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.