Sum of Fibonacci Numbers | Lecture 9 - Fibonacci Numbers and the Golden Ratio

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Sum of Fibonacci Numbers | Lecture 9 - Fibonacci Numbers and the Golden Ratio

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.

The course culminates in an explanation of why the Fibonacci numbers appear unexpectedly in nature, such as the number of spirals in the head of a sunflower.
Recreational Mathematics, Discrete Mathematics, Elementary Mathematics
Great course concept for about one of the most intriguing concepts in the mathematical world, however I found it on the difficult side especially for those who find math as a challenging topic.,Absolutely loved the content discussed in this course! It was challenging but totally worth the effort. Seeing how numbers, patterns and functions pop up in nature was a real eye opener.
We learn about the Fibonacci Q-matrix and Cassini's identity. Cassini's identity is the basis for a famous dissection fallacy colourfully named the Fibonacci bamboozlement. A dissection fallacy is an apparent paradox arising from two arrangements of different area from one set of puzzle pieces. We also derive formulas for the sum of the first n Fibonacci numbers, and the sum of the first n Fibonacci numbers squared. Finally, we show how to construct a golden rectangle, and how this leads to the beautiful image of spiralling squares.
Sum of Fibonacci Numbers | Lecture 9 - Fibonacci Numbers and the Golden Ratio
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