Geometry & Topology Vocabulary

relating to ordinary flat geometry based on Euclid's axioms

“In Euclidean space, the angles of a triangle sum to 180 degrees.”

Origin: From Euclid, Greek mathematician, c. 300 BCE

the study of properties preserved under continuous deformation

“Topologically, a coffee mug and a donut are equivalent.”

Origin: Greek topos `place` + -logy `study of`

a space that locally resembles Euclidean space

“The surface of a sphere is a two-dimensional manifold.”

Origin: From many + fold, calque of German Mannigfaltigkeit

a structure-preserving mapping between two mathematical objects

“The groups are isomorphic if there exists a bijective homomorphism between them.”

Origin: Greek isos `equal` + morphe `form`

invariance under a transformation

“A circle has infinite rotational symmetry.”

Origin: Greek symmetria `agreement in dimensions`, from syn `together` + metron `measure`

having exactly the same size and shape

“Two triangles are congruent if all corresponding sides and angles are equal.”

Origin: Latin congruere `to come together, agree`

touching a curve at exactly one point

“The tangent line represents the instantaneous slope of the curve.”

Origin: Latin tangere `to touch`

at right angles to a line or surface

“The walls are perpendicular to the floor.”

Origin: Latin perpendicularis, from perpendiculum `plumb line`

the number of independent coordinates needed to specify a point

“We live in three spatial dimensions.”

Origin: Latin dimensio `a measuring`, from dimetiri `to measure out`

a pattern of shapes that fit together without gaps or overlaps

“Hexagons form a natural tessellation in honeycombs.”

Origin: Latin tessella `small square stone`, diminutive of tessera `cube`