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.
제공자:
Fibonacci Numbers and the Golden Ratio
홍콩과학기술대학이 강좌에 대하여
최근 조회 9,741회
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지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.
초급 단계
High school mathematics
완료하는 데 약 10시간 필요
영어
자막: 아랍어, 프랑스어, 포르투갈어 (유럽), 이탈리아어, 베트남어, 독일어, 러시아어, 영어, 스페인어
배울 내용
Fibonacci numbers
Golden ratio
Fibonacci identities and sums
Continued fractions
귀하가 습득할 기술
- Recreational Mathematics
- Discrete Mathematics
- Elementary Mathematics
유연한 마감일
일정에 따라 마감일을 재설정합니다.
공유 가능한 수료증
완료 시 수료증 획득
100% 온라인
지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.
초급 단계
High school mathematics
완료하는 데 약 10시간 필요
영어
자막: 아랍어, 프랑스어, 포르투갈어 (유럽), 이탈리아어, 베트남어, 독일어, 러시아어, 영어, 스페인어
제공자:
홍콩과학기술대학
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.
강의 계획표 - 이 강좌에서 배울 내용
완료하는 데 3시간 필요
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.
완료하는 데 3시간 필요
7개 동영상 (총 55분), 8 개의 읽기 자료, 4 개의 테스트
완료하는 데 3시간 필요
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.
완료하는 데 3시간 필요
9개 동영상 (총 65분), 10 개의 읽기 자료, 3 개의 테스트
완료하는 데 3시간 필요
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.
완료하는 데 3시간 필요
8개 동영상 (총 61분), 8 개의 읽기 자료, 3 개의 테스트
검토
- 5 stars82.39%
- 4 stars15.13%
- 3 stars1.87%
- 2 stars0.49%
- 1 star0.09%
FIBONACCI NUMBERS AND THE GOLDEN RATIO의 최상위 리뷰
MH 제공2020년 7월 12일
It was a wonderful experience. I have learnt a lot more about Fibonacci numbers and the golden ratio during this course. I urge the professor to create more and more courses like this.
TP 제공2020년 7월 24일
These kind of courses are always interesting, where the world is full of mathematical calculations and hope to see more videos on nature and maths
AR 제공2021년 1월 13일
Very interesting. Much more math heavy than I was expecting, and would very hard to follow if you don't have at least first year university maths.
UB 제공2018년 6월 5일
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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