Channel Link: https://www.youtube.com/@normalinternetplayer
Documentation link: https://drive.google.com/drive/folders/1OhLosJWGUFFxg3rt7x0up5alWJ-6GSQ8
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Channel Link: https://www.youtube.com/@normalinternetplayer
Documentation Link: https://drive.google.com/drive/folders/1OhLosJWGUFFxg3rt7x0up5alWJ-6GSQ8?usp=drive_link
Channel Link: https://www.youtube.com/@normalinternetplayer
Documentation Link: https://drive.google.com/drive/folders/1OhLosJWGUFFxg3rt7x0up5alWJ-6GSQ8?usp=drive_link
I was messing around with iterative functions and remembered the collatz conjecture.
Hope y'all enjoy!
This was a silly Desmos project I made in my free time.
I was messing around with equations and I rediscovered The Golden Ratio.
It starts with the equation x/y = (x+y)/x , I then put 1 as y and it gave me the equation x=phi.
I then got the y intersection with the original equation and made that into another equation y=1 then calculated the x intersection with it and repeated this process 14 times.
I also created some borders on top to show each square inside the open shape then got their areas.
I then placed a couple circles fit and cut just right so they fit in the squares aka The Fibonacci Spiral (Approximation of The Golden Spiral).
I noticed how there were lots of Euclidean Triangles embedded in the open shape, I calculated the "diagonals" and the areas of the triangles, and because they are Euclidean Triangles, I compared the similarities in side length and area of the couple triangles I defined.
User u/Circumpunctilious pointed out that The (approximated) Golden Spiral could be expressed with parametric equations, and created an approximation for the spiral.
I then modified it so it's closer to the original spiral.
I wanted to try polar equations, so I started copy pasting a bunch of equations and tinkered with them till I got something very close to the spiral.
In the process, I found that no matter how hard I try, I couldn't get them to fit exactly.
This is because The Fibonacci Spiral is an approximation of the actual Golden Spiral (which I didn't know at the time).
- I'm open to any modifications with explanations.
- I'd love to know more about this topic or tangent topics since I'm still learning (so if you got any tips or info, feel free to share them!)
Updated (5/10/2026): Added the Phyllotaxis / Sunflower spiral shape
Hope y'all enjoy it!