The golden ratio as a central point in the formulation of yoga bangles
When discussing yoga bangles, we've considered their use by ancient civilizations, Sri Yukteswar's recommendations to Yogananda and Janakananda, and their relationship with the chakras and granthis. However, we haven't discussed the golden ratio, a fundamental element, along with artisanal craftsmanship and the use of pure metals, in the creation of yoga bracelets.
The golden number, proportion, or golden section* or golden ratio is a division** whose result is: 1.618033988..., represented by the Greek letter phi (Φ), in honor of the Greek sculptor Phidias (named thus in the 20th century).
(The golden ratio is fulfilled if the relationship between a/b = 1,6180...)
Discovered in ancient times, studied by Euclid, Plato, Luca Pacioli, Leonardo da Vinci, Kepler, and so on, it establishes that** "small is to large as large is to the whole." One of its most peculiar characteristics is that Φ2 and 1/Φ have the same infinite decimal places.
The golden ratio is present in nature, in our bodies, and in the cosmos; raising questions, serving as a standard of beauty and even mystique throughout the centuries. Some examples of where Φ is found:
- the ratio of the thickness of the main branches to the trunk of trees,
- the growth rate of the coils of the spiral interior of a snail or nautilus...
- the distance between a person's navel and the sole of their foot, relative to their total height,
- the ratio of the length divided by the width of a DNA molecule...
- the average of the ratios of the distances of consecutive planets in the solar system,
- the shape of spiral galaxies like M51,
- the timing of the cooling of black holes...
The golden ratio appears in the Fibonacci series, introduced in 1202 by Leonardo da Vinci in his book "Liber Abaci". This infinite sequence of numbers results from adding each number to its predecessor (0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.). If we divide each number by its predecessor (e.g., 2/1, 3/2, 5/3, 8/5, 13/8, etc.), this division tends toward the golden ratio.
The golden rectangle is one whose sides are related by the golden ratio (the division of the sides a/b = Φ), with which we can construct the golden spiral.
(Each rectangle meets that a/b = 1,6180...)
In our everyday lives, we find the golden ratio as a pattern of harmony and beauty in all kinds of elements: from the size of cards, web pages, window frames, to buildings like the Pyramid of Giza and the Parthenon...
For all these reasons, it is extraordinary that this universal pattern is also present in the formula passed down through generations of yogis to create yoga bangles.
*Golden section is the name that Leonardo da Vinci could have given when he made some illustrations for Luca Pacioli's book, "De Divina Proportione".
