quizzes
9 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
10 lecturas
Do You Know Matrices?
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
3 ejercicios de práctica
The Fibonacci Bamboozlement15m
Fibonacci Sums15m
Week 250m
Semana
3
4 horas para completar

The most irrational number

In this week's lectures, 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 head of a sunflower.

...
8 videos (Total 61 minutos), 8 readings, 3 quizzes
8 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
8 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
3 ejercicios de práctica
Spirals15m
Fibonacci Numbers in Nature15m
Week 350m
4.7
88 revisionesChevron Right

50%

comenzó una nueva carrera después de completar estos cursos

17%

consiguió un beneficio tangible en su carrera profesional gracias a este curso

Principales revisiones sobre Fibonacci Numbers and the Golden Ratio

por AKMar 23rd 2019

Absolutely loved the content discussed in this course! It was challenging but totally worth the effort. Seeing how numbers, patterns and functions pop up in nature was a real eye opener.

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.

Instructores

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

Acerca de 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....

Preguntas Frecuentes

  • Una vez que te inscribes para obtener un Certificado, tendrás acceso a todos los videos, cuestionarios y tareas de programación (si corresponde). Las tareas calificadas por compañeros solo pueden enviarse y revisarse una vez que haya comenzado tu sesión. Si eliges explorar el curso sin comprarlo, es posible que no puedas acceder a determinadas tareas.

  • Cuando compras un Certificado, obtienes acceso a todos los materiales del curso, incluidas las tareas calificadas. Una vez que completes el curso, se añadirá tu Certificado electrónico a la página Logros. Desde allí, puedes imprimir tu Certificado o añadirlo a tu perfil de LinkedIn. Si solo quieres leer y visualizar el contenido del curso, puedes participar del curso como oyente sin costo.

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