Euclidean geometry
Plane figures, straight lines
Euclidean geometry is the study of points, lines, angles, and shapes on flat surfaces, based on axioms set out by the ancient Greek mathematician Euclid.
For over two thousand years it was simply "geometry"—the discovery of non-Euclidean geometries in the 19th century required the distinguishing label.
Euclidean geometry governs ordinary spatial reasoning: parallel lines never meet, the angles of a triangle sum to 180 degrees, the Pythagorean theorem holds.
- angleGeometric measure of rotation
- interior anglesAngles inside a polygon
- similar trianglesShapes with equal corresponding angles
- symmetryInvariance under transformation
- polygonMultisided plane figure
parallel · straight edge · parallel lines · deductive reasoning · Pythagorean theorem · Thales · area · Platonic solids · circle · tessellation · plane · flat space · bisect · shape · congruence · vertex · theorem · protractor
- geometries
- geometryangles, circles, angle, shapes, lines
- EponymsDarwinian, Alzheimer's disease, Freudian slip, cardigan, Parkinson's disease
- Greek scienceAristotle, Archimedes, Ptolemy, Hippocrates, Galen
- math historyPythagoras, Newton, Leibniz, Euler, Gauss
- Greek mathematicsArchimedes, Pythagoras, theorem, axiom, proof
geometry, Euclid's Elements, geometric, geometrical, Euclid, geometrically, geometers, geometer, Euclidean