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The Hidden Geometry Ruling The World

Princeton Architectural Press reissues Bruno Munari’s Square, Circle, and Triangle books.

During his prolific career, Bruno Munari expressed his creative vision through painting, sculpture, film, and photography, but books were his greatest medium. Three of his most famous publications are Square, Circle, and Triangle, which explore the world’s basic geometric building blocks. Munari unpacks how mathematicians, designers, architects, and artists have used shapes from ancient times to today. In doing so, he demystifies why our environments look like they do.

“The square is the finest expression of a spatial idea complete in itself,” Munari writes. “It’s structural possibilities have helped artists and architects of all generations and styles by giving them a harmonic skeleton to which to apply an artistic construction.” The shape was used as a basis for Babylonian cities, he reveals, and Egyptians used it to lay the groundwork for their art. The organic growth of shells follows a logarithmic spiral, which is derived from a square. A silver square was even worn during the Dark Ages because it was believed to ward off the plague.

Then there is the circle, the shape of all things spiritual. “While the square is closely linked to man and his constructions, to architecture, harmonious structures, writing, and so on, the circle is related to the divine,” Munari writes. Consider the symbolism of rings and halos; how circles are used in folk dancing; how rotating discs create optical illusions; and how mathematicians have explored the proportions and ratios of a perfect circle.

Munari’s final installment centers on the equilateral triangle: “the most stable form with its fixed structure of three equal sides and three equal angles. Its distinctive structure means we find it in lots of complex structures and in many mineral and vegetable forms and structures found in nature ranging from the clover to the oleander.” The inside of a banana and cucumber are essentially divided into triangles; the shape is found in street signs and logos; and triangles are found in traditional Japanese weaving, among other places.

The bigger takeaway here is that geometry–typically a dry topic for anyone who’s taken a high school math class–takes on new import when seen through Munari’s culture-rich lens. Shapes draw out our shared experiences, telling us where we’ve been, and where we’re headed.

Princeton Architectural Press has combined the three tomes into a single volume, Bruno Munari: Square Circle Triangle, which is available to purchase here.

About the author

Diana Budds is a New York–based writer covering design and the built environment.



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