Map · 52
convex and discrete geometry
MSC 52 · Convex and discrete geometry
2,015 declarations (1,792 theorems, 223 definitions) across 60 files. 5 of the 15 famous theorems listed for this area are in Mathlib (33%). 45 open conjectures here are stated in Lean.
Files are assigned to areas by a language model reading each file's documentation. Report a file that is in the wrong area.
Subareas3
- 52A General convexity 1,916
- 52C Discrete geometry 50
- 52B Polytopes and polyhedra 49
Famous theorems5 of 15
From the 1000+ theorems project, which classifies each theorem by MSC area.
Not yet in Mathlib · 10
In Mathlib · 5
- Carathéodory's theorem (convex hull)convexHull_eq_union
- Erdős–Szekeres theoremTheorems100.erdos_szekeres
- Helly's theoremConvex.helly_theorem
- Krein–Milman theoremclosure_convexHull_extremePoints
- Radon's theoremConvex.radon_partition
Open conjectures stated in Lean45
Statements without proofs, collected by the Formal Conjectures project.
- Erdos100.erdos_100Erdős Problems
- Erdos100.erdos_100.variants.strongErdős Problems
- Erdos101.erdos_101Erdős Problems
- Erdos1047.erdos_1047.variants.max_non_convex_componentsErdős Problems
- Erdos105.erdos_105.variants.sub_fourErdős Problems
- Erdos107.erdos_107Erdős Problems
- Erdos1084.erdos_1084.variants.triangular_optimal_d2Erdős Problems
- Erdos1085.erdos_1085.variants.upper_d3Erdős Problems
- Erdos212.erdos_212Erdős Problems
- Erdos213.erdos_213Erdős Problems
- Erdos506.erdos_506Erdős Problems
Structures defined here2
Typeclasses defined in this area's files, most assumed first.
Files60
Largest first. The code after each file is its assigned subarea.
- Mathlib.Analysis.Convex.Between
Betweenness in affine spaces
52A · 167
- Mathlib.Analysis.Convex.Function
Convex and concave functions
52A · 148
- Mathlib.Geometry.Convex.Cone.Basic
Convex cones
52A · 133
- Mathlib.Geometry.Convex.ConvexSpace.Defs
Convex spaces
52A · 113
- Mathlib.Analysis.Convex.Basic
Convex sets
52A · 105
- Mathlib.Analysis.Convex.Segment
Segments in vector spaces
52A · 82
- Mathlib.Geometry.Convex.Cone.Pointed
Pointed cones
52A · 68
- Mathlib.Analysis.Convex.StdSimplex
The standard simplex
52A · 63
- Mathlib.Analysis.Convex.Topology
Topological properties of convex sets
52A · 60
- Mathlib.Analysis.Convex.Combination
Convex combinations
52A · 59
- Mathlib.Analysis.Convex.Intrinsic
Intrinsic frontier and interior
52A · 57
- Mathlib.Analysis.Convex.Star
Star-convex sets
52A · 51