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Fibonacci Numbers and the Golden Ratio

Approx. 10 hours to complete

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Course Summary

Explore the fascinating world of Fibonacci numbers and the golden ratio in this course. Learn about the history, applications, and mathematical properties of these famous sequences.

Key Learning Points

Discover the origins and history of Fibonacci numbers and the golden ratio
Understand the mathematical properties and applications of these sequences
Explore the connection between Fibonacci numbers and nature, art, and music

Job Positions & Salaries of people who have taken this course might have

- USA: $105,030
- USA: $105,030
- USA: $62,453
- USA: $105,030
- USA: $62,453
- USA: $58,614

Learning Outcomes

Understand the history and origins of Fibonacci numbers and the golden ratio
Apply mathematical properties of these sequences to real-world problems
Identify the connection between Fibonacci numbers and nature, art, and music

Prerequisites or good to have knowledge before taking this course

Basic understanding of algebra and geometry
Familiarity with mathematical notation

Course Difficulty Level

Intermediate

Course Format

Self-paced
Online
Video lectures

Similar Courses

Number Theory and Cryptography
Discrete Mathematics

Related Education Paths

Notable People in This Field

Professor of Science and Technology Studies
Astrophysicist and Author

Related Books

Description

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.

Knowledge

Fibonacci numbers
Golden ratio
Fibonacci identities and sums
Continued fractions

Outline

Fibonacci: It's as easy as 1, 1, 2, 3
Promotional Video
The Fibonacci Sequence | Lecture 1
The Fibonacci Sequence Redux | Lecture 2
The Golden Ratio | Lecture 3
Fibonacci Numbers and the Golden Ratio | Lecture 4
Binet's Formula | Lecture 5
Mathematical Induction
Welcome and Course Information
Fibonacci Numbers with Negative Indices
The Lucas Numbers
Neighbour Swapping
Some Algebra Practice
Linearization of Powers of the Golden Ratio
Another Derivation of Binet's formula
Binet's Formula for the Lucas Numbers
Diagnostic Quiz
The Fibonacci Numbers
The Golden Ratio
Week 1 Assessment

Identities, sums and rectangles
The Fibonacci Q-matrix | Lecture 6
Cassini's Identity | Lecture 7
The Fibonacci Bamboozlement | Lecture 8
Sum of Fibonacci Numbers | Lecture 9
Sum of Fibonacci Numbers Squared | Lecture 10
The Golden Rectangle | Lecture 11
Spiraling Squares | Lecture 12
Matrix Algebra: Addition and Multiplication
Matrix Algebra: Determinants
The Fibonacci Addition Formula
The Fibonacci Double Index Formula
Proof of Cassini's Identity
Catalan's Identity
Sum of Lucas Numbers
Sums of Even and Odd Fibonacci Numbers
Sum of Lucas Numbers Squared
Area of the Spiraling Squares
The Fibonacci Bamboozlement
Fibonacci Sums
Week 2 Assessment

The most irrational number
The Golden Spiral | Lecture 13
An Inner Golden Rectangle | Lecture 14
The Fibonacci Spiral | Lecture 15
Fibonacci Numbers in Nature | Lecture 16
Continued Fractions | Lecture 17
The Golden Angle | Lecture 18
A Simple Model for the Growth of a Sunflower | Lecture 19
Concluding remarks
The Eye of God
Area of the Inner Golden Rectangle
Continued Fractions for Square Roots
Continued Fraction for e
The Golden Ratio and the Ratio of Fibonacci Numbers
The Golden Angle and the Ratio of Fibonacci Numbers
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Spirals
Fibonacci Numbers in Nature
Week 3 Assessment

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