Is Golden Ratio real? What does it mean?

The Golden Ratio appears in nature [1, 2, 3, 4] in various ways:

• 

  Maybe "beauty" is symmetry

  spiral patterns in sunflowers, pinecones, and seashells
• growth patterns of certain plants, like the arrangement of leaves around a stem
• proportions of limbs, fingers, and facial features in the human body (such as idealized depictions of the Future Buddha known as the "Friend" Maitreya (shown at right).

But what is it?

In mathematics, two quantities are in the "golden ratio" if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities 𝑎 and 𝑏 with 𝑎 > 𝑏 > 0, 𝑎 is in a golden ratio to 𝑏 if

𝑎 + 𝑏/𝑎 = 𝑎/𝑏 = 𝜑, where the Greek letter phi (𝜑 or 𝜙) denotes the golden ratio [Note a]. The constant 𝜑 satisfies the quadratic equation 𝜑 2 = 𝜑 + 1 and is an irrational number with a value of [1]

1.618033988749.... Golden ratio

Huh, Eggheads? WTH is this gobbledygook supposed to mean? Can it be restated for the innumerate and artists with good taste? Let's see. What makes flowers and the nautilus shell so pretty?

Pretty shells and petals

What is prettier than a pattern?

The chambered nautilus (pictured above) builds roomier chambers in a spiral pattern based on the Golden Ratio.

Other examples include flower petals, seed heads, pinecones, shells, spiral galaxies, hurricanes, and DNA molecules. Learn more:

1. Unraveling the Enigma of the Golden Ratio in Nature… (abakus-center.com)
2. Nature's Golden Ratio | Geophysic… (gi.alaska.edu).
3. The Golden Ratio in Nature – Overview (quantumgravityresearch.org)

• Golden ratio (bing.com), 7/12/24; Sheldon S., Seth Auberon (eds.), Wisdom Quarterly