Theorems · Definition · geometry
EuclideanGeometry.Cospherical
{P : Type u_2} → [MetricSpace P] → Set P → PropA set of points is cospherical if they are equidistant from some point. In two dimensions, this is the same thing as being concyclic.
- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realproof · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
Cited by41
Results whose statement or proof uses this declaration.
- EuclideanGeometry.cospherical_iff_exists_spherestatement and proof · cited by 4
- EuclideanGeometry.exists_circumcenter_eq_of_cospherical_subsetstatement and proof · cited by 3
- EuclideanGeometry.exists_circumradius_eq_of_cospherical_subsetstatement and proof · cited by 3
- EuclideanGeometry.exists_circumsphere_eq_of_cospherical_subsetstatement and proof · cited by 2
- EuclideanGeometry.Cospherical.subtype_valstatement and proof · cited by 2
- EuclideanGeometry.cospherical_emptystatement and proof · cited by 2
- EuclideanGeometry.cospherical_iff_exists_mem_of_finiteDimensionalstatement · cited by 2
- EuclideanGeometry.cospherical_of_two_zsmul_oangle_eq_of_not_collinearstatement · cited by 2
- EuclideanGeometry.Cospherical.affineIndependentstatement and proof · cited by 2
- EuclideanGeometry.mul_dist_eq_mul_dist_of_cosphericalstatement and proof · cited by 2
- Isometry.cosphericalstatement and proof · cited by 2
- EuclideanGeometry.exists_circumcenter_eq_of_cosphericalstatement and proof · cited by 1