Euclidean
Classical geometry's foundation
Euclidean describes geometry based on the principles of the ancient Greek mathematician Euclid—the familiar geometry of flat surfaces, straight lines, and consistent angles taught in schools.
In Euclidean space, parallel lines never meet and the angles of a triangle sum to 180 degrees.
The term often appears in contrast to non-Euclidean geometries, where these rules don't hold: Euclidean distance, Euclidean algorithm.
Winged flying vehicle
- spaceUnoccupied area or interval
- distanceSpace between two points
- pointExact location or meaning
- lineContinuous mark or queue
angle · triangle · circle · polygon · parallel · perpendicular · congruence · symmetry
Self-evident starting principle
- postulateAssumed starting point
- theoremDemonstrated logical conclusion
- proofDemonstration of truth
- propositionStatement expressing a judgment
deductive · logical · rigorous · self-evident · systematic · derivation · corollary · lemma
Egyptian Mediterranean port
- GreekOf Athenian origin
- PythagorasAncient Greek mathematician
- ArchimedesGreek polymath, physicist
- classicalOf ancient Greece/Rome
ancient · Hellenistic · academy · Plato · Aristotle · antiquity · scrolls · compass
plane
Winged flying vehicle
line · angle · triangle · circle · polygon · parallel · perpendicular · congruence · symmetry · area
axiom
Self-evident starting principle
proposition · deductive · logical · rigorous · self-evident · systematic · derivation · corollary · lemma · definition
Alexandria
Egyptian Mediterranean port
- GreekOf Athenian origin
- PythagorasAncient Greek mathematician
- ArchimedesGreek polymath, physicist
classical · ancient · Hellenistic · academy · Plato · Aristotle · antiquity · scrolls · compass · straightedge
hyperbolic
Exaggerated beyond reason
Gauss · spacetime · relativity · curvature · geodesic · manifold
- EponymsDarwinian, Alzheimer's disease, Freudian slip, cardigan, Parkinson's disease
- geometryangles, circles, angle, shapes, lines
- dimensionsdimension, spatial dimension, third dimension, fourth dimension, fifth dimension
Euclideannon-Euclidean
Geometry without parallel postulate
curved · hyperbolic · spherical · elliptical · warped
Euclideannon-Euclidean
Geometry without parallel postulate
hyperbolic · elliptic · spherical · projective · fractal
- Euclidean geometryStudy of flat planes