Elementary facts about triangles were presented by Euclid, in books 1–4 of his Elements, written around 300 BC. In rigorous treatments, a triangle is therefore called a 2- simplex (see also Polytope). Triangles are assumed to be two- dimensional plane figures, unless the context provides otherwise (see § Non-planar triangles, below). This article is about straight-sided triangles in Euclidean geometry, except where otherwise noted.Ī triangle with vertices A, īasic facts A triangle, showing exterior angle d. A curvilinear triangle is a shape with three curved sides, for instance a circular triangle with circular-arc sides. A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides which are straight relative to the surface. In non-Euclidean geometries three straight segments also determine a triangle, for instance a spherical triangle or hyperbolic triangle. More generally, several points in Euclidean space of arbitrary dimension determine a simplex. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points, when non- collinear, determine a unique triangle situated within a unique flat plane. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex. The triangle's interior is a two-dimensional region. The corners, also called vertices, are zero- dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |