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I need help with a tricky puzzle.
Let's say we have a straight line: A---------------------D
The line has two points, B and C. Each of the two points split the line formed by outer points in two with respect to golden section:
A--------B--------C---------D
So AD is to AC as AC is to CD. And AD is to BD as BD is to AB.
The distance between B and C is 8314 cm. How long is the whole line AD?
Any help is greatly appreciated!
Best regards,
Katti
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Let's say for the moment that AD has a length of 1 and AC has a length of x.
Then CD has a length of (1-x).
Using the matching ratios, we can write the equation 1/x = x/(1-x).
Rearrange to form a quadratic, and this solves to give x = (√5-1)/2.
The diagram is symmetric, in that AC = BD.
Therefore, we can work out distance BC by finding C's distance from the halfway point and doubling it.
The distance from the halfway point will be (√5-2)/2, and naturally doubling that gets us √5-2.
So we now know that 1 is to √5-2 as AD is to BC.
From there, we do 8314/(√5-2) to get the final answer of ~35219cm.
Why did the vector cross the road?
It wanted to be normal.
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Amazing! What a thorough explanation, thank you!
Best regards,
Katti
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