MHB Golden section and yin-yang symbol proportions

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The discussion centers on the relationship between the golden section and the proportions of the yin-yang symbol. A user initially questions the existence of an algebraic or trigonometric proof for a claim regarding the angles in the symbol, specifically a 45º angle. After some inquiry, they clarify that the solution can be found on the referenced website, Cut the Knot. The user concludes by providing specific values for segments related to the golden ratio, indicating that they have resolved their question. The conversation highlights the intersection of mathematical concepts with cultural symbols.
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Hello, dear friends of mathhelpboards;

I stumbled with a striking claim in https://www.cut-the-knot.org/do_you_know/GoldenRatioInYinYang.shtml

Sorry, I couldn't paste the pic. The question is if there is an algebraical or trig proof for this claim, as the angle seems to be just 45º. Then, is there an EXACT proof for this claim?
 
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What angle are you referring to? What do you mean by an "exact" proof?
 
Greg said:
What angle are you referring to? What do you mean by an "exact" proof?

Sorry, I got it. The solution is now in Cut the knot. Assuming, AB=1, AE=12 and BE=5‾√2. It follows that

BI=5‾√2+12=φ

BH=5‾√2−12=φ−1.

Problem solved! Thanks and sorry again.
 

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