Golden section and yin-yang symbol proportions

In summary, the conversation discusses a claim about the golden ratio in yin yang symbols and whether there is an algebraic or trigonometric proof for it. There is a question about the exact proof and the angle being referred to, which is clarified to be 45 degrees. The solution is provided on Cut the knot, with further information about the values of AB, AE, and BE and their relation to the golden ratio. The problem is ultimately solved and apologies are given for previously not understanding the solution.
  • #1
tongtu
2
0
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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  • #2
What angle are you referring to? What do you mean by an "exact" proof?
 
  • #3
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.
 

1. What is the Golden Section?

The Golden Section, also known as the Golden Ratio or Divine Proportion, is a mathematical ratio of approximately 1.618. It is found in various natural and man-made forms, such as in the proportions of the human body, architecture, and art.

2. How is the Golden Section related to the Yin-Yang symbol?

The Yin-Yang symbol, also known as the Taijitu, is based on the concept of duality and balance in Chinese philosophy. The Golden Section is used to create the proportions of the symbol, with the circle representing the ratio of 1.618 and the smaller circle representing the ratio of 0.618.

3. Why are the Golden Section and Yin-Yang symbol proportions considered significant?

Both the Golden Section and Yin-Yang symbol proportions are considered significant because they represent harmony, balance, and perfection. They can be found in many aspects of nature, art, and design, and are believed to create a sense of visual appeal and balance.

4. How have the Golden Section and Yin-Yang symbol proportions been used in art and design?

The Golden Section and Yin-Yang symbol proportions have been used in art and design for centuries. Many artists and architects, such as Leonardo da Vinci and Le Corbusier, have incorporated these proportions into their works to create visually pleasing and balanced compositions. They have also been used in graphic design, product design, and advertising.

5. Is there any scientific evidence to support the significance of the Golden Section and Yin-Yang symbol proportions?

While the use of the Golden Section and Yin-Yang symbol proportions in art and design is widely accepted, there is no scientific evidence to support their significance. Some studies have shown that people do tend to find objects with these proportions more aesthetically pleasing, but this is subjective and varies from person to person.

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