Statements (99)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:analyzes |
geometric constructions
|
| gptkbp:applies_to |
conic sections
hexagons inscribed in conics |
| gptkbp:can_be_generalized_to |
higher-dimensional spaces
|
| gptkbp:can_be_proven_using |
homogeneous coordinates
|
| gptkbp:curriculum |
advanced mathematics courses
|
| gptkbp:depicts |
the power of projective methods
|
| gptkbp:describes |
a property of conic sections
a hexagon inscribed in a conic section |
| gptkbp:example |
a theorem in mathematics
a projective invariant |
| gptkbp:field |
projective geometry
|
| gptkbp:has_applications_in |
gptkb:Graphics_Processing_Unit
gptkb:robotics computer-aided design |
| gptkbp:has_been_generalized_by |
various mathematicians
|
| gptkbp:has_implications_for |
the study of polynomials
|
| https://www.w3.org/2000/01/rdf-schema#label |
Pascal's Theorem
|
| gptkbp:illustrated_by |
a hexagon inscribed in a conic
Pascal's hexagon theorem |
| gptkbp:is_a |
geometric theorem
result in projective geometry |
| gptkbp:is_a_foundation_for |
modern geometry
|
| gptkbp:is_a_result_that_has_been |
proven in multiple ways
|
| gptkbp:is_a_subject_of |
mathematical competitions
|
| gptkbp:is_a_theorem_in |
Euclidean geometry
|
| gptkbp:is_a_theorem_that_can_be_applied_in |
the field of robotics
|
| gptkbp:is_a_theorem_that_can_be_applied_to |
various geometric configurations
|
| gptkbp:is_a_theorem_that_can_be_expressed_in |
algebraic terms
|
| gptkbp:is_a_theorem_that_can_be_related_to |
the concept of affine transformations
|
| gptkbp:is_a_theorem_that_can_be_visualized_through |
dynamic geometry software
|
| gptkbp:is_a_theorem_that_has_connections_to |
the study of symmetry in geometry
|
| gptkbp:is_a_theorem_that_has_historical_significance_in |
the development of geometry.
|
| gptkbp:is_a_theorem_that_has_implications_for |
the study of curves and surfaces
|
| gptkbp:is_a_theorem_that_involves |
the intersection of lines
|
| gptkbp:is_applied_in |
gptkb:architecture
engineering computer algorithms real-world problems in engineering |
| gptkbp:is_cited_in |
academic papers
mathematical journals dissertations |
| gptkbp:is_connected_to |
the concept of duality
the concept of duality in projective geometry the theory of determinants the concept of projective space |
| gptkbp:is_considered |
a fundamental theorem
|
| gptkbp:is_described_as |
geometry textbooks
|
| gptkbp:is_discussed_in |
mathematical conferences
mathematical literature geometry seminars |
| gptkbp:is_essential_for |
the field of algebraic geometry
|
| gptkbp:is_explored_in |
research studies
online courses geometry workshops |
| gptkbp:is_fundamental_to |
the history of mathematics
|
| gptkbp:is_influential_in |
modern geometry
|
| gptkbp:is_often_described_as |
the theorem of Pascal
|
| gptkbp:is_often_discussed_in |
mathematical seminars
|
| gptkbp:is_often_referenced_in |
mathematical literature
|
| gptkbp:is_often_used_in |
computer-aided design
|
| gptkbp:is_part_of |
the history of mathematics
the curriculum of mathematics education the foundation of projective geometry the study of conics |
| gptkbp:is_proven_using |
projective transformations
|
| gptkbp:is_related_to |
algebraic geometry
projective geometry the concept of harmonic division the study of polytopes projective duality the concept of collinearity the properties of cyclic polygons synthetic geometry the concept of incidence the study of transformations the theory of perspective |
| gptkbp:is_significant_for |
the development of modern geometry
|
| gptkbp:is_studied_in |
many mathematicians
|
| gptkbp:is_taught_in |
geometry courses
|
| gptkbp:is_used_in |
gptkb:Physics
image processing geometry computer vision mathematical proofs synthetic geometry |
| gptkbp:is_used_in_proofs_of |
other geometric theorems
|
| gptkbp:key |
the study of conic sections
|
| gptkbp:key_concept |
the study of projective spaces
|
| gptkbp:legal_principle |
the subject of many research papers
|
| gptkbp:named_after |
gptkb:Blaise_Pascal
|
| gptkbp:proposed_by |
gptkb:Blaise_Pascal
|
| gptkbp:published_by |
Pascal's work on conics
|
| gptkbp:state |
the three intersection points of the pairs of opposite sides of a hexagon lie on a straight line
the intersection points of the pairs of opposite sides are collinear |
| gptkbp:was_involved_in |
the duality principle
|
| gptkbp:bfsParent |
gptkb:Blaise_Pascal
|
| gptkbp:bfsLayer |
5
|