Acerca de este curso: 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

Para quién es esta clase: This course is suitable for anyone who loves mathematics, and should be accessible to those that remember their high school algebra.

Creada por: The Hong Kong University of Science and Technology

Enseñado por: Jeffrey R. Chasnov, Professor
Department of Mathematics

Nivel	Principiante
Idioma	Inglés (English)
Requerimientos de hardware	Pen, paper and the power of your brain.
Cómo aprobar	Aprueba todas las tareas calificadas para completar el curso.
Calificaciones del usuario	4.7 estrellas Calificación promedio del usuario 4.7Ve los que los estudiantes dijeron

Programa

SEMANA 1

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, 9 lecturas, 3 cuestionarios de práctica

Reading: Welcome and Course Information
Practice Quiz: Diagnostic Quiz
Reading: Get to Know Your Classmates
Vídeo: The Fibonacci Sequence
Reading: Fibonacci Numbers with Negative Indices
Reading: The Lucas Numbers
Vídeo: The Fibonacci Sequence Redux
Reading: Neighbour Swapping
Practice Quiz: The Fibonacci Numbers
Vídeo: The Golden Ratio
Reading: Some Algebra Practice
Vídeo: Fibonacci Numbers and the Golden Ratio
Reading: Linearization of Powers of the Golden Ratio
Vídeo: Binet's Formula
Reading: Another Derivation of Binet's formula
Reading: Binet's Formula for the Lucas Numbers
Practice Quiz: The Golden Ratio
Vídeo: Mathematical Induction
Discussion Prompt: Week One Discussion

Calificado: Week 1

SEMANA 2

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, 10 lecturas, 2 cuestionarios de práctica

Reading: Do You Know Matrices?
Reading: The Fibonacci Addition Formula
Reading: The Fibonacci Double Index Formula
Reading: Do You Know Determinants?
Vídeo: Cassini's Identity
Reading: Proof of Cassini's Identity
Reading: Catalan's Identity
Vídeo: The Fibonacci Bamboozlement
Practice Quiz: The Fibonacci Bamboozlement
Vídeo: Sum of Fibonacci Numbers
Reading: Sum of Lucas Numbers
Reading: Sums of Even and Odd Fibonacci Numbers
Vídeo: Sum of Fibonacci Numbers Squared
Reading: Sum of Lucas Numbers Squared
Practice Quiz: Fibonacci Sums
Vídeo: The Golden Rectangle
Vídeo: Spiraling Squares
Reading: Area of the Spiraling Squares
Vídeo: Matrix Algebra: Addition and Multiplication
Vídeo: Matrix Algebra: Determinants
Discussion Prompt: Week Two Discussion

Calificado: Week 2

SEMANA 3

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, 8 lecturas, 2 cuestionarios de práctica

Reading: The Eye of God
Vídeo: An Inner Golden Rectangle
Reading: Area of the Inner Golden Rectangle
Vídeo: The Fibonacci Spiral
Practice Quiz: Spirals
Vídeo: Fibonacci Numbers in Nature
Vídeo: Continued Fractions
Reading: Continued Fractions for Square Roots
Reading: Continued Fraction for e
Reading: The Golden Ratio and the Ratio of Fibonacci Numbers
Vídeo: The Golden Angle
Reading: The Golden Angle and the Ratio of Fibonacci Numbers
Vídeo: A Simple Model for the Growth of a Sunflower
Practice Quiz: Fibonacci Numbers in Nature
Discussion Prompt: Week Three Discussion
Vídeo: Concluding remarks
Reading: Please Rate this Course
Reading: Acknowledgments

Calificado: Week 3

Preguntas Frecuentes

¿Cuándo podré acceder a las lecciones y tareas?

¿Qué sucede si necesito más tiempo para completar el curso?

¿Qué recibiré si pago este curso?

¿Puedo tomar este curso de manera gratuita?

¿Cuál es la política de reembolsos?

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Cómo funciona

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Creadores

The Hong Kong University of Science and Technology

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Calificaciones y revisiones

Calificado 4.7 de 5 218 calificaciones

Really enjoyed the course. The instructor makes the material very interesting and explains the Fibonacci numbers and their different identities and uses very clearly and easy to understand. The course gave me a better understanding of the Fibonacci numbers and their applications than I previously had. The course also made me think the mathematics through thoroughly and carefully. Highly recommended.

Very interesting and well presented mathematics course. Amazing how many applications and relationships the Fibonacci Sequence has. Some of the formulas could have been explained in a little more detail as they were incredibly difficult to get my head around (I am an A-Level student).

This is a very good course to introduce Fibonacci numbers, their appearances in nature, and their fascinating properties. The instructor explains everything very well, and his overall speed of teaching is also quite flexible and aptly manged. The course can serve as a good one to introduce one to the idea of advanced mathematics, or to assist one to appreciate the intricate ways in which mathematics appears in the nature.