Examples for


Topology is the study of the properties of space preserved under continuous deformations, including twisting and stretching. Topology originated from the study of geometry and set theory and has many branches today. Wolfram|Alpha has the knowledge and ability to handle multiple topological topics, like computing the homotopy groups of an n-sphere (algebraic topology) or visualizing a knot (geometric topology).

Real Intervals

Compute properties for one real interval or compare multiple intervals.

Compute properties of an interval of real numbers:

Compare intervals:

More examples

Homotopy Groups of Spheres

Compute the homotopy groups of an n-sphere.

Compute homotopy groups of a sphere:

Compute a specified homotopy group:

Knot Theory

Find and visualize knots, either by specifying a common name or using knot notation.

Compute properties of a knot:

Specify a knot using Alexander–Briggs notation:

Compare several knots:

More examples