Mathematicians use lines and angles as the cornerstone of all geometric forms, and all first year geometry students study them. Historians have found lines on the cave drawings and hieroglyphics of early civilizations. Artists use them more than any other element of geometry. Lines and angles make up the foundation of any object. Artists use them to make objects appear closer or more distant, a technique called perspective.
Shapes comprise another aspect of geometry commonly found in art. Geometers manipulate lines to create shapes. Artists use these shapes as the building blocks of objects. They can break down most real-world objects into a series of basic geometric shapes. For example, a computer consists of rectangles and squares, a car has circular wheels and a house looks like a box with a pyramid on top. Artists use these shapes when drawing, sculpting or painting any object.
Historically, mathematicians and artists prescribed a special meaning to five specific shapes called "the platonic solids." The platonic solids combine triangles, squares and pentagons to make five three-dimensional shapes that geometers use to understand various aspects of nature. They classify these shapes into a group called polyhedra. Polyhedra show up in many religious and Renaissance paintings and are especially prevalent in Islamic artworks.
You find repeating patterns in nearly every style of art. They appear in Middle Eastern art, optical art and the drawings and paintings of artists like M.C. Escher. A special type of repeating pattern in which shapes interlock with one another without any gaps shows up in many forms of art. Geometers call these patterns tessellations. They use tessellations to describe the effect of an infinite mathematical series. In fine art, tessellations show up in drawings, paintings, sculptures and pottery.
Geometers use proportion to better understand the behavior of large shapes from smaller ones. The idea extends to the ratios they use to solve geometric equations. Artists use this concept to create aesthetically pleasing images. You find a common use of proportion in artwork of the human body. The artist attempts to make the image as real as possible by making each body part proportional to its real-life counterpart. You find proportion in any artwork representing a scaled-down version of a real-world object.