This is an interactive visual demonstration that composing two reflections produces a rotation. The key insight: if you reflect a vector across line *u*, then reflect the result across line *v*, the net effect is rotating the original vector by twice the angle between *u* and *v*. The page includes live 2D diagrams where you can drag the reflector vectors and watch the rotation happen, plus a clean implementation showing the math uses only dot and cross products—no sin/cos needed. It extends the pattern to 3D (reflection planes instead of lines) and to circle inversion, showing that reflection is a foundational operation in geometric algebra. The code snippets show the actual functions: `reflect()` handles vector reflection, and `rotate()` chains two reflections. This trades trigonometric thinking for geometric composition, which is computationally and conceptually elegant. One sharp question: does the page demonstrate that this approach has practical advantages over standard rotation matrices or quaternions in real applications, or is it primarily pedagogical?