Beauty in maths topic

Topology and Surfaces

Topology studies properties of shape that survive stretching, bending and deformation without cutting or gluing.

live pages

prototype tools

planned ideas

What this area includes

Mobius strips, surfaces and orientation

Knots, tangles and invariants

Euler characteristic and holes

Connections between maps, graphs and surfaces

Bridges to geometry, fractals and proof

What stays the same when a shape is stretched?

How can we tell two spaces are genuinely different?

Why do holes matter?

These ideas are not built yet, but they show where this topic could grow next.

ideaPlanned

Planned visualisation of one-sided surfaces, orientation and what happens when a surface is cut.

ideaPlanned

Planned exploration of knots, crossings, invariants and why some tangled loops are different.

ideaPlanned

Planned tool connecting vertices, edges, faces, polyhedra and the idea of holes.

ideaPlanned

Planned page for spheres, tori, projective-plane ideas and classification through invariants.

A portal for connected mathematical explorations: pattern, surprise, structure, nature and emergence.

Matrices, complex numbers, transformations, symmetry and visual structure.

Nodes, edges, algorithms, networks, colourings and connected structures.

Self-similarity, recursion, iteration, dimension and patterns that repeat at different scales.

This section should feel hands-on: twist, cut, classify and look for the property that refuses to change.