As you adjust the eye size, the tool checks whether the current ratio is near a mathematically notable value — a power of φ or Φ, a Fibonacci ratio, a harmonic fraction, or a geometric/transcendental constant. The match is labelled by how close it is:
- Exact (within ~1 billionth)
- The ratio is computationally indistinguishable from the known value at double-precision. Use a formula in Equation Input such as Phi/6 or phi^3 to ensure precision.
- Near-Exact (within ±0.1%)
- Extremely close — well within any perceptible visual difference. The ratio could serve as a practical stand-in for the known value.
- Adjacent (within ±0.5%)
- Clearly related. The deviation is small enough that the proportions feel the same, though a careful measurement would reveal it.
- Near (within ±2%)
- A visible family resemblance. The ratio shares the character of the reference value.
- Vicinal (within ±5%)
- In the neighbourhood. "Vicinal" is borrowed from crystallography, where it describes a face or ratio just off a principal plane.
Powers of Φ and φ are checked up to the 9th power. Fibonacci sequence ratios, simple harmonic fractions (½, ⅓, ⅝ …), geometric constants (√2, √3, √5-based), and transcendental ratios (π and e based) are also catalogued.