How Wide Is the Margin? (the Named Boundary)

The squared norm of w is exact rational arithmetic. Turning that squared norm into a numeric width uses a square root, so the width is rendered as a named radical symbol rather than a decimal.

highlighted = computed this step

The exact squared norm

Both candidate lines use the same w, so the squared norm is w·w=1/2. The signed scores and supports are recomputed from the same points.

w\cdot w=1/2

Why the width is named

Line A has named gap width 1/√(1/2). Line B has wider named gap width 2/√(1/2). The square-root step is named, so no decimal width is pinned.

\text{wide width}=2/\sqrt{1/2}

Summary

The geometry values are exact; the numeric width crosses the square-root boundary. The renderer keeps it as a symbol.

\sqrt{\ } \text{ is named here}