Minkowski sum
E14947
The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Minkowski sum canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T130826 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Minkowski sum Context triple: [Hermann Minkowski, knownFor, Minkowski sum]
-
A.
Minkowski space-time
Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
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B.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
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C.
Namba
Namba is a major commercial and entertainment district in Osaka, Japan, known for its bustling nightlife, shopping, and iconic neon-lit streets.
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D.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
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E.
Huygens–Fresnel principle
The Huygens–Fresnel principle is a fundamental concept in wave optics that explains how every point on a wavefront acts as a source of secondary wavelets whose interference determines the wave’s subsequent propagation and diffraction.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Minkowski sum Target entity description: The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
-
A.
Minkowski space-time
Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
-
B.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
-
C.
Namba
Namba is a major commercial and entertainment district in Osaka, Japan, known for its bustling nightlife, shopping, and iconic neon-lit streets.
-
D.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
-
E.
Huygens–Fresnel principle
The Huygens–Fresnel principle is a fundamental concept in wave optics that explains how every point on a wavefront acts as a source of secondary wavelets whose interference determines the wave’s subsequent propagation and diffraction.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
binary operation on sets
ⓘ
concept in convex analysis ⓘ geometric operation ⓘ |
| alsoKnownAs | vector sum of sets ⓘ |
| appliesTo |
convex sets
ⓘ
non-convex sets ⓘ |
| belongsTo | convex geometry ⓘ |
| definedOn |
subsets of Euclidean space
ⓘ
subsets of a vector space ⓘ |
| distributesOver | scalar multiplication of sets ⓘ |
| field |
computational geometry
ⓘ
convex analysis ⓘ geometry ⓘ mathematical morphology ⓘ optimization ⓘ robotics ⓘ |
| generalizationOf | addition of vectors ⓘ |
| hasDefinition | A + B = { a + b | a ∈ A, b ∈ B } ⓘ |
| hasHistoricalOrigin | early 20th century ⓘ |
| hasIdentityElement | set containing only the zero vector ⓘ |
| hasProperty |
distributes over finite unions
ⓘ
is compatible with linear transformations ⓘ sum of closed sets is closed ⓘ sum of compact sets is compact ⓘ sum of polytopes is a polytope ⓘ sum of two convex sets is convex ⓘ |
| isAssociative | true ⓘ |
| isCommutative | true ⓘ |
| isMonotone | true ⓘ |
| isTranslationInvariant | true ⓘ |
| namedAfter | Hermann Minkowski ⓘ |
| preservesBoundedness | true ⓘ |
| preservesClosedness | true ⓘ |
| preservesConvexity | true ⓘ |
| relatedConcept |
Minkowski difference
ⓘ
Minkowski functional ⓘ convex hull ⓘ support function ⓘ |
| usedFor |
computing reachability regions
ⓘ
shape offsetting ⓘ summing random sets in stochastic geometry ⓘ tolerance analysis in CAD ⓘ |
| usedIn |
collision detection
ⓘ
configuration space obstacles in robotics ⓘ linear programming geometry ⓘ morphological dilation ⓘ motion planning ⓘ polyhedral computations ⓘ support function calculations ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Minkowski sum Description of subject: The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.