Mathematics
# 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
compute properties of a geometric solid

sphere, surface area=1
compute properties of a polyhedron

tetrahedron
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
visualize a rotation and compute its matrix

rotate 30 degrees
visualize a reflection in 3D

reflect across x+y+z=1
compute values of trigonometric functions

sin(pi/5)
solve a trigonometric equation

sin x + cos x = 1
compute properties of a named curve

cardioid
compute properties of a named surface

Dini's surface
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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
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?
get information about a periodic plane tiling

rhombille tiling
get information about a nonperiodic tiling

Ammann A4 tiling
explore moirĂ© patterns

moire pattern
investigate interference patterns with offsets or angles

moire pattern at 30 degrees
get information about a class of polyforms

polyominoes
specify the order of the polyforms

hexiamonds
compute properties of a knot

trefoil knot
compute homotopy groups of a sphere

homotopy 3-sphere
draw a fractal set

Koch snowflake
plot a Julia set

Julia set -0.40+0.65i