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

Trigonometry

compute values of trigonometric functions

sin(pi/5)

solve a trigonometric equation

sin x + cos x = 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

Fractals

draw a fractal set

Koch snowflake

plot a Julia set

Julia set -0.40+0.65i