Parallelogram
✖
Parallelogram
Details and Options
- Parallelogram is also known as rhomboid and rhombus.
- Parallelogram represents , where the vectors vi have to be linearly independent.
- Parallelogram[] is equivalent to Parallelogram[{0,0},{{1,0},{1,1}}].
- CanonicalizePolygon can be used to convert a parallelogram to an explicit Polygon object.
- Parallelogram can be used as a geometric region and graphics primitive.
- Parallelogram can be used in Graphics.
- In graphics, the point p and vectors vi can be Scaled and Dynamic expressions.
- Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, and color.
Examples
open allclose allBasic Examples (3)Summary of the most common use cases
https://wolfram.com/xid/0dc0043pid26-3kbklo
Different styles applied to a parallelogram:
https://wolfram.com/xid/0dc0043pid26-g664m7
https://wolfram.com/xid/0dc0043pid26-u6g79l
Compute the Area of a parallelogram:
https://wolfram.com/xid/0dc0043pid26-lpcmcg
https://wolfram.com/xid/0dc0043pid26-d77jwr
https://wolfram.com/xid/0dc0043pid26-hrk6ci
Scope (16)Survey of the scope of standard use cases
Graphics (6)
Specification (2)
Styling (2)
Regions (10)
Embedding dimension is the dimension of the space in which the vertices exist:
https://wolfram.com/xid/0dc0043pid26-7y1i98
Geometric dimension is the dimensionality of the region itself:
https://wolfram.com/xid/0dc0043pid26-h86bsz
https://wolfram.com/xid/0dc0043pid26-1q11cp
https://wolfram.com/xid/0dc0043pid26-bw1vkb
Get conditions for point membership:
https://wolfram.com/xid/0dc0043pid26-bu58cs
https://wolfram.com/xid/0dc0043pid26-og6iba
https://wolfram.com/xid/0dc0043pid26-10rtwm
https://wolfram.com/xid/0dc0043pid26-l1r3hc
Distance from a point to a parallelogram:
https://wolfram.com/xid/0dc0043pid26-dvgon5
https://wolfram.com/xid/0dc0043pid26-8yh4wx
https://wolfram.com/xid/0dc0043pid26-bepoya
Signed distance to a parallelogram:
https://wolfram.com/xid/0dc0043pid26-pqep2t
https://wolfram.com/xid/0dc0043pid26-ynxl5f
https://wolfram.com/xid/0dc0043pid26-4pg6vy
https://wolfram.com/xid/0dc0043pid26-1ixzj8
https://wolfram.com/xid/0dc0043pid26-kac5li
https://wolfram.com/xid/0dc0043pid26-bo143a
https://wolfram.com/xid/0dc0043pid26-yecudt
A parallelogram is bounded and convex:
https://wolfram.com/xid/0dc0043pid26-2he09i
https://wolfram.com/xid/0dc0043pid26-h83yqs
https://wolfram.com/xid/0dc0043pid26-ob2jyv
https://wolfram.com/xid/0dc0043pid26-no6cil
Integrate over a parallelogram:
https://wolfram.com/xid/0dc0043pid26-njhdd8
https://wolfram.com/xid/0dc0043pid26-0d6ucc
https://wolfram.com/xid/0dc0043pid26-wcw40i
Optimize over a parallelogram:
https://wolfram.com/xid/0dc0043pid26-uqf85n
https://wolfram.com/xid/0dc0043pid26-01tr5b
Solve equations in a parallelogram:
https://wolfram.com/xid/0dc0043pid26-popyfw
https://wolfram.com/xid/0dc0043pid26-k3g63
Applications (5)Sample problems that can be solved with this function
A rhombus is a parallelogram in which all edges are the same length:
https://wolfram.com/xid/0dc0043pid26-dkn8xo
https://wolfram.com/xid/0dc0043pid26-bfgp4e
https://wolfram.com/xid/0dc0043pid26-iu15rb
https://wolfram.com/xid/0dc0043pid26-r36e35
A parallelogram with sides that form right angles is a rectangle:
https://wolfram.com/xid/0dc0043pid26-bf3o4w
https://wolfram.com/xid/0dc0043pid26-x57t6
https://wolfram.com/xid/0dc0043pid26-gj5001
Any rectangle can easily be converted to a parallelogram:
https://wolfram.com/xid/0dc0043pid26-jkwx2i
https://wolfram.com/xid/0dc0043pid26-qsv7a
https://wolfram.com/xid/0dc0043pid26-bzd4qd
The area of a parallelogram can easily be computed from the direction vectors:
https://wolfram.com/xid/0dc0043pid26-3k3ot
Simply treat the vectors as a matrix and take the absolute value of the determinant:
https://wolfram.com/xid/0dc0043pid26-cpb2we
Compare with Area:
https://wolfram.com/xid/0dc0043pid26-kp9kxi
A Parallelogram can tile the plane:
https://wolfram.com/xid/0dc0043pid26-y1pdi
Properties & Relations (6)Properties of the function, and connections to other functions
Rectangle is a special case of Parallelogram:
https://wolfram.com/xid/0dc0043pid26-6dnzw1
https://wolfram.com/xid/0dc0043pid26-480ckv
Polygon is a generalization of Parallelogram:
https://wolfram.com/xid/0dc0043pid26-bgriyc
https://wolfram.com/xid/0dc0043pid26-rf19ll
Parallelepiped generalizes Parallelogram to any dimension:
https://wolfram.com/xid/0dc0043pid26-6u0lw5
https://wolfram.com/xid/0dc0043pid26-ip9o39
ImplicitRegion can represent any parallelogram:
https://wolfram.com/xid/0dc0043pid26-t1wgy7
https://wolfram.com/xid/0dc0043pid26-8r4yt2
ParametricRegion can represent any parallelogram:
https://wolfram.com/xid/0dc0043pid26-8uijm8
https://wolfram.com/xid/0dc0043pid26-gdajfh
A parallelogram can be represented as the union of two triangles:
https://wolfram.com/xid/0dc0043pid26-qd7i83
https://wolfram.com/xid/0dc0043pid26-418m2k
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
]}
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
]}