# Fibonacci Numbers and the Golden Ratio

The Hong Kong University of Science and Technology

Embark on a captivating journey to unravel the secrets of the Fibonacci numbers and the golden ratio in this comprehensive course. Delve into the mathematical foundations of these intriguing topics and discover their unexpected presence in natural phenomena. From the Fibonacci sequence to the golden rectangle, you'll explore the profound implications of these concepts.

• Discover the origins and properties of the Fibonacci sequence
• Uncover the mystical allure of the golden ratio
• Explore Fibonacci identities, sums, and their relationship to rectangles
• Investigate the appearance of Fibonacci numbers in nature and continued fractions

With engaging lectures and thought-provoking assessments, this course offers a unique opportunity to expand your mathematical horizons and appreciate the enchanting beauty of these numerical phenomena.

Certificate Available ✔

##### Course Modules

Embark on a captivating journey to unravel the secrets of the Fibonacci numbers and the golden ratio in this comprehensive course. Delve into the mathematical foundations of these intriguing topics and discover their unexpected presence in natural phenomena.

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

Module 1 introduces the fundamental concepts of Fibonacci numbers and the golden ratio, providing a solid foundation for further exploration. From the basics of the Fibonacci sequence to Binet's formula, you'll gain a deep understanding of these mathematical phenomena.

#### Identities, sums and rectangles

Module 2 delves into the identities, sums, and rectangles associated with Fibonacci numbers, offering insights into their intricate relationships and properties. Explore topics such as Cassini's identity, Fibonacci sums, and the golden rectangle to uncover the fascinating connections within this numerical realm.

#### The most irrational number

Module 3 delves into the most irrational number, the golden ratio, and its presence in nature. Explore the golden spiral, continued fractions, and the appearance of Fibonacci numbers in natural phenomena. This module offers a captivating exploration of the real-world implications of these mathematical concepts.

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