Which of these is a famous theorem formulated by Carathéodory?
Carathéodory's Theorem
Pythagorean Theorem
Fermat's Last Theorem
Gödel's Incompleteness Theorem
Answer
Carathéodory's Theorem states that any point in the convex hull of a set of points in Euclidean space can be expressed as a convex combination of at most n+1 of those points, where n is the dimension of the space. This theorem is widely used in convex geometry and optimization, and has applications in fields such as economics, engineering, and computer science.
Mastering the Mind of Constantin Carathéodory: A Mathematical Adventure
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