What is φ?
The golden ratio is the unique positive solution of x² = x + 1:
φ = (1 + √5) / 2 ≈ 1.6180339887498948…
The reciprocal 1/φ equals φ − 1 ≈ 0.618, and its square φ² equals φ + 1 ≈ 2.618. These self-similar relationships are why φ shows up in nature, architecture, and design.
How to compute the segments
- From A:
B = A / φ, total= A + B = A · φ. - From B:
A = B · φ, total= A + B. - From total (A + B):
A = total / φ,B = total − A.
FAQ
Where does φ appear in nature?
Approximate appearances include sunflower seed spirals, pinecone scales, and the arrangement of leaves on stems (phyllotaxis) — all because φ is the "most irrational" number, which spreads things apart most evenly.
Is φ related to the Fibonacci sequence?
Yes — the ratio of consecutive Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, …) approaches φ. So 21/13 ≈ 1.615, 34/21 ≈ 1.619, and so on.
How accurate is φ here?
The calculator uses double-precision floating point, so values are accurate to about 15 significant digits.