# Triangle

From Encyclopedia of Mathematics

*in the Euclidean plane*

Three points (the vertices) and the straight line segments (the sides) with ends at these points. Sometimes the definition of a triangle refers to the convex part of the plane that is bounded by the sides of the triangle (the solid triangle).

The notion of a triangle can be introduced in manifolds different from the Euclidean plane. A triangle is usually defined as three points and three geodesic segments with ends at these points. Such are *e.g.* spherical triangles in spherical geometry, and triangles in the hyperbolic or Lobachevskii plane (see Non-Euclidean geometries).

#### Comments

For relations between angles and sides of a triangle, see Plane trigonometry.

#### References

- [1] H.S.M. Coxeter, S.L. Greitzer, "Geometry revisited" , Math. Assoc. Amer. (1975) MR3155265
- [2] H.S.M. Coxeter, "Introduction to geometry" , Wiley (1969)
- [3] S.I. Zetel', "A new geometry of triangles" , Moscow (1962) (In Russian)
- [4] J. Hadamard, "Leçons de géométrie élémentaire. Géométrie plane" , J. Gabay, reprint (1990) pp. Chapt. 1
- [5] D. Efremov, "A new geometry of triangles" , Odessa (1902) (In Russian)
- [a1] M. Berger, "Geometry" ,
**1–2**, Springer (1987) Chapt. 9 (Translated from French)

**How to Cite This Entry:**

Triangle.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Triangle&oldid=54033

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article