Golden section and yin-yang symbol proportions

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SUMMARY

The discussion centers on the mathematical relationship between the golden ratio (φ) and the proportions of the yin-yang symbol. The user references a claim from Cut the Knot, which outlines a geometric proof involving specific lengths: AB=1, AE=12, and BE=5√2. The conclusion confirms that the lengths lead to the relationships BI=5√2+12=φ and BH=5√2−12=φ−1, providing an exact proof of the claim.

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  • Understanding of the golden ratio (φ) and its properties.
  • Basic knowledge of geometry, particularly triangle properties.
  • Familiarity with algebraic manipulation and proof techniques.
  • Knowledge of trigonometric concepts, specifically angles and their relationships.
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  • Research the properties of the golden ratio in geometric figures.
  • Explore geometric proofs involving the yin-yang symbol.
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Mathematicians, geometry enthusiasts, and students seeking to understand the relationship between the golden ratio and geometric shapes, particularly in cultural symbols like the yin-yang.

tongtu
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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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