WOLFRAM

Parallelogram[p,{v1,v2}]

represents a parallelogram with origin p and directions v1 and v2.

Details and Options

Examples

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Basic Examples  (3)Summary of the most common use cases

A standard parallelogram:

Out[1]=1

Different styles applied to a parallelogram:

Out[2]=2

Compute the Area of a parallelogram:

Out[2]=2

Centroid:

Out[3]=3

Scope  (16)Survey of the scope of standard use cases

Graphics  (6)

Specification  (2)

A standard parallelogram:

Out[1]=1

A parallelogram with specified origin and directions:

Out[3]=3

Styling  (2)

Color directives specify the face color:

Out[1]=1

FaceForm and EdgeForm can be used to specify the styles of the interior and boundary:

Out[1]=1

Coordinates  (2)

Use Scaled coordinates:

Out[1]=1

Use Offset coordinates:

Out[1]=1

Regions  (10)

Embedding dimension is the dimension of the space in which the vertices exist:

Out[2]=2

Geometric dimension is the dimensionality of the region itself:

Out[2]=2

Point membership test:

Out[2]=2

Get conditions for point membership:

Out[3]=3

Measure and centroid:

Out[2]=2
Out[3]=3

Distance from a point to a parallelogram:

Out[2]=2

Visualizing:

Out[3]=3

Signed distance to a parallelogram:

Out[2]=2

Visualizing:

Out[3]=3

Nearest point:

Out[2]=2

Visualizing:

Out[4]=4

A parallelogram is bounded and convex:

Out[2]=2

Compute a bounding box:

Out[3]=3
Out[4]=4

Integrate over a parallelogram:

Out[2]=2
Out[3]=3

Optimize over a parallelogram:

Out[2]=2

Solve equations in a parallelogram:

Out[2]=2

Applications  (5)Sample problems that can be solved with this function

A rhombus is a parallelogram in which all edges are the same length:

Out[4]=4

Visualize:

Out[10]=10

A parallelogram with sides that form right angles is a rectangle:

Out[2]=2

Visualize:

Out[3]=3

Any rectangle can easily be converted to a parallelogram:

Out[2]=2
Out[3]=3

The area of a parallelogram can easily be computed from the direction vectors:

Simply treat the vectors as a matrix and take the absolute value of the determinant:

Out[2]=2

Compare with Area:

Out[3]=3

A Parallelogram can tile the plane:

Out[1]=1

Properties & Relations  (6)Properties of the function, and connections to other functions

Rectangle is a special case of Parallelogram:

Out[3]=3

Polygon is a generalization of Parallelogram:

Out[2]=2

Parallelepiped generalizes Parallelogram to any dimension:

Out[2]=2

ImplicitRegion can represent any parallelogram:

Out[2]=2

ParametricRegion can represent any parallelogram:

Out[2]=2

A parallelogram can be represented as the union of two triangles:

Out[2]=2
Wolfram Research (2014), Parallelogram, Wolfram Language function, https://reference.wolfram.com/language/ref/Parallelogram.html (updated 2019).
Wolfram Research (2014), Parallelogram, Wolfram Language function, https://reference.wolfram.com/language/ref/Parallelogram.html (updated 2019).

Text

Wolfram Research (2014), Parallelogram, Wolfram Language function, https://reference.wolfram.com/language/ref/Parallelogram.html (updated 2019).

Wolfram Research (2014), Parallelogram, Wolfram Language function, https://reference.wolfram.com/language/ref/Parallelogram.html (updated 2019).

CMS

Wolfram Language. 2014. "Parallelogram." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/Parallelogram.html.

Wolfram Language. 2014. "Parallelogram." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/Parallelogram.html.

APA

Wolfram Language. (2014). Parallelogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Parallelogram.html

Wolfram Language. (2014). Parallelogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Parallelogram.html

BibTeX

@misc{reference.wolfram_2024_parallelogram, author="Wolfram Research", title="{Parallelogram}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Parallelogram.html}", note=[Accessed: 09-January-2025 ]}

@misc{reference.wolfram_2024_parallelogram, author="Wolfram Research", title="{Parallelogram}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Parallelogram.html}", note=[Accessed: 09-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_parallelogram, organization={Wolfram Research}, title={Parallelogram}, year={2019}, url={https://reference.wolfram.com/language/ref/Parallelogram.html}, note=[Accessed: 09-January-2025 ]}

@online{reference.wolfram_2024_parallelogram, organization={Wolfram Research}, title={Parallelogram}, year={2019}, url={https://reference.wolfram.com/language/ref/Parallelogram.html}, note=[Accessed: 09-January-2025 ]}