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Fibonacci Numbers and the Golden Ratio
  • Level Foundation
  • المدة 9 ساعات hours
  • الطبع بواسطة The Hong Kong University of Science and Technology
  • Offered by

عن

Learn the mathematics behind the Fibonacci numbers, the golden ratio, and their relationship to each other. These topics may not be taught as part of a typical math curriculum, but they contain many fascinating results that are still accessible to an advanced high school student. The course culminates in an exploration of the Fibonacci numbers appearing unexpectedly in nature, such as the number of spirals in the head of a sunflower. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/fibonacci.pdf Watch the promotional video: https://youtu.be/VWXeDFyB1hc

الوحدات

Welcome

    • 1 Readings
    • 1 Quiz
Show info about module content

1 Readings

  • Welcome and Course Information

1 Quiz

  • Diagnostic Quiz

The Fibonacci Numbers

    • 2 Videos
    • 3 Readings
    • 1 Quiz
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2 Videos

  • The Fibonacci Sequence | Lecture 1
  • The Fibonacci Sequence Redux | Lecture 2

3 Readings

  • Fibonacci Numbers with Negative Indices
  • The Lucas Numbers
  • Neighbour Swapping

1 Quiz

  • The Fibonacci Numbers

The Golden Ratio

    • 3 Videos
    • 4 Readings
    • 1 Quiz
Show info about module content

3 Videos

  • The Golden Ratio | Lecture 3
  • Fibonacci Numbers and the Golden Ratio | Lecture 4
  • Binet's Formula | Lecture 5

4 Readings

  • Some Algebra Practice
  • Linearization of Powers of the Golden Ratio
  • Another Derivation of Binet's formula
  • Binet's Formula for the Lucas Numbers

1 Quiz

  • The Golden Ratio

Supplemental Videos

    • 1 Videos
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1 Videos

  • Mathematical Induction

Quiz

    • 1 Quiz
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1 Quiz

  • Week 1 Assessment

The Fibonacci Bamboozlement

    • 3 Videos
    • 6 Readings
    • 1 Quiz
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3 Videos

  • The Fibonacci Q-matrix | Lecture 6
  • Cassini's Identity | Lecture 7
  • The Fibonacci Bamboozlement | Lecture 8

6 Readings

  • Do You Know Matrices?
  • The Fibonacci Addition Formula
  • The Fibonacci Double Index Formula
  • Do You Know Determinants?
  • Proof of Cassini's Identity
  • Catalan's Identity

1 Quiz

  • The Fibonacci Bamboozlement

Fibonacci Sums

    • 2 Videos
    • 3 Readings
    • 1 Quiz
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2 Videos

  • Sum of Fibonacci Numbers | Lecture 9
  • Sum of Fibonacci Numbers Squared | Lecture 10

3 Readings

  • Sum of Lucas Numbers
  • Sums of Even and Odd Fibonacci Numbers
  • Sum of Lucas Numbers Squared

1 Quiz

  • Fibonacci Sums

The Golden Rectangle

    • 2 Videos
    • 1 Readings
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2 Videos

  • The Golden Rectangle | Lecture 11
  • Spiraling Squares | Lecture 12

1 Readings

  • Area of the Spiraling Squares

Supplemental Videos

    • 2 Videos
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2 Videos

  • Matrix Algebra: Addition and Multiplication
  • Matrix Algebra: Determinants

Quiz

    • 1 Quiz
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1 Quiz

  • Week 2 Assessment

Spirals

    • 3 Videos
    • 2 Readings
    • 1 Quiz
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3 Videos

  • The Golden Spiral | Lecture 13
  • An Inner Golden Rectangle | Lecture 14
  • The Fibonacci Spiral | Lecture 15

2 Readings

  • The Eye of God
  • Area of the Inner Golden Rectangle

1 Quiz

  • Spirals

Fibonacci Numbers in Nature

    • 4 Videos
    • 4 Readings
    • 1 Quiz
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4 Videos

  • 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

4 Readings

  • 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

1 Quiz

  • Fibonacci Numbers in Nature

Quiz

    • 1 Quiz
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1 Quiz

  • Week 3 Assessment

Farewell

    • 1 Videos
    • 2 Readings
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1 Videos

  • Concluding remarks

2 Readings

  • Please Rate this Course
  • Acknowledgments

Auto Summary

Discover the intriguing mathematics of Fibonacci numbers and the golden ratio with Coursera's "Fibonacci Numbers and the Golden Ratio." This foundational course, suitable for advanced high school students, delves into their fascinating relationships and unexpected appearances in nature. With a duration of 540 minutes, learners can subscribe with a Starter plan. Join now to explore these captivating mathematical concepts with expert guidance.

Jeffrey R. Chasnov
Instructor

Jeffrey R. Chasnov