Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
simple closed curves in 3-dimensional space
|
| gptkbp:field |
differential geometry
knot theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Fáry–Milnor theorem
|
| gptkbp:implies |
Every nontrivial knot has total curvature greater than 4π.
|
| gptkbp:namedAfter |
gptkb:István_Fáry
gptkb:John_Milnor |
| gptkbp:publishedIn |
gptkb:American_Journal_of_Mathematics
|
| gptkbp:state |
A knot in three-dimensional Euclidean space with total curvature at most 4π is unknotted.
|
| gptkbp:yearProved |
1949
|
| gptkbp:bfsParent |
gptkb:Milnor's_theorem_on_the_total_curvature_of_knots
|
| gptkbp:bfsLayer |
5
|