 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/26i/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

C^{2}

regular curve; torsion requires

C^{3}

and nonzero curvature. The parameter-independent formulas are

κ = \frac{∣ γ ^{'} \times γ ^{''} ∣}{∣ γ ^{'} ∣ ^{3}}, τ = \frac{det ( γ ^{'} , γ ^{''} , d ^{3} γ / d t ^{3} )}{∣ γ ^{'} \times γ ^{''} ∣ ^{2}} .

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