Arts Curriculum

Geometric Shapes

"That early kindergarten experience with the straight line; the flat plane; the square; the triangle; the circle! If I wanted more, the square modified by the triangle gave the hexagon, the circle modified by the straight line would give the octagon. Adding thickness, getting 'sculpture' thereby, the square became the cube, the triangle the tetrahedron, the circle the sphere." (quoted at http://www.froebelweb.org/web2000.html)

Geometric Shapes

Frank Lloyd Wright once said, "the maple wood blocks . . . are in my fingers to this day." He acknowledged that his early exposure to the Froebel blocks had a lasting influence on his work. These wooden blocks were developed in the 1830s by Friedrich Froebel, a German educator and inventor of kindergarten, to help children learn about geometric forms, mathematics, and creative design. Wright’s career choice was determined by his mother, who wanted her son to grow up to build beautiful buildings and purchased the blocks for her young son. He was fascinated by them and acknowledged that his architectural designs were influenced by the geometric shapes he experimented with as a child.

As an architect Wright developed a system of rotating geometric forms that became one of his principal methods of design. Wright believed that geometry had cosmic meaning and that its use as the means of ordering design connected man to the cosmos. In this idealistic and romantic view, architecture could provide a means of harmony between the individual, society, and the universe (Anthony Alofsin, Frank Lloyd Wright: The Lost Years, 1910–1922: A Study of Influence [Chicago: University of Chicago Press, 1993], pp. 4–5).

Most buildings contain interior spaces that are rectilinear. Frank Lloyd Wright thought in curves and straight lines—triangles, circles, ovals, squares, and spirals—as well as shapes adapted from nature. For Wright, geometry was the basic building block of nature. Geometric forms also held symbolic significance. The circle, he said, suggested infinity; the triangle, structural unity; the spire, aspiration; the spiral, organic progress; and the square, integrity. Nearly all of these forms can be found in the architecture of the Guggenheim Museum (Frank Lloyd Wright: From Within Outward Audioguide [New York: Antenna Audio, Inc. and the Solomon R. Guggenheim Foundation, 2009]). Look down and you find circles in the terrazzo floor beneath your feet. Look up at the underside of the ramp and you see it punctuated by triangular lighting panels.

Wright believed that structure created beauty and geometric forms gave his work a consistent and systematic quality. This comprehensive vision in which aesthetics are inseparable from the universal principles of form informed Wright's work throughout the decades.

Frank Lloyd Wright

Frank Lloyd Wright

1. Look closely at the architectural drawing that provides a layout for the building. Which geometric shapes can you identify?

2. For the Guggenheim Museum, Wright used many geometric shapes but chose not to use rectangles or squares. Describe the experience of being in a building that is created without 90º angles.

3. Although most people associate circular forms with the Guggenheim Museum, Wright actually used many geometric shapes in its construction. Here is an inventory of some of them. As you explore the building, try to find them all!





  • Ask students to look around their classroom and perceive it as a series of shapes and forms, rather than as “a room.” How many different shapes and forms can they find? What shapes are the windows, doors, closets, and lighting fixtures? Make an inventory of the architectural shapes and spaces in your classroom. Some of the shapes and forms will have common names (circles, triangles, cylinders), while others either have less common names (trapezoids) or no names at all.
    Architecture/Design

  • Take a walk around a block in your neighborhood. Bring a sketchpad with you. Take notes and draw the geometric forms that you find as you look around.
    Visual Arts

  • Frank Lloyd Wright was around nine years old when his mother gave him his set of Froebel blocks. Many architects and educators believe that building blocks should be available to children more widely, and not just at the early childhood level. If you have a set of wooden blocks available, create a unique structure that uses geometric forms. Then describe how you incorporated various geometric shapes into your structure.
    Architecture/Design