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.
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Fibonacci Numbers and the Golden Ratio
香港科技大学课程信息
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初级
High school mathematics
完成时间大约为10 小时
英语（English）
字幕：阿拉伯语（Arabic）, 法语（French）, （欧洲人讲的）葡萄牙语, 意大利语, 越南语, 德语（German）, 俄语（Russian）, 英语（English）, 西班牙语（Spanish）
您将学到的内容有
Fibonacci numbers
Golden ratio
Fibonacci identities and sums
Continued fractions
您将获得的技能
- Recreational Mathematics
- Discrete Mathematics
- Elementary Mathematics
可灵活调整截止日期
根据您的日程表重置截止日期。
可分享的证书
完成后获得证书
100% 在线
立即开始，按照自己的计划学习。
初级
High school mathematics
完成时间大约为10 小时
英语（English）
字幕：阿拉伯语（Arabic）, 法语（French）, （欧洲人讲的）葡萄牙语, 意大利语, 越南语, 德语（German）, 俄语（Russian）, 英语（English）, 西班牙语（Spanish）
提供方
香港科技大学
HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world.
授课大纲 - 您将从这门课程中学到什么
完成时间为 3 小时
Fibonacci: It's as easy as 1, 1, 2, 3
We learn about the Fibonacci numbers, the golden ratio, and their relationship. We derive the celebrated Binet's formula, an explicit formula for the Fibonacci numbers in terms of powers of the golden ratio and its reciprical.
完成时间为 3 小时
7 个视频 （总计 55 分钟）, 8 个阅读材料, 4 个测验
完成时间为 3 小时
Identities, sums and rectangles
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.
完成时间为 3 小时
9 个视频 （总计 65 分钟）, 10 个阅读材料, 3 个测验
完成时间为 3 小时
The most irrational number
We learn about the golden spiral and the Fibonacci spiral. Because of the relationship between the Fibonacci numbers and the golden ratio, the Fibonacci spiral eventually converges to the golden spiral. You will recognise the Fibonacci spiral because it is the icon of our course. We next learn about continued fractions. To construct a continued fraction is to construct a sequence of rational numbers that converges to a target irrational number. The golden ratio is the irrational number whose continued fraction converges the slowest. We say that the golden ratio is the irrational number that is the most difficult to approximate by a rational number, or that the golden ratio is the most irrational of the irrational numbers. We then define the golden angle, related to the golden ratio, and use it to model the growth of a sunflower head. Use of the golden angle in the model allows a fine packing of the florets, and results in the unexpected appearance of the Fibonacci numbers in the sunflower.
完成时间为 3 小时
8 个视频 （总计 61 分钟）, 8 个阅读材料, 3 个测验
审阅
- 5 stars82.25%
- 4 stars15.25%
- 3 stars1.89%
- 2 stars0.49%
- 1 star0.09%
来自FIBONACCI NUMBERS AND THE GOLDEN RATIO的热门评论
由 BS 提供Aug 29, 2017
Very well designed. It was a lot of fun taking this course. It's the kind of course that can get you excited about higher mathematics. Sincere thanks to Prof. Chasnov and HKUST.
由 HR 提供Nov 7, 2021
The course looks at perfection level, clear and fun. The patience and the generosity of Professor Chesnov throughout the whole course are commendable.
由 CN 提供Feb 13, 2021
Very neat and well organized, all material at hand. I liked the skipped math bits that the others mentioned, so that I could myself engage in figuring out.
由 UB 提供Jun 5, 2018
This course blends the rational thinking of mathematics and the aesthetics of art in nature. Enjoyed it. Thanks Coursera and Hong Kong University of Science and Technology
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