Art and Geometry: a connected vision

Geometry is also beauty, rhythm, and balance, and few spaces reveal this connection as clearly as the world of art.

From Islamic art to Cubism, through Renaissance domes and the intricate structures of contemporary art, geometric shapes have been essential tools for artists throughout history. Understanding these forms not only enhances students’ visual analysis skills, but also invites them to discover that mathematics lives beyond the classroom in the colors and shapes of a painting or a sculpture.

Cubism revolutionized the way reality was represented. Using geometric figures such as triangles, trapezoids, rectangles, and straight lines, artists broke down objects and faces into planes, allowing viewers to see how geometric forms create depth and multiple perspectives within a single image.

Figure 1: Picasso’s Cubism.

The golden ratio (proporción áurea) has been used for centuries to achieve visual harmony in paintings, sculptures, and architecture.

Figure 2: The golden ratio.

Without depicting human figures, Islamic art is based on symmetry, tessellations, and complex patterns featuring shapes such as hexagons, eight-pointed stars, and regular polygons. The mosaics of the Alhambra are an impressive example of how geometry becomes pure art.

Figure 3: mosaics of the Alhambra.

 

Regarding the Renaissance domes mentioned earlier, architects like Brunelleschi designed incredible structures by combining art, geometry, and technology. The dome of Santa Maria del Fiore in Florence is an iconic example of the use of shapes such as the ellipse, the octagon, and the semicircle.

Figure 4: dome of Santa Maria del Fiore (Florence).

An excellent way to explore the relationship between art and geometry is to organize a museum visit. Before the trip, a visual guide can be prepared in class introducing key concepts such as symmetry, patterns, flat shapes in painting (triangles, circles, rectangles), and volumes in sculpture (spheres, cylinders, prisms). During the visit, students can engage in a “geometric scavenger hunt” with challenges like finding a painting with a clearly visible triangle and identifying its role in the composition, locating a sculpture based on cylindrical shapes, recognizing symmetries in an artwork, or spotting repeated patterns. Students can take notes, make sketches, or take photos (if allowed) to later work with this material in class. As a follow-up activity, they can create an artwork inspired by geometric figures, such as an abstract design using rulers and compasses, a geometric reinterpretation of a famous work (for example, by Mondrian or Picasso), or the creation of a pattern based on the Alhambra mosaics, exploring translations, rotations, and symmetries.