I was working on differential geometry and I wondered the next question: "given a curve contained in a surface, can it always be ensured that the osculating plane at a point on the curve coincides with the tangent plane to the surface at that point?". Some idea?
2026-04-06 01:09:04.1775437744
Question about the coincidence between osculating plane and the tangent one.
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Certainly not. Consider any surface, for instance a sphere S, and intersect it with a transverse plane P. In the example you have a circle. The osculating plane along at any point on this curve is P, which is not the tangent plane ( they are transverse).