Euclidean geometry

E451827

branch of mathematics geometry

Euclidean geometry is the classical mathematical system that studies flat space and shapes using axioms about points, lines, and angles, forming the foundation of much of traditional mathematics and physics.

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Observed surface forms (1)

Surface form	Occurrences
Euclidean plane	1

Statements (52)

Predicate	Object
instanceOf	branch of mathematics ⓘ geometry ⓘ
appliedIn	architecture ⓘ classical mechanics ⓘ computer graphics ⓘ engineering ⓘ
basedOnWorkBy	Euclid NERFINISHED ⓘ
contrastedWith	elliptic geometry ⓘ hyperbolic geometry ⓘ non-Euclidean geometry ⓘ
describedIn	Elements NERFINISHED ⓘ
formalizedBy	Hilbert's axioms NERFINISHED ⓘ
foundationFor	analytic geometry ⓘ classical trigonometry ⓘ
hasAxiomSystem	Euclid's postulates NERFINISHED ⓘ
hasDimension	three-dimensional ⓘ two-dimensional ⓘ
hasGeneralization	n-dimensional Euclidean space ⓘ
hasKeyConcept	Cartesian coordinates ⓘ Euclidean distance NERFINISHED ⓘ Pythagorean theorem NERFINISHED ⓘ angle sum of triangle ⓘ congruence ⓘ parallel lines ⓘ perpendicularity ⓘ similarity ⓘ
hasParallelPostulateFormulation	given a line and a point not on it there is exactly one parallel line through the point ⓘ
hasPostulate	a circle can be drawn with any center and radius ⓘ a finite straight line can be extended continuously in a straight line ⓘ all right angles are equal to one another ⓘ parallel postulate ⓘ through any two points there is exactly one straight line ⓘ
hasProperty	distance satisfies Euclidean metric ⓘ rectangles exist ⓘ similar triangles with equal angles are proportional in sides ⓘ space is flat ⓘ triangle angle sum equals 180 degrees ⓘ zero curvature ⓘ
historicalPeriod	ancient Greek mathematics ⓘ
namedAfter	Euclid NERFINISHED ⓘ
studies	angles ⓘ area ⓘ circles ⓘ distance ⓘ lines ⓘ planes ⓘ points ⓘ polygons ⓘ triangles ⓘ volume ⓘ
usesTool	compass ⓘ straightedge ⓘ

Referenced by (19)

Full triples — surface form annotated when it differs from this entity's canonical label.

Book II → uses → Euclidean geometry ⓘ

subject surface form: Book II (De revolutionibus orbium coelestium)

Pythagorean theorem → field → Euclidean geometry ⓘ

John Playfair → academicDiscipline → Euclidean geometry ⓘ

De Corpore → influencedBy → Euclidean geometry ⓘ

Fermat point → definedIn → Euclidean geometry ⓘ

Euclid → knownFor → Euclidean geometry ⓘ

Euclid → subjectOf → Euclidean geometry ⓘ

Euclides adauctus et methodicus → mainSubject → Euclidean geometry ⓘ

Euclides adauctus et methodicus → workExpanded → Euclidean geometry ⓘ

Commentary on the Difficulties of Certain Postulates of Euclid → mainSubject → Euclidean geometry ⓘ

Archimedes' spiral → liesIn → Euclidean geometry ⓘ

this entity surface form: Euclidean plane

geometrization conjecture → hasCanonicalGeometry → Euclidean geometry ⓘ

Ethics, Part I → structureModeledOn → Euclidean geometry ⓘ

Tarski’s theorem on the completeness of elementary algebra and geometry → mainSubject → Euclidean geometry ⓘ

Penrose stairs → defies → Euclidean geometry ⓘ

Thales’ theorem → field → Euclidean geometry ⓘ

Introduction to Geometry → field → Euclidean geometry ⓘ

Introduction to Geometry → hasSubject → Euclidean geometry ⓘ

Non-Euclidean Geometry → contrastsWith → Euclidean geometry ⓘ

subject surface form: Non-Euclidean geometry