In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial di
Caratheodory's theorem illustration
Curve
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In mathematics, a curve is an object similar to a line, but that does not have to be straight.
Frobenius theorem (differential topology)
…the theorem, both concepts must be clearly defined. One begins by noting that an arbitrary smooth vector field X on a manifold M defines a family of curves, its integral curves u : I → M (for intervals I ). These are the solutions of u ˙ ( t ) = X u ( t ) , which is a system of first-order ordinary…
Megalithic art from Newgrange showing an early interest in curves
A dragon curve with a positive area