Examples for
Geometry
Geometry is the field of mathematics that studies properties of figures and the underlying space. Wolfram|Alpha has the ability to analyze and compute with geometric figures of different dimensions, including polygons and polyhedra. It can also solve many applied problems using geometry, like tilings or packing problems. Additionally, Wolfram|Alpha can tell you about more advanced areas such as analytic geometry and topology.
Compute properties of 2D geometric figures.
Compute properties of a plane figure:
annulus, inner radius=2, outer radius=5Compute properties of a triangle with given side lengths:
5, 12, 13 triangleSpecify geometric figures by coordinates or algebraic equations.
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 = 1High-Dimensional Geometry
Compute properties of geometric figures with dimensions higher than three.
Compute properties of a high-dimensional geometric object:
tesseractcross polytopeSpecify parameters for a high-dimensional object:
glome of radius 2Visualize a moiré pattern.
Explore moiré patterns:
moire patternInvestigate interference patterns with offsets or angles:
moire pattern at 30 degreesCompute properties of 3D geometric figures.
Compute properties of a geometric solid:
sphere, surface area=1Compute properties of a polyhedron:
tetrahedronVisualize and compute properties for different kinds of geometric transformations.
Visualize a rotation and compute its matrix:
rotate 30 degreesVisualize a reflection in 3D:
reflect across x+y+z=1Determine the optimal packing of geometric figures or generate estimates using real‐life objects.
Compute properties of a geometric packing:
pack 24 circles in a circleSpecify dimensions of the container:
pack 9 squares in a triangle of side 10Estimate the number of objects required to fill a container:
How many baseballs fit in a Boeing 747?Compute properties of a class of polyforms.
Get information about a class of polyforms:
polyominoesSpecify the order of the polyforms:
hexiamondsGO FURTHER
Step-by-Step Solutions for GeometryRELATED EXAMPLES
RELATED WOLFRAM RESOURCES
Visualize and compute properties of curves and surfaces.
Compute properties of a named curve:
cardioidCompute properties of a named surface:
Dini's surfaceVisualize both periodic and nonperiodic tilings.
Get information about a periodic plane tiling:
rhombille tilingGet information about a nonperiodic tiling:
Ammann A4 tilingCompute topological properties for various kinds of geometric objects.