Voltar para Fibonacci Numbers and the Golden Ratio

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1,011 classificações

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.
Download the lecture notes:
https://www.math.ust.hk/~machas/fibonacci.pdf
Watch the promotional video:
https://youtu.be/VWXeDFyB1hc...

JR

12 de jul de 2020

Someone has said that God created the integers; all the rest is the work of man. After seeing how the Fibonacci numbers play out in nature, I am not so sure about that. A very enjoyable course.

BH

28 de out de 2020

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.

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por Giovanni M

•16 de mar de 2017

Finally I studied the Fibonacci sequence and the golden spiral. I used to say: one day I will.

Very interesting course and made simple by the teacher in spite of the challenging topics

por Susannah R

•8 de ago de 2019

This course gives a fascinating insight in the logic behind some of nature's beauty. It requires a lot of maths, far more than I did at school (A Level) many years ago. It is definitely aimed at keen maths students. I found that many of the examples in the videos and the model answers to the questions missed lots of steps that I needed. These logic jumps may be second nature to somebody regularly studying maths , but for the 'casual' MOOCer at home who thinks "Ooh! that looks interesting", it left me struggling.

por Víctor P V

•12 de ago de 2016

The theory explained and the exercises are not at the same level.

por Eleanor H

•21 de mar de 2021

The class is fantastic! The material is fascinating and just challenging enough. The length of the class was good—for keeping motivated for the entire 3 weeks. The instructor’s videos are very clear, precise, thorough and I loved being able to print out the class notes as well as solutions to problems and practice tests. The only thing that I think could be improved would be to include a clear definition of “origin” of the golden spiral. It seems to me that in the problems the origin is sometimes assumed to be the accumulation point, whereas in the proof of problem one for lecture 13 the origin is used as the origin ( of the coordinate system) and assumed to be the lower left hand corner of the largest golden rectangle. This confused me.

por Janet M

•26 de jun de 2021

This is a very exciting course. I was pleased the instructor told us we could continue without worrying about the maths. Although I passed the initial diagnostic maths test and mostly scored high on the quizzes I found the maths well beyond me and could not even follow the solutions to the extra problems at the end of each section let alone attempt the questions. I would nevertheless recommend this course to anyone who finds numbers fascinating. Even if some of the maths goes over your head it is still possible to appreciate the main ideas. The enthusiasm of the instructor encouraged me to persist, thank you

por Bruna B

•3 de dez de 2021

I really liked this course, and I think the instructor is great. Everything is well explained, both in algebra as well as in theory and geometrically. Music and visual representations both fit, as well. I find incredible how these patterns are reproduced in nature and in ancient forms, and, how they inner correlate numerically with each other, also. I've always wanted to explore better this issue, as I find it very interesting and I know these patterns are used in trading. It is still incredible to think that nature replicated this pattern into many of its designs.

por Thilanka L

•13 de nov de 2020

This course is wonderfully composed to give you a good foundation to the Fibonaccci numbers. A basic knowledge in Algebra is sufficient to follow this course since much of the other required information are delivered during the lecture or as supplementary videos. The best thing about this course is how Professor Casnov step by step explains interesting details which when combines gives a beautiful meaning even towards the nature. Loved every minute of the lecture, and I highly recommend this course to anyone who is curious about this topic.

por CARLOS R A H

•12 de fev de 2021

Great course, as expected from Prof. Chaznov. This course was fun and very interesting. As an Informatics Engineer student, I thought I knew about Fibonacci numbers but wow, I really didn't. There's a whole more to it, and anyone can learn from it. The course is challenging, but fun as well. It takes a while to get used to prove a lot of identities by mathematical induction, with wasn't my favorite thing ever but after this course I think I've learned to like it, it's very satisfying. Looking forward to more math courses like this.

por Mufti M

•4 de jul de 2021

This is a great course which delivered an in-depth of analysis on Fibonacci number to many more related topic like golden ratio to Cassini's / Catalans identity and many more. It was an exceptional course on introduction to advanced mathematical thinking and how Fibonacci number appears in nature like construction of sunflower head with respect to florets arrangement by using golden angle. To complete each assignment need thorough understanding of each derivations.

por Sasha W

•2 de ago de 2020

Very interesting course. By far the most interesting and challenging I have found so far in my preparation to go study maths at uni in a years time. Used some of my previous mathematical knowledge such as matrices and proof by induction, whilst pushing me to use them in different problems and derive new formulas and use new mathematical methods. Will definitely be talking about this on my personal statement!

por Dr. S V C

•30 de set de 2020

I joined this course out of interest about the existence and visibility of Fibonacci sequence and the Golden Ratio in nature as also its connection with ancient Indian texts. Found this course very interesting. The instructor was very clear with the concepts and presented them very lucidly. Would recommend this course to those who want to understand the basics of Fibonacci Numbers and golden ratio.

por Tenzin D

•5 de fev de 2021

One of the best course ive taken so far. The assignments were fun to solve due to its challenging nature, cant deny the booklet of being extremely beneficial at such times. Overall, i had an interest on Fibonacci Numbers and after taking this course, it completely changed what i thought and how i thought about Fibonacci. Feeling lucky and grateful to have taken this course.

por Ravi V C

•5 de ago de 2020

This course is well explained. Interesting. Surprisingly takes less time to complete but consumes a lot of time to dwell deeper into it with proofs and their applications. I would like to repeat all the exercises and want to learn more about the topic, whenever I get a chance. It has opened new world to think. Thanks for the beautiful course.

por Aldrich W

•28 de mai de 2021

This is my third course with Prof. Chasnov on Coursera. I really love his teaching styles and truly appreciate the greatness of mathematics and its application to our real world. Through this course, I enjoyed seeing the beauty of Fibonacci Numbers, the sequence, the Golden Ratios, the model of sunflowers, etc.

por Nithin T S

•20 de out de 2020

I had a great time going through this course. I highly recommend students to take up this course as it will change the very imaginative concept of mathematics. I also liked the mentor Mr.Jeffrey. He is so much interested and patient in taking classes. I really liked this course a lot. Thank you.

por Kien T P

•9 de set de 2021

Very interesting Course!

It has so much enriched resource and was so useful for me, a high school's math teacher, who looking forward to the material to develop my course and keep it touching to the spirit of Math.

Thank you so much for sharing a delightful course like this!

por fez99@libero.it

•11 de abr de 2022

Very enjoyable. The course material is very well explained. Assignments are interesting and have the right level of difficulties. Not much mathematical background is needed (just very very basic matrix algebra) but some sort of "mathematical mindset" is useful.

por Muhammad B A

•21 de abr de 2020

This is really a very wonderful course. This is the first course, I enrolled on Coursera and started it just as a fun course. But at the end, it is much more than my expectations. I learned a lot and revised many concepts. Thank you Professor Chasnov.

por K B

•24 de out de 2016

In this course so far I have been able to see what different types of patterns are and I have been able to see what kind of counting ways there are. I have also learned that the Fibonacci Sequence is everywhere in nature so I really like this course.

por TAI C C

•19 de jun de 2021

This course is very interesting and I just cant imagine a prof is willing to teach all of us online free in charge! I have been hearing from the famous Fibonacci sequence and the golden ratio and finally , I could learn it and it was amazing !!!!!

por dominic t

•4 de ago de 2021

All around interesting. Not a lot of prerequisites, and the course provides additional information if you are not familiar with proof by induction or elementary linear algebra. Very informative and nice layout. Had a lot of fun with the course.

por Kevin D

•10 de jun de 2020

Very interesting and entertaining course. I have had many years of advance Math & Engineering courses, and had never covered the subject matter that was provided by this course.

Thanks to everyone that created and provided this course.

por Daniel A

•23 de mar de 2020

Great material; both instructive and fun.

The exercises were just challenging enough to make me think, but achievable with some effort (with one exception so far (Catalan´s identity), but I´ll come back to that).

And a great instructor!!!!

por Patali T

•14 de dez de 2020

I really enjoyed this course! My wholehearted thanks go to Prof.Chasnov. What I really love about the course is you don't have to know a lot of algebra, even if you don't know from watching the lecture videos you can easily understand.

por Soham J

•27 de abr de 2019

This course is absolutely out of the world. It truly showed me how much I didn't know and how fascinating nature is. The best part is that anyone with basic understanding of algebra can take this course. I had a really fun time here.

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