The History of Golden Ratio, Fibonacci, and Continued Fractions (School Project)

I made this video as part of my final project for MATH446 at UBC 2022W! I thought that I would share it on here as well, had tons of fun researching and writing the scripts for this. I hope that you guys all learned something new from this video :)

Timestamps:
00:00 Intro
00:15 Golden ratio
02:19 Fibonacci sequence
04:06 Continued fractions
05:03 Relations
05:30 Importance
02:57 Summary

Music:    • K/DA Beats for Lo-fi Legends | Legend...  

Topic chosen: History of the golden ratio, the Fibonacci sequence, continued fractions, and their relations

Sources:
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Fink, K. (1903). Brief history of mathematics. Nabu Press.

Gies, F. C. (1998). Fibonacci. Retrieved November 30, 2022, from https://www.britannica.com/biography/...

The golden ratio and aesthetics. (2002). Retrieved November 30, 2022, from https://plus.maths.org/content/os/iss...

Herz-Fischler, R. (1998). A mathematical history of the Golden Number. Mineola, NY: Dover Publications.

Herzinger, K., & Wisner, R. (2014). Connecting greek ladders and continued fractions - history of continued fractions. Retrieved November 30, 2022, from https://www.maa.org/press/periodicals...

Knott, R. (2016). Fibonacci numbers and nature. Retrieved November 30, 2022, from https://r-knott.surrey.ac.uk/Fibonacc...

Knott, R. (2016). The Golden Section Ratio: PHI. Retrieved November 30, 2022, from https://r-knott.surrey.ac.uk/Fibonacc...

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Livio, M. (2002). The golden ratio: The story of phi, the world's most astonishing number. New York: Broadway Books.

Markowsky, G. (1992). Misconceptions about the golden ratio. The College Mathematics Journal, 23(1), 2-19. doi:10.1080/07468342.1992.11973428
O'Connor, J. J., & Robertson, E. F. (2000). Aryabhata - Biography. Retrieved November 30, 2022, from https://mathshistory.st-andrews.ac.uk...

O'Connor, J. J., & Robertson, E. F. (2001). Golden Ratio. Retrieved November 30, 2022, from https://mathshistory.st-andrews.ac.uk...

Pettofrezzo, A. J., & Byrkit, D. R. (1970). Elements of number theory. Englewood Cliffs, N.J,: Prentice-Hall.

Pizy, L. Z., & Sigler, L. E. (2002). Fibonacci's Liber Abaci: A translation into Modern English of Leonardo Pisano's Book of calculation. New York: Springer Verlag.

Posamentier, A. S., & Lehmann, I. (2011). The glorious golden ratio. Amherst, N.Y: Prometheus Books.

Robinson, E. (1982). A Note on the Geometry of the Great Pyramid. ON A CONVOLUTION PRODUCT FOR THE TRANSFORM WHICH MAPS DERIVATIVES INTO DIFFERENCES, 343.

Scott, J. F. (1981). The mathematical work of John Wallis. New York: Chelsea.

Singh, P. (1985). The so-called Fibonacci numbers in ancient and medieval India. Historia Mathematica, 12(3), 229-244. doi:10.1016/0315-0860(85)90021-7

#zeleonscience #maths #goldenratio