Bernstein partition-of-unity n=2: Σ_k B_{k,2}(x) ≡ 1; midpoint (1/4,1/2,1/4)

Sympy-exact symbolic verification of the Bernstein partition-of-unity identity at n = 2: the sum (1 − x)² + 2x(1 − x) + x² = 1 − 2x + x² + 2x − 2x² + x² = 1 identically, confirmed by sp.simplify over the symbol x. Midpoint pins at x =…