Definition: Lagrange's theorem is a fundamental result in algebraic geometry that relates volumes of surfaces with certain constraints. It states that if you're given three points on a curve, then there exists an infinite set of lines (called Lagrange's equations) that are perpendicular to those points and intersect each other exactly once at the curve’s midpoint. This theorem has many applications in physics, engineering, and geometry, especially in studying surfaces like ellipsoids or hyperboloids.
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