Triangle

Triangle[{p1,p2,p3}]

represents a filled triangle with corner points p1, p2, and p3.

Triangle[{{p11,p12,p13},}]

represents a collection of triangles.

Details and Options

Background & Context

Examples

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Basic Examples  (4)

A standard triangle in 2D:

A triangle in 3D:

Different styles applied to Triangle:

Area and centroid:

Scope  (18)

Graphics  (8)

Specification  (3)

A standard triangle in 2D:

A triangle in 3D:

Multiple triangles:

Styling  (2)

Color directives specify the face color:

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

Coordinates  (3)

Use Scaled coordinates:

Use ImageScaled coordinates:

Use Offset coordinates:

Regions  (10)

Embedding dimension is the length of the coordinates:

Geometric dimension refers to the region it specifies:

Membership testing:

Conditions for point membership:

Area:

Centroid:

Distance from a point to a Triangle:

Plot it:

Signed distance from a point to the triangle:

Plot it:

Nearest point:

Visualize it:

A triangle is bounded:

The bounding range:

Integrate over a triangle:

Optimize over a triangle:

Plot the function over the region:

Solve equations with triangle constraints:

Applications  (6)

The standard simplex and Kuhn simplex in 2D are triangles:

Define an equilateral triangle by side length:

Visualize it:

Compute its Area:

Equivalently use SSSTriangle:

Define an isosceles triangle by base length and height:

Visualize it:

Compute its Area:

Find a perpendicular bisector of a triangle:

Visualize circumcenter and bisectors in red:

One way of measuring the quality of a triangle is the radius/edge ratio:

A lower ratio indicates that the triangle will not be unusually thin:

A triangle can be subdivided into four sub-triangles:

This can be done recursively:

Properties & Relations  (5)

Triangle is a special case of Polygon:

Triangle is a special case of Simplex:

ImplicitRegion can represent any Triangle region:

ParametricRegion can represent any Triangle region:

BoundaryMeshRegion can represent any Triangle region:

Neat Examples  (1)

A collection of random triangles:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_triangle, author="Wolfram Research", title="{Triangle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Triangle.html}", note=[Accessed: 17-June-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_triangle, organization={Wolfram Research}, title={Triangle}, year={2019}, url={https://reference.wolfram.com/language/ref/Triangle.html}, note=[Accessed: 17-June-2021 ]}

CMS

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

APA

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