triangle, in mathematics
triangle, in mathematics, plane figure bounded by three straight lines, the sides, which intersect at three points called the vertices. Any one of the sides may be considered the base of the triangle. The perpendicular distance from a base to the opposite vertex is called an altitude. The area of a triangle is equal to one half the product of the base and the corresponding altitude. The line segment joining the midpoint of a side to the opposite vertex is called a median. All three altitudes of a triangle go through a single point, and all three medians go through a single (usually different) point. In Euclidean geometry the sum of the angles of a triangle is equal to two right angles (180°). If all three angles of a triangle are equal, the triangle is called equilateral. An isosceles triangle has two equal angles. A scalene triangle is one in which all three angles are different. A right triangle has one right angle. In geometry it is shown that two triangles are congruent (i.e., are the same shape and size) if, in general, any three independent parts (sides or angles) of one are the same as the corresponding three parts of the other. The rules of congruency make it possible, in trigonometry, to compute the sides and the angles of a triangle when three of these values are known. The triangle is the simplest of the polygons (i.e., it has the least possible number of sides). Since any polygon can be broken up into triangles by drawing various diagonals, a complete theory of the measurement of triangles provides a complete theory of the measurement of all polygons. In non-Euclidean geometries, the angles of a triangle are either less than two right angles (hyperbolic geometry) or more than two right angles (elliptic geometry).triangle, in music
triangle, in music, percussion instrument consisting of a steel rod bent into a triangle, open at one angle, and struck with a steel rod. Only since the end of the 18th cent. has it been an orchestral instrument, although it appeared in Europe much earlier. Its tinkling sound is of indefinite pitch and therefore blends with whatever harmonies the orchestra produces.triangle
Geometric figure with three sides and three angles. Each two sides meet at a point called a vertex, and the three angles sum to 180°. A triangle with one 90° (right) angle is a right triangle. A triangle with all sides (and thus all angles) equal is equilateral, one with two sides equal is isosceles, and one with no two sides equal is scalene. Triangles are particularly useful in surveying, astronomy, and navigation. Two observation points (sight lines) form a triangle with a reference object serving as one vertex and the observation points as the other two. Knowing the angles of the sight lines and the distance between the observation points allows the calculation of the lengths of the other sides using the methods of trigonometry.
triangle
A three-sided polygon. In 3D graphics, the surfaces of 3D objects are broken down into triangles. Small numbers of triangles are used for flat surfaces, while large numbers are used to mold curved surfaces similar to the way a geodesic dome is constructed. The three points of every triangle (vertices) are computed on an X-Y-Z scale and must be recomputed each time the object is moved. See triangle setup and geometry calculations.
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| The smaller the triangle, the more realistic the curve. It takes an enormous number of triangles to simulate totally round objects. (Image courtesy of Intergraph Computer Systems.) |
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