Triangle - Using the side lengths and a numerically stable formula

A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. Triangle - Types of triangles. Triangles can be classified according to the relative lengths of their sides: In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon In an isosceles triangle two sid ...

Including:

• Triangle - Types of triangles
• Triangle - Basic facts
• Triangle - Points lines and circles associated with a triangle
• Triangle - Computing the area of a triangle
• Triangle - Using geometry
• Triangle - Using vectors
• Triangle - Using trigonometry
• Triangle - Using coordinates
• Triangle - Using Heron's formula
• Triangle - Using the side lengths and a numerically stable formula
• Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia - Triangle

There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...

See also:

Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Points lines and circles associated with a triangle

Calculating the area of a triangle is an elementary problem encountered often in many different situations. Various approaches exist, depending on what is known about the triangle. What follows is a selection of frequently used formulae for the area of a triangle. Triangle - Using geometry. The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base. ...

See also:

Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Computing the area of a triangle

Elementary facts about triangles were presented by Euclid in books 1-4 of his Elements around 300 BCE. A triangle is a polygon and a 2-simplex (see polytope). Two triangles are said to be similar if and only if the angles of one are equal to the corresponding angles of the other. In this case, the lengths of their corresponding sides are proportional. This occurs for example when two triangles share an angle and the sides opposite to that angle are parallel. Using right triangles and the concept of similarity, the trigonometric functions sine and cosine can be defined. These are functions of an angle ...

See also:

Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Basic facts

Triangles can be classified according to the relative lengths of their sides: In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon In an isosceles triangle two sides are of equal length. An isosceles triangle also has two equal internal angles (namely, the angles where each of the equal sides meets the third side). In a scalene triangle all sides have different lengths. The internal angles ...

See also:

Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Types of triangles

There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...

See also:

Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points, lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Points, lines and circles associated with a triangle