Introducing Mathematics

This is
Mathematics.

The Future of Mathematics

Interactive mathematical Worlds, narrated tours, and lessons.

Explore MathematicsFREE

Free Worlds, tours & lessons.
No account required.

An intricate nine-generation Apollonian sphere packing: luminous chrome spheres nestled among smaller spheres on pure black. — Apollonian Gasket · Captured in Mathematics

Available now
All free to explore.

18interactive
mathematical Worlds

75narrated
lessons & tours

An invitation from The Bhakti Math Guru

Interactive mathematics

Mathematics is an app for exploring mathematical form and relationship through direct perception and interaction.

Its 18 interactive Worlds cover geometry, algebra, trigonometry, fractals, and higher-dimensional structures.

Rotate forms, change parameters, and view the relationships between mathematical objects.

Now with free tours & lessons

Narrated tours
and lessons

Spoken guidance.
Interactive demonstrations.

Narrated tours introduce each World and its controls. Lessons focus on specific mathematical topics, with spoken guidance synchronized to demonstrations.

Pause the narration to use the controls, then resume the demonstration. Lessons include Building a New Dimension, Sine and Cosine Are Coordinates, and See the Product in the Rectangle.

Open a World and choose Guided to find its tour and lessons.

75 narrated lessons & tours. AI-generated voice synchronized with mathematical demonstrations.

Six of 18 Worlds

Mathematical Worlds

Geometry, algebra, trigonometry, and fractals.

A luminous tesseract projection with nested cubic structures connected by blue and violet edges.

Hypercubes

Explore hypercubes from a point to 11 dimensions. Rotate higher-dimensional projections and unfold a tesseract into a net of eight cubic cells.

Explore Hypercubes

A snub dodecahedron with jewel-colored metallic triangular and pentagonal faces.

Polyhedra

Explore 123 convex polyhedra. View faces, edges, and vertices; unfold solids into nets; and compare polyhedra with their duals.

Explore Polyhedra

An Apollonian packing of reflective chrome spheres, revealing smaller spheres in the spaces between.

Apollonian Gasket

Generate packings of tangent circles and spheres. Change the starting configuration and display successive generations of the packing.

Explore the Gasket

An intricate blue Julia fractal with repeating spirals, delicate branches, and luminous boundaries.

Julia & Mandelbrot

Change the complex parameter of a Julia set. Zoom into fractal boundaries, trace orbits, and compare the 2D image with a 3D field surface.

Explore Julia & Mandelbrot

Colored squares built on a right triangle, making the Pythagorean identity visible through their areas.

Trigonometry

Explore the unit circle, all six trigonometric functions, and the identity sin²θ + cos²θ = 1. Relate angles to coordinates, curves, and the areas of squares.

Explore Trigonometry

A colorful metallic cube separated into a base cube, slabs, bars, and a small corner cube.

Visual Cubes

Separate a binomial cube into a base cube, slabs, bars, and a corner cube. Change the lengths and relate each algebraic term to its volume.

Explore Visual Cubes

Graphics engine

MaGE

Mathematical Graphics Engine

MaGE supplies shared geometry, materials, and rendering to several Worlds in Mathematics. Its GPU-powered graphics run directly in the browser.

These rendering tools support interactive projections, recursive packings, and fractal surfaces. Materials and lighting distinguish surfaces and spatial relationships.

Higher-dimensional
projections
Recursive circle
and sphere packings
Fractal fields
in 2D and 3D

Free access

Explore Mathematics

The current Worlds, narrated tours, and lessons are free to explore. No account is required.

Additional lessons and a fuller curriculum are planned.

Share Mathematics with others, or send feedback and requests for mathematical topics.