Among all curves of fixed perimeter, the circle encloses maximum area: 4πA ≤ L²
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Modes: 4
Perimeter L: —
Area A: —
Isoperimetric ratio 4πA/L²: —
1.0 = circle (optimum)
Isoperimetric inequality: 4πA ≤ L² with equality iff the curve is a circle.
Fourier decomposition r(θ) = R + Σ aₙcos(nθ)+bₙsin(nθ). The ratio 4πA/L² ≤ 1 always, and converges to 1 as all modes vanish (calculus of variations: circle is the unique extremal).