ToolPrototype
Matrix Transformation Visualiser
See how 2 by 2 matrices move vectors, shapes, area and orientation.
Beauty in maths topic
Geometry and Transformations
Geometry and transformations turn abstract operations into movement, shape, symmetry and structure.
5
live pages
2
prototype tools
7
planned ideas
What this area includes
Matrix transformations and invariant directions
Complex numbers as rotation and scaling
Fourier ideas, waves and decomposing patterns
Visual links between algebra and geometry
Questions to explore
What stays fixed when everything else moves?
How does multiplication become geometry?
Can a transformation explain the algebra?
Working pages and tools
These are the pages currently available to open from this topic.
Planned directions
These ideas are not built yet, but they show where this topic could grow next.
ideaPlanned
Fourier Patterns
Planned bridge from waves and rotations to complex numbers, calculus and signal patterns.
ideaPlanned
GCSE Geometry Construction Kit
Planned tool for angles, loci, bearings, transformations and circle theorems with interactive diagrams.
ideaPlanned
Further Maths Complex Roots Toolkit
Planned explorer for De Moivre's theorem, roots of unity, loci and transformations on the Argand diagram.
ideaPlanned
Further Maths Matrices and Eigenvectors
Planned visualiser for eigenvectors, determinants, invariant directions and repeated matrix transformations.
ideaPlanned
Non-Euclidean Music
Planned exploration of musical patterns generated by curved, warped or graph-like spaces.
ideaPlanned
Fractal Dimension Explorer
Planned tool for measuring roughness, box-counting dimension and why dimension does not have to be whole.
ideaPlanned
Elliptic Curve Cryptography
Planned advanced bridge from geometry and modular arithmetic to modern secure communication.
Connected topics
themeLive
Beauty in Maths
A portal for connected mathematical explorations: pattern, surprise, structure, nature and emergence.
themeLive
Maths in Music
Rhythm, tuning, symmetry, timing, pattern and musical structure through mathematics.
themeLive
Fractals and Infinite Detail
Self-similarity, recursion, iteration, dimension and patterns that repeat at different scales.
themeLive
Topology and Surfaces
Shape, connectedness, holes, surfaces, knots and geometry that survives stretching.
themeLive
Data Geometry
Clustering, dimensions, similarity, projection and the hidden shape of high-dimensional data.
How to use this section
Use the tools here to see structure before formalising it.