Geometric patterns can be found in a number of classical works, although they are concealed from view. Leonardo Da Vinci used a geometric formula known as the golden ratio, which he called the divine proportion, in many of his works. The geometric application of this ratio results in rectangles that have sides whose lengths, when divided, equal approximately 1.618. Da Vinci's famous "The Vertruvian Man" sketch can be broken down into a series of these rectangles, known as golden rectangles. The golden ratio pattern can be overt and represented by geometric figures whose sides conform to the ratio, or like Da Vinci's work, the pattern can be hidden.
Geometric patterns also play a significant role in the artworks of different cultures. Islamic art, in particular, features thousands of pieces that display geometric patterns of all kinds. Artists looking for ideas on how to use geometric patterns need only study the carpets and stained windows of the Ottoman Empire to see how sharp lines and a myriad of shapes can combine to form complex patterns. Intricate tile patterns, known as tessellations, prominent in Islamic art influenced the style of Dutch artist M.C. Escher, who was well known for his works that featured patterns, which repeated across a two-dimensional plane without overlapping.The Plains Indians of North America also make use of geometric patterns in their art. Specifically, the loom bead work of these tribes feature multi-colored geometric patterns of diamonds and triangles.
Abstract art makes use of basic geometric shapes and patterns to convey, in part, ideas about the reformation of form and space. Abstract art evolved from cubism, a form pioneered by Pablo Picasso. Artists looking to gain inspiration for geometric patterns in abstract art should also study Piet Mondrian. According to the Metropolitan Museum of Art, Mondrian became the main proponent for geometric abstract language in art during the early 20th century. His style, dubbed "Neoplasticism," intended to convey the reality that geometric forms act as the basis for reality. His works feature canvasses segmented by straight black lines and adorned with large squares of primary colors.
Optical art, or op art, is an attempt by artists to create a three-dimensional perspective on a two-dimensional surface. The disorienting effects of op art appear due to the use of geometric patterns arranged in specific ways. Artists looking for inspiration in op art can study the works of Victor Vasarely or Bridget Riley. Specific patterns of op art, such as rokuyo stars, can be viewed in a number of online galleries, as well.