The triangle is used as a tool in composition to indicate the important elements in a work of art. The artist will create the primary subject inside the boundaries of a large imaginary triangle. The viewer will intuitively be drawn into the important elements of the picture through the use of triangular composition. There may be smaller triangular compositions that complement the main subject. There are no rules as to the size or placement of the triangular composition. The neoclassical painter Jacques Louis David and the renaissance painter Leonardo Da Vinci make use of strong triangular compositions.
In the cubist movement of the early 20th century, the artists used triangles as a means of showing a three-dimensional object flattened on a two-dimensional surface. As the artists deconstructed and segmented an object into flat planes, the triangle emerged as a component and visual representation of their efforts. This is particularly apparent in Marcel Duchamp's, Nude Descending a Staircase.
The pyramids of Egypt take advantage of the golden triangle based on the golden ratio. The golden ratio is a mathematical calculation that describes an aesthetically pleasing rectangle used in art and architecture as early as 490 BC. The John Hancock building in Chicago is a modern example of blending art with architecture. Architects used a series of X shapes up the walls of the building resulting in decorative and structural triangular spaces. Buckminster Fuller's geodesic dome is a structure built of connected triangles that become both a structural and a design element.
Triangles are also used as formal geometric elements of design. The triangle actually becomes the subject of many modern painters and designers. It is used in furniture, architecture, industrial design, interior design and graphic arts. Tessellations make use of a triangular grid pattern to create decorative designs. A good example of tessellation can be found in the work of MC Escher.