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  2. Convex polygon - Wikipedia

    en.wikipedia.org/wiki/Convex_polygon

    An example of a convex polygon: a regular pentagon. In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). [1]

  3. Template:Infobox polygon - Wikipedia

    en.wikipedia.org/wiki/Template:Infobox_polygon

    Infobox for polygons, for example, triangles and squares. Template parameters [Edit template data] This template has custom formatting. Parameter Description Type Status Name of shape name no description Example Square String required Image of shape image no description File suggested Image caption caption no description Content optional Type type General type of this shape Content optional ...

  4. Convex geometry - Wikipedia

    en.wikipedia.org/wiki/Convex_geometry

    Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.

  5. List of regular polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_regular_polytopes

    The regular finite polygons in 3 dimensions are exactly the blends of the planar polygons (dimension 2) with the digon (dimension 1). They have vertices corresponding to a prism ({n/m}#{} where n is odd) or an antiprism ({n/m}#{} where n is even). All polygons in 3 space have an even number of vertices and edges.

  6. Regular polyhedron - Wikipedia

    en.wikipedia.org/wiki/Regular_polyhedron

    A regular polygon is a planar figure with all edges equal and all corners equal. A regular polyhedron is a solid (convex) figure with all faces being congruent regular polygons, the same number arranged all alike around each vertex.

  7. Convex curve - Wikipedia

    en.wikipedia.org/wiki/Convex_curve

    In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes. Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions.

  8. Shoelace formula - Wikipedia

    en.wikipedia.org/wiki/Shoelace_formula

    Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]

  9. Wallace–Bolyai–Gerwien theorem - Wikipedia

    en.wikipedia.org/wiki/Wallace–Bolyai–Gerwien...

    The minimum number n of pieces required to compose one polygon Q from another polygon P is denoted by σ(P,Q). Depending on the polygons, it is possible to estimate upper and lower bounds for σ(P,Q). For instance, Alfred Tarski proved that if P is convex and the diameters of P and Q are respectively given by d(P) and d(Q), then [3]

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