A triangle as an orchestral instrument is not just any sort of metal triangle or something that may be used to call the wagons in for dinner.

A true triangle, properly tuned, is autonomous of the overtone series and is actually in tune with anything the orchestra may produce. This means that it produces a harmonic matching every perfect harmonic, perfect tone, and perfect overtone that can occur in nature.
An important definition in geometry about triangles is that the three vertices of any triangle are non-collinear. Which means the corners do not lie on the same line. This useful definition is often needed for many theorems about triangles to hold, including the uniqueness of barycentric coordinates in regard to a triangle.

More triangle nodes!

The Triangle is by far one of the most important shapes you will ever encounter, and that's not just because it looks cool. It is by far the most important shape to those of us in engineering analysis.

Triangles are used in a staggeringly large number of applications to create piecewise linear approximations to surfaces and volumes. Triangles and tetrahedrons are very adaptable in modeling the surface and volumetric curvature of many realistic shapes. Countless computer modeling packages exist that will create triangularized surface and volume meshes of an object and output this description to disk file.

Triangles are great for computer graphics because they are easy to transform and rasterize, and FAST. Practically all high-performance graphics accelerators are geared toward the rendering of texture-mapped triangles.

The right triangle is fundamentally bound to the sine and cosine, and there exist many geometric tricks to be used in analyzing triangles.

The triangle is fundamentally a rigid shape, and is used in countless structural designs for support members.

Triangles are great for electrical and mechanical engineering because they get along extremely well with finite element analysis. There are many very useful sets of linear and even higher order basis functions that have been developed specifically for triangular domains. There are closed form solutions for the two-dimensional fourier transform over an arbitrary triangle. This is extremely important when doing frequency-domain surface integrals involving triangular subdomains.

Moreover, triangles are also easy for the average person to see and understand. Three vertices, three interior angles, all adding up to 180 degrees, or pi radians. Really an awesome shape.

Inverted triangles of different colors were used by the Nazis to identify concentration camp and death camp prisoners' race/religion/arrest status.

Yellow Triangle: Jew
Red Triangle: Political prisoner (if the triangle pointed up it denoted a German political prisoner)
Pink Triangle: Homosexual
Green Triangle: Criminal
Black Triangle: Gypsies and "asocials" (mostly the homeless and prostitutes)
Blue Triangle: Emigrants
Purple Triangle: Jehovah's Witnesses

A letter in the middle of the triangle identified the person's nationality. For example, a T meant Czech, B meant Belgium, F meant France, and an I meant Italy.

Tri"an`gle (?), n. [L. triangulum, fr. triangulus triangular; tri- (see Tri-) + angulus angle: cf. F. triangle. See Angle a corner.]

1. Geom.

A figure bounded by three lines, and containing three angles.

⇒ A triangle is either plane, spherical, or curvilinear, according as its sides are straight lines, or arcs of great circles of a sphere, or any curved lines whatever. A plane triangle is designated as scalene, isosceles, or equilateral, according as it has no two sides equal, two sides equal, or all sides equal; and also as right-angled, or oblique-angled, according as it has one right angle, or none; and oblique-angled triangle is either acute-angled, or obtuse-angled, according as all the angles are acute, or one of them obtuse. The terms scalene, isosceles, equilateral, right-angled, acute-angled, and obtuse-angled, are applied to spherical triangles in the same sense as to plane triangles.

2. Mus.

An instrument of percussion, usually made of a rod of steel, bent into the form of a triangle, open at one angle, and sounded by being struck with a small metallic rod.

3.

A draughtsman's square in the form of a right-angled triangle.

4.

A kind of frame formed of three poles stuck in the ground and united at the top, to which soldiers were bound when undergoing corporal punishment, -- now disused.

5. Astron. (a)

A small constellation situated between Aries and Andromeda.

(b)

A small constellation near the South Pole, containing three bright stars.

Triangle spider Zool., a small American spider (Hyptiotes Americanus) of the family Ciniflonidae, living among the dead branches of evergreen trees. It constructs a triangular web, or net, usually composed of four radii crossed by a double elastic fiber. The spider holds the thread at the apex of the web and stretches it tight, but lets go and springs the net when an insect comes in contact with it.