Fibonacci Numbers and the Golden Ratio
The Hong Kong University of Science and Technology
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.
About this Course
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.
What You'll Learn
- Fibonacci sequence and its relationship to the golden ratio
- Fibonacci Q-matrix, Cassini's identity, sums of Fibonacci numbers
- Golden rectangle, golden spiral, Fibonacci spiral
- Continued fractions, golden angle, the most irrational number, and the Fibonacci numbers in nature
Instructors
Jeffrey R. Chasnov
Department of Mathematics