It’s an adorable subject for me,” Mark Reynolds says about geometry. “It has a consciousness. It’s not dry; it’s musical, poetic, and speculative.” The San Francisco–based artist is known for his obsessive, seductive drawings that derive primarily from mathematical relations, expressed, as he describes it, in “shape, size, relative position of figures, and the properties of space.”

Dizzyingly shifting perspectives and kaleidoscopic effects entrap viewers in such a way that their eyes can never rest. Reynolds likes to work mostly with 15-by-22-inch paper, and he draws primarily with powdered pigments, graphite, pen and ink, and pastel—“usually dry media,” he says.

The 69-year-old Baltimore-born artist teaches at the Academy of Art University in San Francisco in the liberal arts department. He spends considerable time in Italy and is represented by Pierogi Gallery in New York.

Reynolds attended Towson University in Maryland, where he studied fine art and art education. He started out doing freelance illustration and design, including advertising art and romance-book covers. “At the beginning, I was doing kind of surreal work—I looked for subject matter in clouds,” Reynolds says, emphasizing how he focused on color, line, and shape—“not narrative.” And that inclination persists in his art, which draws inspiration from music, art history, and architecture.

His drawings are distinguished by the disjunctions between their soft-colored lines and sharp angles. Filled with surprises, his work disarmingly calls to mind that of Piero della Francesca, in its colors and deep perspectives, Paul Klee, in its musicality and lyricism, and Sol LeWitt, in its varying geometries. Reynolds’s most recent pieces, he says, are based on the golden section family of ratios, or divine proportion, which governs ratios in patterns found throughout nature and the human body. “One new series has put mirror symmetry—bilateral like our faces—into my work, big time. It’s taken some getting used to for me.”

Explaining his approach, Reynolds says, “I deal with irrational numbers that can’t be measured. I try to begin with two ratios and put unlikely ones together. It’s like rap and Mozart, or Beethoven and the Beastie Boys—you put them together and something new emerges.”

Music itself, with its emotional and spiritual associations and effects, is very much a part of the work. The relationship between two lines of different lengths could equate with the strings of a piano, for example. The compositional grids in his drawings can be viewed as the result of the vibrations of two strings. “I’m working with harmonics,” Reynolds explains, “which change based on the lengths of the lines.” A high sound is produced by a short string on an instrument, whereas a long string yields a low sound. Reynolds can hear sound through such visual cues as the length of lines, as in his Marriage of Incommensurables Series: 1.902 and Root 2, 4.13 (2013).

Studies have shown that “the minor third is the saddest sound in music,” he says. So if you produce an image of a minor chord, visualizing it can have the effect of the sound, and that’s one source of emotional resonance in his work.

“While many art students go through their drawing courses working from life,” Reynolds says, “I don’t have many external references.” Geometry enables him to avoid, he points out, “narrative, social, political, sexual, athletic, hierarchical, fashionable, and other debate-filled issues.”

“I know I’m an artist, not a mathematician,” Reynolds says, “but sometimes when I’m around artists, I feel that I am a mathematician. The funny thing is, I’m not gifted with numbers, just geometry.”

A version of this story originally appeared in the September 2014 issue of ArtNews on page 56 under the title “Rational Art About Irrational Numbers”.