Beauty in maths topic

Data Geometry

Data geometry asks what shape data has when there are too many dimensions to draw directly.

live pages

prototype tools

planned ideas

What this area includes

Clustering, distance and similarity

Projection and dimensionality reduction

Principal component analysis and variation

Nearest-neighbour classification and Voronoi thinking

Manifolds and hidden low-dimensional structure

What does it mean for two data points to be close?

What information is lost when high-dimensional data is projected?

When can a picture of data mislead us?

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

ideaPlanned

Planned visualiser for projecting high-dimensional data while preserving as much variation as possible.

ideaPlanned

Planned tool comparing k-means, distance, cluster choice and when grouping data can mislead.

ideaPlanned

Planned page about similarity, classification, Voronoi regions and high-dimensional distance.

ideaPlanned

Planned advanced bridge asking whether complicated data can lie near a simpler hidden shape.

ideaPlanned

Planned AI visualisation connecting functions, optimisation, data and model training.

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

Randomness, evidence, simulation, modelling, optimisation and machine learning ideas.

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

This strand should help students see that data is not just rows in a table: it has geometry, shape and structure.