The Dream of St. Joseph, Anton Raphael Mengs 1774

Geometry

The United States needs some theology and geometry, some taste and decency. I suspect that we are teetering on the edge of the abyss.

—A Confederacy of Dunces

A religious scene with a kneeling woman in a green gown at the front, holding out her arms. Behind her, a large seated man with a beard, surrounded by angels and people, some holding hands and others looking up at the sky. The background has a bright sky with clouds and a cross at the top center.

Louis Janmot, Génération divine 1854

Stone relief sculpture of a man working at a desk, surrounded by tools, with a grid overlay

Relief from Florence, Italy

A richly decorated painting with angels and cherubs on the borders, a central depiction of a woman in the sky surrounded by radiant clouds, with two children sitting on the grass looking at a geometric pattern overlay. The scene is illuminated with warm, divine light.

Morning, Philp Otto Runge, 1808

A classical painting depicting the death of Socrates, with Socrates calmly drinking poison, surrounded by his disciples and followers in ancient Greek attire.

The Death of Socrates, Jaques Louis David, 1787

Black and white classical painting depicting a heavenly scene with angels, gods, and mythological figures amidst clouds, some holding weapons and banners, surrounded by cherubs and divine beings.

Virgin of the Apocalypse, Miguel Cabrera, 1760

A painting of a group of people, including women and children, gathered together indoors, with a dog lying in front. The scene appears to be from the Renaissance period.

Las Meninas, Diego Velazquez, 1656

When you want to draw on a wall, first level the surface and then attach pieces of wood to the legs of a pair of metal compasses, to make them as long as you want, and tie a brush to one end so that you can mark with color the proportions of the figure and describe their halos. When you have marked the proportions of the figure, take some ochre and draw first with a watery solution. —Dionysius of Fourna, Painter's Manual, 1734

Albrecht Dürer, Knight, Death and the Devil (1513); it’s only about 9 ½ inches tall, remarkable for an engraving with such detail. There is a small lizard in the lower right-hand corner, that and the knight’s index finger were the two points I used, and they happen to lay a grid that’s perfectly oriented.

​Considering, however, that this is the true foundation for all painting, I have proposed myself to propound the elements for the use of all eager students of Art, and to instruct them how they may employ a system of Measurement with Rule and Compass, and thereby learn to recognize the real Truth, seeing it before their eyes. —Albrecht Dürer, The Painter’s Manual (1525)

​Michelangelo thought Dürer’s reliance on geometry was excessive, and is reported by Vasari to have said “It is necessary to keep one's compass in one's eyes and not in the hand, for the hands execute, but the eye judges.”

Last Judgment, Rubens, 1617

A classical religious painting of the resurrection of Jesus Christ, with figures emerging from a dark background, overlaid with geometric lines and star shapes.

Die Plejaden (The Pleiades), Moritz von Schwind, 1855

A surrealist artwork featuring a nude woman with wings sitting on a stacked platform with books and objects, a flying bird, and geometric shapes, with a landscape background. Next to it is a sketch of the same composition with construction lines, geometric guides, and rough details.

Fifty Secrets of Magic Craftsmanship, Salvador Dali:

As I do not wish you to spend days and killing hours which you might devote to painting at your mathematical calculations, I shall now reveal to you the secret of the compass—and this is Secret Number 47—by means of which you will be able automatically to find as many golden sections as you wish, without having recourse to the painful geometric operation for which you often need an immense compass, requiring that you go beyond the area of your painting, and this is often so inconvenient that your laziness will counsel you at last to get along without such a proportion... And the fact that such compasses are not currently for sale at paint dealers is but the proof of the lack of geometric rigor of schools of art, and of modern painters in particular.

Classical painting of the biblical story of Adam and Eve in the Garden of Eden, with numerous nude figures, trees, and a landscape background, overlaid with network lines.
A detailed drawing of Saint George slaying a dragon. Saint George is on horseback, wielding a spear, with a castle or city in the background and evidence of a battle scene around him.
Baroque painting depicting a chariot pulled by horses, surrounded by mythological figures, with dynamic movement and dramatic light.

The Fall of Phaeton, Rubens, 1605

The image depicts a detailed classical painting with numerous figures, including mythological or historical characters, engaging in various activities. There is a focus on a dynamic scene with figures in motion, some holding shields and weapons, suggesting a scene of conflict or storytelling from ancient times.

Forge of Vulcan, Giorgio Vasari, 1564

Painting of the Christian biblical scene of the body of Jesus Christ after crucifixion, surrounded by mourners, with a halo around Jesus' head, depicting the Pietà.
A painting of the last supper, with Jesus Christ at the center surrounded by his disciples, some of whom are reaching out or looking at him. The scene is illuminated by a candle held by one of the disciples.

The Mocking of Christ, Gerard van Honthorst, 1617

A classical painting depicting a religious scene with multiple figures, some holding globes representing celestial bodies, engaging in conversation or observation.

School of Athens, Raphael, 1511

A painting depicting the Madonna and Child surrounded by six saints, set against a classical background with columns and trees.
A religious painting depicting the Madonna and Child, featuring detailed floral and landscape background, with a nearly symmetrical floral geometric pattern overlay.

Lenti Madonna, Carlo Crivelli 1480

A classical painting depicting the biblical story of the resurrection of Lazarus, with figures gathered around Lazarus' grave, including an angel above and people observing him.

Nativity with Saint Francis and Saint Lawrence, Caravaggio 1609

A religious painting depicting Jesus Christ with a beard and long hair, resting his head on his hand and appearing thoughtful, seated with a robe draped over his shoulder, and an angelic figure with blonde hair, wearing a white garment, reaching out towards Jesus with a caring expression.
A surreal painting depicting mythological and fantastical figures, partially obscured by white geometric lines forming a web, with humanoid bodies, mythical creatures, and dark stormy clouds in the background.

The Witches Going to Their Sabbath, Luis Ridardo Falero, 1878

A vintage black and white illustration of a circus or carnival scene featuring a woman performing an acrobatic act on a horse, surrounded by an audience of men, women, and children in a theater setting.
Painting of a lively scene with an assortment of men, some in historical costumes, gathered around a table outdoors with a background of a cloudy sky and soldiers with flags.
A historical painting depicting a scene of people gathered in an ancient Roman setting, with some figures engaged in a discussion or activity, and others observing, illuminated by natural light from large arches.

The Wedding at Cana, Carl Bloch, 1870

The Circus, Georges Seurat, 1891

Black and white classical painting of a woman surrounded by children, with lines overlaying the image.

Charity, Francesco Salviati, 1548

Madonna Enthroned with Child and Saints, Giovanni Bellini 1605

A classical religious painting depicting Jesus Christ surrounded by various figures, including angels and people, with a sky background and a horizon line.

The Death of Moses, Alexandre Cabanel 1851

A religious artwork depicting the Virgin Mary surrounded by angels and children, with Christ at the center, as seen in Renaissance style.

Annunciation, Bartolomé Esteban Perez Murillo, 1660

A classical painting depicting a mythological scene with a winged figure, possibly an angel or mythic creature, holding a transparent orb or sphere. The scene appears dynamic, with figures in movement, set against a dark background with energetic brushstrokes and a sense of drama.

Leda and the Swan, Gustave Moreau 1882

A classical painting depicting a tumultuous scene of people on a makeshift boat amidst a stormy sea, capturing emotional expressions of distress, struggle, and chaos.

The Raft of the Medusa, Théodore Géricault, 1819

Reply of the Zaporozhian Cossacks, Ilya Repin, 1891

Two children, a boy and a girl, dancing outside on a path surrounded by plants, under a nighttime sky with stars, with geometric line overlays.

The Storm, Pierre Auguste Cot, 1880

A historical painting depicting a biblical scene with multiple figures, some with animals, set against a landscape background with hills and buildings, overlaid with white geometric lines connecting various points.

The Liberation of Andromeda, Piero di Cosimo, 1510

A classical painting depicting a scene with angels, a woman, and a mythical creature, overlaid with a network of white lines connecting various points across the image.
A complex, surreal painting with many fantastical and bizarre creatures, figures, and elements intertwined across the canvas. There are angels, animals, human figures, and mythical beings in a chaotic arrangement.

Le Passage des âmes (The Passage of the Soul), Louis Janmot, 1854

The Fall of the Rebel Angels, Pieter Bruegel the Elder, 1562


A black and white painting depicting a lively outdoor scene with children and adults dancing and socializing in a rural village setting, with trees and houses in the background.

The Peasant Dance, Pieter Brueguel the Elder, 1567

Painting of a woman with long dark hair and a flowing dress, surrounded by two cherubs, one with a bow and arrow, and the other with a book, set against a dark background.

Night with the Geniuses of Love and Study, Pedro Americano, 1883

The image depicts a classical painting of the biblical scene of the baptism of Jesus, with Jesus standing in a large shell-shaped basin, a woman pouring water over his head, with angels and a dove representing the Holy Spirit nearby, and lush trees in the background.

The Birth of Venus, Sandro Botticelli, 1480

Black and white illustration of a man in a suit observing a mural with dancing women, musical notes, and abstract patterns.

Le Chahut, Georges Seurat, 1890

A classical painting of nude women by a pond, with a woman lying on the grass in the foreground, surrounded by others sitting and standing, amid lush green trees.

The Nymphaeum, William-Adolphe Bouguereau, 1878

Christ Blessing the Children, Lucas Cranach the Elder, 1537

Pietà, William-Adolphe Bouguereau, 1876

A religious artwork depicting the Annunciation, with the angel Gabriel kneeling and extending a hand towards the Virgin Mary, who is praying with hands crossed over her chest, surrounded by cherubs and angels in the sky.
A historical scene with a crowd of people dressed in 18th-century clothing, including men, women, and children, engaging in a social gathering outdoors. Some are talking, while others appear to be listening or watching something. There are buildings and trees in the background.

The Card Sharp on the Boulevard, Louis-Léopold Boilly, 1806

A classical painting depicting the Nativity scene with Mary, Joseph, baby Jesus, angels, and other figures, overlaid with geometric lines.

Allegory of the Night, Jan van den Hoecke, 1650

A mural depicts a woman with dark hair taking a selfie, seated on a pedestal, with a flying eagle and geometric shapes around her.

Leda Atomica, Salvador Dali, 1949

The Golden Age (detail) (1862), Ingres. “I began from the background, with the architecture. Once the lines were marked out, I called all my figures, one by one, and they came obediently to take their places in the perspective.” Charles Blanc, quoting Ingres in Ingres, sa vie et ses ouvrages, Paris 1870


A classical religious painting depicting the Last Judgment with Jesus Christ in a red robe at the center, surrounded by angels and saints. Beneath, numerous naked souls are shown in various states of suffering and salvation, with some ascending to heaven and others descending to hell. The scene is dramatic with a cloud-filled sky in the background.

​Charles Bouleau, The Painter's Secret Geometry:

​In the Middle Ages the 'geometry' of a work of art, whether picture, bas-relief or page of manuscript, consisted chiefly in the use of the regular polygons as an armature, as an interior framework, figures that were sometimes quite complicated, with five, six, or eight sides, not forgetting the double figures formed by the star pentagons and hexagons.

Dropbox file with examples of geometric grids used in paintings: www.dropbox.com/sh/15peqzgebsok8zy/AAAXy4W00NuipnfgD3s-q6xva?dl=0