09-15-2026, 04:35 PM
The article “The geometric theorems of Almada Negreiros” by Pedro J. Freitas examines the unusual intersection of mathematics and art in the work of Portuguese artist Almada Negreiros (1893–1970). Negreiros believed that a universal geometric system—his “Canon”—underlay visual art across cultures and historical periods. His artistic constructions made extensive use of geometric proportions, the golden ratio, divisions of the circle, and geometric shapes such as pentagrams.
Remarkably, many of his drawings were not merely artistic compositions: they encoded geometric constructions and mathematical relationships. For example, some constructions produce rectangles with exact proportions involving the golden ratio, while others approximate divisions of a circle into 9, 10, or 14 equal parts.
A particularly interesting aspect is the tension between exact mathematics and visual approximation. By the Gauss–Wantzel theorem, a circle cannot be divided exactly into 9 or 14 parts using only straightedge and compass, yet Negreiros produced remarkably accurate visual constructions; his approximation for a ninth of a circle has an error of only about 0.001% in one construction.
He was more concerned with visual harmony and symbolic meaning than with rigorous mathematical distinction between exact and approximate results. The article argues that his work is therefore significant both artistically and mathematically: it demonstrates how geometric intuition can inspire original constructions while also revealing a distinctive philosophy in which geometry becomes a universal language connecting mathematics, art, history, and culture.
ARTICLE [PDF]
Remarkably, many of his drawings were not merely artistic compositions: they encoded geometric constructions and mathematical relationships. For example, some constructions produce rectangles with exact proportions involving the golden ratio, while others approximate divisions of a circle into 9, 10, or 14 equal parts.
A particularly interesting aspect is the tension between exact mathematics and visual approximation. By the Gauss–Wantzel theorem, a circle cannot be divided exactly into 9 or 14 parts using only straightedge and compass, yet Negreiros produced remarkably accurate visual constructions; his approximation for a ninth of a circle has an error of only about 0.001% in one construction.
He was more concerned with visual harmony and symbolic meaning than with rigorous mathematical distinction between exact and approximate results. The article argues that his work is therefore significant both artistically and mathematically: it demonstrates how geometric intuition can inspire original constructions while also revealing a distinctive philosophy in which geometry becomes a universal language connecting mathematics, art, history, and culture.
ARTICLE [PDF]
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│ KONSTANTINOS MICHAILIDIS │
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