Art, Design, and Biology

The Art and the Artists

When talking about shapes in paintings, Piet Mondrian is often the first artist to come to mind. He is famous for his big squares and rectangles in primary colors, as well as his bold intersecting black lines. Mondrian seems like the natural choice as the first artist to use to draw students into this unit because his work is relatively ubiquitous within school art classrooms around the country. Mondrian was a painter from the Netherlands, born in the late nineteenth century. He began his career as a teacher, painting as a hobby. His early works were representational; many of them featuring trees. As cubism began to take hold of the art world in the 1910s, Mondrian’s work became more and more cubist-inspired although still representational while being dominated by geometric shapes.⁶ He was intrigued by the idea of French painter Paul Cézanne that “Everything in Nature is modeled like spheres, cones, and cylinders.⁷”  From 1921-1944, Mondrian produced his most iconic works, his abstracted shapes in primary colors positioned in a grid laid out with thick black lines. Mondrian’s work is all under copyright by the Mondrian/Holtz Trust, and can be viewed on their website, in addition to the websites of the museums at which they are housed. Specific art pieces to look at for this unit: Broadway Boogie Woogie, Victory Boogie Woogie, Composition with Red, Yellow, and Blue, and Composition A. Although his works are unavailable for publication, the photo below of a stone wall is oddly similar to Mondrian’s compositions and can be sufficient for example until his actual work can be viewed online.

Wall. Photographed July 2025, New Haven, CT, by author.

(Fig. 1)

Another artist big into shapes, and also popular in the elementary art studio, is Wassily Kandinsky. Kandinsky was a Russian painter who lived roughly around the same time as Piet Mondrian, and experienced a similar transition from representational art to abstract art. Unlike Mondrian, Kandinsky’s work is curvy, angular, and highly colorful⁸. Whereas one could say that Mondrian’s work is organized and calm, Kandinsky’s work is energetic and chaotic. These two artists’ works together make a rich set of examples to draw from in a geometry classroom to get students excited about and engaged with the math as well as the art. Some of his work is in the public domain, such as his Composition VIII (1923), seen below.

Composition VIII. Wassily Kandinsky (1923)

(Fig. 2)

Moving on into symmetry (and translations,) we come to Georgia O’Keeffe and her larger than life paintings of natural forms O’Keeffe was an American artist, born in Wisconsin at the end of the nineteenth century.  She traveled often for inspiration for her art, and favored New Mexico for the landscapes and other natural features. Beginning around 1916, her depictions of nature often contain some degree of symmetry. Many of her paintings of flowers, landscapes, and animal skulls contain a high degree of bilateral symmetry. Even many of her later abstract paintings show bilateral symmetry.

Breaking from traditional study of art in schools, I intend to bring in the works of textile artist William Morris. Morris’s work shows perfect symmetry, unlike O’Keeffe’s work that is less than perfect. Morris was a nineteenth century British designer, and his textiles are almost exclusively nature-inspired. His works portray flowers, fruits, birds, and plants¹⁰. Given the nature of prints, his works show symmetry in a way that will be very clear to students where lines of symmetry are, and help them to understand transformations on the coordinate plane. Strawberry Thief is a great illustration, as a textile, of symmetry that shows both plants and animals. His wallpaper design Trellis, as introduced to me in Professor Barringer’s class, shows symmetry in small places but not in the overall design.

(Fig. 3)

Strawberry Thief Furnishing Fabric. 1883 (designed), 1883-1919 (made)

William Morris

The Victoria and Albert Museum, United Kingdom

Pattern comes into play in high school geometry as it applies to similarity and congruence. Reinforcing the idea that all circles are similar to one another, Yayoi Kusama brings an eccentricity and contemporary flair to art installations. Kusama is a modern artist from Japan, she’s known for her large installations covered in dots. Her work is evocative of hallucinations, which she herself experienced as a child¹¹. Kusama uses differently sized dots to create illusions of movement and dimension by repeating patterns of dots of varying diameters all over her work. She still lives and works in her studio in Japan. Any of her large installations are fantastic for students to look at and analyze, as well as her individual works on canvas.

Moving into more cultural and traditional patterns; Sydney Parkinson, an artist introduced to me in Tim Barringer’s seminar, drew Maori men’s faces showing their traditional face tattoos. Parkinson was an 18th century Scottish artist who primarily made botanical art, but drew several famous works of Maori men with heavily tattooed faces while on expedition with Captain Cook¹². These tattoos are very detailed and highly patterned, as well as symmetrical. The repeated lines and swirls in the tattoo depictions show the importance of ritual to the Maori, and represent the importance of pattern in ritual and decorative design and tattoos over the ages.

Finally, tessellations come in to tie it all together and close out the introduction to geometry, and we turn to none other than M.C. Escher. Maurits Cornelis Escher was born in the Netherlands at the turn of the 20th century, and is most famous for his illusion drawings. Escher also has some relatively famous drawings featuring creatures that repeat, rotate, and tessellate¹³. These are prime examples of tessellations, and are reminiscent of tiling which is a more practical application of tessellation. All of Escher’s work is owned by the M.C.Escher Foundation, which Escher established while he was still alive to preserve his work and legacy, and can be found at the foundation’s website.

Another celebrated application of historical tessellation can be found in Islamic art, both in illuminated texts and in mosaic works. These designs, sometimes known as “girih,” use many different geometric shapes to tessellate into a larger patterned design. These focus on abstract designs often resulted from the aniconism of Islam, many branches of which forbids depiction of people and animals.