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.

Plane Geometry

Compute properties of 2D geometric figures.

Compute properties of a plane figure:

Compute properties of a triangle with given side lengths:

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Coordinate Geometry

Specify geometric figures by coordinates or algebraic equations.

Specify a line through two points:

Plot a conic section and identify its type:

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High-Dimensional Geometry

Compute properties of geometric figures with dimensions higher than three.

Compute properties of a high-dimensional geometric object:

Specify parameters for a high-dimensional object:

Moiré Patterns

Visualize a moiré pattern.

Explore moiré patterns:

Investigate interference patterns with offsets or angles:

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Solid Geometry

Compute properties of 3D geometric figures.

Compute properties of a geometric solid:

Compute properties of a polyhedron:

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Geometric Transformations

Visualize and compute properties for different kinds of geometric transformations.

Visualize a rotation and compute its matrix:

Visualize a reflection in 3D:

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Packing & Covering Problems

Determine the optimal packing of geometric figures or generate estimates using real‐life objects.

Compute properties of a geometric packing:

Specify dimensions of the container:

Estimate the number of objects required to fill a container:

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Polyforms

Compute properties of a class of polyforms.

Get information about a class of polyforms:

Specify the order of the polyforms:

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GO FURTHER

Step-by-Step Solutions for Geometry

RELATED EXAMPLES

  • Fractals
  • Plotting & Graphics
  • Trigonometry
  • RELATED WOLFRAM RESOURCES

  • Community: Geometry
  • Curves & Surfaces

    Visualize and compute properties of curves and surfaces.

    Compute properties of a named curve:

    Compute properties of a named surface:

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    Tilings

    Visualize both periodic and nonperiodic tilings.

    Get information about a periodic plane tiling:

    Get information about a nonperiodic tiling:

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    Topology

    Compute topological properties for various kinds of geometric objects.

    Compute properties of a knot:

    Compute homotopy groups of a sphere:

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