Parametric Ring Designer | mysimulator.uk

Band Profile

Band width 2.4 mm

Band thickness 1.6 mm

Motif Symmetry

Repeats (C_n symmetry) 8

Center Stone

Stone diameter 4.5 mm

Metal

Design Readouts

Metal volume

— mm³

Est. weight

— g

Ring size (US)

—

Stone / band ratio

—

How it works

The band is a closed profile (a rounded rectangle, width × thickness) swept once around a circular centerline of radius R — a surface and solid of revolution. Its volume follows directly from Pappus's Centroid Theorem, with no need to integrate the swept solid directly:

V = 2π · R · A
R = centerline radius of the band (fixed at ring size 7 ≈ 8.65 mm)
A = cross-section area = width × thickness (mm²)

Weight then follows from density ρ of the chosen metal:

mass (g) = V (mm³) × ρ (g/cm³) / 1000
gold ρ = 19.30, silver ρ = 10.49, platinum ρ = 21.45 g/cm³

The filigree studs around the band are placed with C_n rotational symmetry — n copies of one motif spaced by 360°/n around the centerline, the same discrete symmetry group used to classify decorative patterns in jewelry, architecture and crystallography. Increasing n densifies the pattern without changing its unit motif.

The stone/band ratio (stone diameter ÷ band width) is a classic proportion guide jewelers use: ratios near the golden ratio φ ≈ 1.618 are traditionally read as balanced, while much larger ratios read as "stone-heavy" and much smaller ones as "band-heavy".

Metal band Center stone

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