triangle

Types of triangles:

• equilateral triangle - All sides are congruent.
• isosceles triangle - Two sides are congruent.
• scalene triangle (yet to be noded) - No two sides are congruent.
• right triangle - One angle is a right angle.

Some centers of triangles:

• incenter
• centroid
• orthocenter
• circumcenter
• nine point circle center - See: Nine Point Circle Theorem.

Theorems about triangles:

• Napoleon's Theorem
• Theorem of Snapper
• Pythagorean Theorem
• Nine Point Circle Theorem
• Hero's formula for the area of a triangle
• Theorem of Menelaus
• Theorem of Ceva

More triangle nodes!

• barycentric coordinates
• trilinear coordinates (yet to be noded)
• parallel postulate
• Euler line
• isogonal (YTBN)
• isotomic (YTBN)

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.

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.

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.

© Webster 1913.