Mathematical Worlds
Explore mathematical objects and relationships through interactive Worlds. Choose a World below, or browse the visual collection and guided lessons.
Created by The Bhakti Math Guru.
Polyhedra Explorer
Explore 123 convex polyhedra as intricate solids rotate, unfold into multiple nets, construct their geometric duals, and reveal space-filling structures.
Circles & π
Perceive circumference through radius, diameter, π, and τ; rearrange sectors to see why circle area is πr²; then magnify π among ever-closer rational bounds.
Visual Cubes
Explore cubic expansion as a three-dimensional structure of a base cube, face slabs, edge bars, and corners.
Visual Multiplication
See multiplication geometrically through area, place value, and decomposition in different number bases.
Polygon Triangles
Explore how regular polygons reveal their triangles, interior angles, exterior angles, and the full 360° turn.
Ximals
See a fraction unfold as a recursive place-value expansion across different number bases.
Arithmetic Series
Pair an arithmetic sequence with its reversed copy to see why Sₙ = n(a₁ + aₙ) ÷ 2.
Count Tetris
Watch skip-counting sequences build rows, layers, and cubes while modular patterns emerge across different number bases.
Numbers & Sequences
Perceive quantity through geometric arrangements, three-dimensional structures, and important number sequences while writing every value in bases 2 through 16.
Hypercubes
Construct hypercubes from 0D through 11D, rotate genuine higher-dimensional projections, connect geometry with graph structure, and explore the equations governing every dimensional face.
Product Rule
Watch changing dimensions sweep out area strips and volume slabs, then see higher-order overlaps vanish as Δx approaches zero.
Pascal's Triangle
Turn Pascal's Triangle as a geometric object and reveal how each cell simultaneously encodes parent addition, simplex diagonals, combinations, paths, symmetry, binomial expansions, Fibonacci sums, and modular fractals.
Fractal Tree
Grow self-similar trees from one repeated rule, then carry the same construction into three dimensions through rotational symmetry around every parent branch.
Polar Graph Explorer
Wrap familiar functions around the origin, trace their polar geometry through angle and radius, and unwrap curves back into their rectilinear forms.
Completing the Square
Perceive quadratic roots through equal shares, completed corners, and equal-length subtraction, retaining their semantic form.
Factoring & Multiplication
Rearrange signed algebra tiles, compare every integer factor rectangle, and perceive polynomial identities and place-value diagonals.
Harmonic Modes
Explore spherical harmonics and Bessel drumheads through nodal patterns, oscillation and radial profiles.
Probability
Explore coin trials, dice sample spaces, binomial distributions and conditional probability through exact probabilities and repeatable experiments.
Fractional Dimensions
Explore fractional dimension through Cantor sets, recursive curves, Sierpiński constructions, the Menger sponge and four-dimensional fractals.
Mathematical tools
AI Calc: graph in two and three dimensions with AdamAI.
AI Math Tutor: work through mathematics with AdamAI.