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
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 circle packing
pack 24 circles in a circle
specify size of packed circles and container
pack circles of radius 1cm in a circle of radius 12cm
get information about a periodic plane tiling
rhombille tiling
get information about a nonperiodic tiling
Ammann A4 tiling
explore moiré 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