Sur la décomposition des ensembles de points en parties respectivement congruentes

Target entity: Sur la décomposition des ensembles de points en parties respectivement congruentes
Context triple: [Banach–Tarski paradox, originalTitle, Sur la décomposition des ensembles de points en parties respectivement congruentes]

• A. Hilbert's third problem
  Hilbert's third problem is one of David Hilbert’s famous list of 23 problems, asking whether every polyhedron of a given volume is equidecomposable with any other of the same volume, a question that led to the development of the Dehn invariant and the discovery of counterexamples.
• B. Minkowski’s theorem on convex sets
  Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
• C. On Divisions of Figures
  On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
• D. Application de l’analyse à la géométrie
  Application de l’analyse à la géométrie is a foundational mathematical treatise by Gaspard Monge that helped establish descriptive geometry by systematically applying analytical methods to geometric problems.
• E. On the Principles of Geometry
  "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Sur la décomposition des ensembles de points en parties respectivement congruentes
Target entity description: "Sur la décomposition des ensembles de points en parties respectivement congruentes" is the 1924 French paper by Stefan Banach and Alfred Tarski that first formulated the Banach–Tarski paradox in set-theoretic geometry.

• A. Hilbert's third problem
  Hilbert's third problem is one of David Hilbert’s famous list of 23 problems, asking whether every polyhedron of a given volume is equidecomposable with any other of the same volume, a question that led to the development of the Dehn invariant and the discovery of counterexamples.
• B. Minkowski’s theorem on convex sets
  Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
• C. On Divisions of Figures
  On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
• D. Application de l’analyse à la géométrie
  Application de l’analyse à la géométrie is a foundational mathematical treatise by Gaspard Monge that helped establish descriptive geometry by systematically applying analytical methods to geometric problems.
• E. On the Principles of Geometry
  "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
• F. None of above. chosen