Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Glossary

Box Diagram

Box diagrams, also known as gluing diagrams, are a convenient way to examine intrinsic topology.

Configuration Space

A configuration space is a topological object that can be used to study the allowable states of a given system.

Euler Characteristic

The Euler characteristic is a topological invariant that relates a surface's vertices, edges, and faces.

Extrinsic View

Extrinsic topology is the study of shape from an external perspective.

Genus

Topological objects are categorized by their genus (number of holes). The genus of a surface is a feature of its global topology.

Intrinsic View

Intrinsic topology is the study of shape from the perspective of being on the surface of the shape.

Non-Orientability

If on a surface there is no meaningful way to tell an object's orientation (left or right handedness), the surface is said to be non-orientable.

Irrational

Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.

Topology

Topology, originally known as analysis situs—roughly, "geometry of position," seeks to describe what is fundamental about shape in general.