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
Related Topics for further study
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
IntermediateCourse 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
- Please Rate this Course
- Spirals
- Fibonacci Numbers in Nature
- Week 3 Assessment
Jeffrey R. Chasnov
4.8 Raiting
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