Plane Geometry

Compute properties of a plane figure:

annulus, inner radius=2, outer radius=5

Compute properties of a triangle with given side lengths:

5, 12, 13 triangle

Solid Geometry

Compute properties of a geometric solid:

sphere, surface area=1

Compute properties of a polyhedron:

tetrahedron

Coordinate Geometry

Specify a line through two points:

line through (1,2) and (2,1)

Plot a conic section and identify its type:

x^2 - 2 y^2 = 1

Geometric Transformations

Visualize a rotation and compute its matrix:

rotate 30 degrees

Visualize a reflection in 3D:

reflect across x+y+z=1

Curves & Surfaces

Compute properties of a named curve:

cardioid

Compute properties of a named surface:

Dini's surface

High-Dimensional Geometry

Compute properties of a high-dimensional geometric object:

tesseract

cross polytope

Specify parameters for a high-dimensional object:

glome of radius 2

Packing & Covering Problems

Compute properties of a geometric packing:

pack 24 circles in a circle

Specify dimensions of the container:

pack 9 squares in a triangle of side 10

Estimate the number of objects required to fill a container:

How many baseballs fit in a Boeing 747?

Tilings

Get information about a periodic plane tiling:

rhombille tiling

Get information about a nonperiodic tiling:

Ammann A4 tiling

Moiré Patterns

Explore moiré patterns:

moire pattern

Investigate interference patterns with offsets or angles:

moire pattern at 30 degrees

Polyforms

Get information about a class of polyforms:

polyominoes

Specify the order of the polyforms:

hexiamonds

Topology

Compute properties of a knot:

trefoil knot

Compute homotopy groups of a sphere:

homotopy 3-sphere