课程信息
4.7
224 个评分
79 个审阅
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立即开始,按照自己的计划学习。
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初级

初级

完成时间(小时)

完成时间大约为8 小时

建议:6 hours/week...
可选语言

英语(English)

字幕:英语(English)
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
初级

初级

完成时间(小时)

完成时间大约为8 小时

建议:6 hours/week...
可选语言

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 3 小时

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

In this week's lectures, we learn about the Fibonacci numbers, the golden ratio, and their relationship. We conclude the week by deriving the celebrated Binet's formula, an explicit formula for the Fibonacci numbers in terms of powers of the golden ratio and its reciprical. ...
Reading
7 个视频 (总计 55 分钟), 9 个阅读材料, 4 个测验
Video7 个视频
The Fibonacci Sequence8分钟
The Fibonacci Sequence Redux7分钟
The Golden Ratio8分钟
Fibonacci Numbers and the Golden Ratio6分钟
Binet's Formula10分钟
Mathematical Induction7分钟
Reading9 个阅读材料
Welcome and Course Information10分钟
Get to Know Your Classmates10分钟
Fibonacci Numbers with Negative Indices10分钟
The Lucas Numbers10分钟
Neighbour Swapping10分钟
Some Algebra Practice10分钟
Linearization of Powers of the Golden Ratio10分钟
Another Derivation of Binet's formula10分钟
Binet's Formula for the Lucas Numbers10分钟
Quiz4 个练习
Diagnostic Quiz10分钟
The Fibonacci Numbers6分钟
The Golden Ratio6分钟
Week 120分钟
2
完成时间(小时)
完成时间为 3 小时

Identities, sums and rectangles

In this week's lectures, 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. ...
Reading
9 个视频 (总计 65 分钟), 10 个阅读材料, 3 个测验
Video9 个视频
Cassini's Identity8分钟
The Fibonacci Bamboozlement6分钟
Sum of Fibonacci Numbers8分钟
Sum of Fibonacci Numbers Squared7分钟
The Golden Rectangle5分钟
Spiraling Squares3分钟
Matrix Algebra: Addition and Multiplication5分钟
Matrix Algebra: Determinants7分钟
Reading10 个阅读材料
Do You Know Matrices?10分钟
The Fibonacci Addition Formula10分钟
The Fibonacci Double Index Formula10分钟
Do You Know Determinants?10分钟
Proof of Cassini's Identity10分钟
Catalan's Identity10分钟
Sum of Lucas Numbers10分钟
Sums of Even and Odd Fibonacci Numbers10分钟
Sum of Lucas Numbers Squared10分钟
Area of the Spiraling Squares10分钟
Quiz3 个练习
The Fibonacci Bamboozlement6分钟
Fibonacci Sums6分钟
Week 220分钟
3
完成时间(小时)
完成时间为 3 小时

The most irrational number

In this week's lectures, 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 head of a sunflower. ...
Reading
8 个视频 (总计 61 分钟), 8 个阅读材料, 3 个测验
Video8 个视频
An Inner Golden Rectangle5分钟
The Fibonacci Spiral6分钟
Fibonacci Numbers in Nature4分钟
Continued Fractions15分钟
The Golden Angle7分钟
A Simple Model for the Growth of a Sunflower8分钟
Concluding remarks4分钟
Reading8 个阅读材料
The Eye of God10分钟
Area of the Inner Golden Rectangle10分钟
Continued Fractions for Square Roots10分钟
Continued Fraction for e10分钟
The Golden Ratio and the Ratio of Fibonacci Numbers10分钟
The Golden Angle and the Ratio of Fibonacci Numbers10分钟
Please Rate this Course10分钟
Acknowledgments10分钟
Quiz3 个练习
Spirals6分钟
Fibonacci Numbers in Nature6分钟
Week 320分钟
4.7
79 个审阅Chevron Right

热门审阅

创建者 BSAug 30th 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.

创建者 HJDec 4th 2016

Good course for introduction to Fibonacci Numbers. Should include more introduction lectures such as group theory, category theory, type theory, number theory, and algorithms.

讲师

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Jeffrey R. Chasnov

Professor
Department of Mathematics

关于 The Hong Kong University of Science and Technology

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....

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