Examples
Eight areas of school and college math, each solved step by step and shown as a live 3D model. Pick one and try it yourself.
See a solved example
Solid Geometry
Pyramids, prisms, cones, cross-sections
Polyhedra slicing planes, dihedral angles, distance between skew lines, and revolution solid volumes.
Build a rectangular cuboid with dimensions 4 × 5 × 6.
Plane Geometry
Triangles, circles, chords, theorems
Law of sines & cosines, incircles and circumcircles, similarity theorems, and radical axes.
Plot the triangle A(0,0), B(4,0), C(0,3) and rotate it 90 degrees about the origin.
3D Function Graphs
Surfaces, paraboloids, saddles, levels
Multivariable surfaces z = f(x,y), contour lines, critical saddle points, gradients, and tangent planes.
Plot the surface z = x^2 + y^2.
Trigonometry
Unit circle, 3D spirals, identities
Spatial projection of the unit circle, visualizing sin(x), cos(x), tan(x) and 3D wave periodicity.
Find sin and cos of 30° on the unit circle.
3D Vectors
Dot product, Cross product a × b
Collinearity, coplanarity, angle between vectors, cross product a × b and scalar triple products.
Given vectors a = (1, 2, 2) and b = (2, 0, 0), find the magnitude of their cross product.
Graph Transformations
Shifts, stretches, parametric curves
Dynamic affine transformations f(ax+b)+c, 3D parametric curves, and spatial projections.
Plot the graphs y = x^2 and y = 4 and find the area of the region between them.
Complex Numbers
Argand plane, roots of unity
Geometric meaning of complex multiplication, De Moivre's formula, and n-th roots as regular n-gons.
Multiply the complex numbers z1 = 1 + i and z2 = 1 + i and show them on the complex plane.
Limits & Sequences
Epsilon tubes, spatial convergence
Visual convergence cylinders, asymptotes, and Cauchy's epsilon-delta spatial definition of limits.
Find the limit of the sequence a_n = (n+1)/n.
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