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.”

the study of properties preserved under continuous deformation

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

a space that locally resembles Euclidean space

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

a structure-preserving mapping between two mathematical objects

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

invariance under a transformation

“A circle has infinite rotational symmetry.”

having exactly the same size and shape

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

touching a curve at exactly one point

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

at right angles to a line or surface

“The walls are perpendicular to the floor.”

the number of independent coordinates needed to specify a point

“We live in three spatial dimensions.”

a pattern of shapes that fit together without gaps or overlaps

“Hexagons form a natural tessellation in honeycombs.”