Editing Triangle (section)

=== Circular triangles ===
{{main article|Circular triangle}}
[[File:Circular_triangles_convex_concave.png|thumb|upright=1.35|Circular triangles with a mixture of convex and concave edges]]
A [[circular triangle]] is a triangle with circular [[Arc (geometry)|arc]] edges. The edges of a circular triangle may be either convex (bending outward) or concave (bending inward).{{efn|1=A subset of a plane is [[convex set|convex]] if, given any two points in that subset, the whole line segment joining them also lies within that subset.}} The intersection of three [[Disk (mathematics)|disk]]s forms a circular triangle whose sides are all convex. An example of a circular triangle with three convex edges is a [[Reuleaux triangle]], which can be made by intersecting three circles of equal size. The construction may be performed with a compass alone without needing a straightedge, by the [[Mohr–Mascheroni theorem]]. Alternatively, it can be constructed by rounding the sides of an equilateral triangle.<ref>{{multiref
|{{harvnb|Hann|2014|p=[https://books.google.com/books?id=-CX-AgAAQBAJ&pg=PA34 34]}}
|{{harvnb|Hungerbühler|1994}}
}}</ref>

A special case of concave circular triangle can be seen in a [[pseudotriangle]].{{sfn|Vahedi|van der Stappen|2008|p=[https://books.google.com/books?id=SLo6okq4wVgC&pg=PA73 73]}} A pseudotriangle is a [[Simply connected space|simply-connected]] subset of the plane lying between three mutually tangent convex regions. These sides are three smoothed curved lines connecting their endpoints called the ''cusp points''. Any pseudotriangle can be partitioned into many pseudotriangles with the boundaries of convex disks and [[Bitangent|bitangent lines]], a process known as pseudo-triangulation. For <math> n </math> disks in a pseudotriangle, the partition gives <math> 2n - 2 </math> pseudotriangles and <math> 3n - 3 </math> bitangent lines.{{sfn|Pocchiola|Vegter|1999|p=[https://books.google.com/books?id=vtkaCAAAQBAJ&pg=PA259 259]}} The [[convex hull]] of any pseudotriangle is a triangle.{{sfn|Devadoss|O'Rourke|2011|p=[https://books.google.com/books?id=InJL6iAaIQQC&pg=PA93 93]}}