Drawing the Golden Ratio Geometrically

Hello,

I am not completely certain as to why The Golden Ratio can be drawn as shown in this video https://www.youtube.com/watch?v=6nSfJEDZ_WM @3:27. It's somewhat of a new concept for me.

Give it a try, and see if you can calculate that length. You can start by finding the length of the blue diagonal (the diameter of the circle), and find the length of the red segment as the sum of a radius and another segment. You will find that it adds up to phi.

Let us know what you come up with, and we can help you with any steps you have trouble with.
 
Give it a try, and see if you can calculate that length. You can start by finding the length of the blue diagonal (the diameter of the circle), and find the length of the red segment as the sum of a radius and another segment. You will find that it adds up to phi.

Let us know what you come up with, and we can help you with any steps you have trouble with.

The radius is sqrt(5)/2 and the other segment is 0.5 which add to 1.61

I also just noticed that this relates to the previous rule on the video, phi=[1+sqrt(5)]/2

Thank you for your guidance.
 
The radius is sqrt(5)/2 and the other segment is 0.5 which add to 1.61

I also just noticed that this relates to the previous rule on the video, phi=[1+sqrt(5)]/2

Thank you for your guidance.

Exactly: the construction is designed to obtain that length, 1/2 + sqrt(5)/2 = [1+sqrt(5)]/2 = phi.
 
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