The Circle, the Square, and Botticelli with Parmigianino

Nested within my as-of-yet-unpublished book on composition are numerous artwork case studies, as well as discussions of compositional forms. This article’s compositional form can be described as the circle-square, which was inspired in part by the old mathematical puzzle of squaring the circle. One flawed example of it in 20th Century interpretations of composing, is this painting, a famous tondo by Botticelli:


(Botticelli, The Adoration of the Magi, National Gallery UK… the best place to see the painting online is at the National Gallery, UK (click this link for a scalable image).

[UPDATE: please note the terms above... what follows in this article is from 20th Century interpretations of composition, which is NOT how Botticelli composed. It is how some arts writers in the 20th Century superimposed their beliefs about geometry on everything they thought about older art forms, because they themselves were sometimes trying to justify their own use of geometry in abstract painting... they wanted to link it with tradition, even though there is little or not evidence of such geometry's use in the Renaissance.]

If you’re familiar with linear perspective, then you can figure out the central vanishing point from the big blocks of stone in the foreground; these lead towards the center and a bit high, where there is a hole in the wall and perhaps the manger in the story of Jesus’ birth. The perspective’s primary vanishing point is placed at that portion of the story dealing with beginnings. Therein is a huge concept, that the central point of the new perspective (new in Botticelli’s time) is also emblemizing the new beginnings of the new Christian story – such consistency of  perspective and message! This is typical of Renaissance art: the most important parts of a story are placed at the central vanishing point of the perspective, or at a location central to any larger symmetrical geometry, in order to emphasize the characters of the story. But the psychological center of our attention is not the same point, and is definitely the middle of the whole circle, where the Madonna and Child sit together, surrounded by their visitors.

You can also see right away that the arches of the ruins in the background repeat the circular format of the whole, as do the horse’s butts and arcing necks. Clearly this a very symmetrical composition, pointing our attention towards the center of the image, either the perspective’s center or the circle’s center. But why are the various figures and architectures placed where they are? Why did Botticelli put them there, and not at some other location? To form responses to these questions, we need to look at a more ornate form of the circle-cross pattern, extended into the square in the circle format. First you’ll need a basic understanding of the circle-cross, which is a form commonly found all over the world and in children’s art when they start combining scribbles into organized patterns. It’s just a circle with an x inside it. If you connect the intersections of the cross and the circle with straight lines, then you get the circle-square, which can be repeated and revised as needed.


Aligning major shapes by their centers or their edges to the axis of such a pattern is in the 20th Century said to be typical of classical and neoclassical composition, which was often governed by geometry, according to Kandinsky, Klee, Bouleau and other 20th Century artists interested in geometrics (falsely, I might add, because there’s no realistic evidence that Botticelli actually thought this way. But 20th Century artists did…)  The pattern’s simple, really – if you took one  of these patterns, you could take any other shape, and align it by its center, edges, or points of tangency (like a corner), to the compositional pattern:

Any of these formations could look good; but the non-aligned form would not be a classical type of composition. Only the geometric ones would be. The square shown above in many classical artworks would be a group of figures, in other words, an outline and shadow pattern arrangement that’s far more complex than a square – I’m just using the square to illustrate the main procedures: match to center, edge or tangency. Of these, the square centered on the middle of the circle was the main priority and requirement of the art, as specified by the Catholic Church, an expectation well-known to artists.

The circle-square compositional form in Renaissance  20th Century examples of  interpeting painting becomes ornate, and much more angular than rounded, like so:

The squaring of the circle pattern can nest within itself over and over again; it can be quite pretty. I didn’t draw in all repetitions of the square pattern, but you can see along the outer edges how if you repeat the squaring then you approximate a circle within the circle – if you kept going you’d get circles within the circles, all centered on the outermost circle’s center. The compositional form is repeating, scalable, and self-referentially centering. A drawing like this always includes some imprecision too, due to the thickness of the lines; the less careful you are with the layout, the more likely that angles and squares go a bit off center. This thickness problem happens with all grid and grid-like forms (which is why the ‘grid transfer’ method of moving one image to another surface is so unreliable).

According to Bouleau, in Painter’s Secret Geometry, Sandro Botticelli’s composition of the Adoration of the Magi (tondo), relies on the repeated circle in the square pattern. In his diagram, Bouleau removed most of the squares, and simplified this pattern so that you can see its parts more easily, and then he overlaid it onto Botticelli’s painting. The result is something like this (this is my graphic, based on Bouleau’s)

There are a variety of notation and perspective lines in Bouleau’s diagram that I didn’t draw in here, and my own notations are in blue. These blue lines reveal the location of the pillars of the ruins in the background of the painting, as given by the caesura lines from the circle-square compositional form. There are many other applicable caesura – such as through the middle of the painting. I haven’t really followed up on the idea but I wonder if, given the story’s cycle towards the idea of Ascension, if these upright movements might not be a kind of hint towards the future of this well-known story’s plot? This is a really, really loaded question. When looking at Bouleau’s diagrams, we must always keep in mind his role as an artist in the 20th Century… most of his book is rooted in his inventions that have nothing to do with the methods or ideas of composition used by prior generations of artists. He invented these forms, however, and we must understand them as 20th century geometric ways of looking at older pictures.

I think it’s fairly clear from Bouleau’s interpretation and my own analysis of the composition that Botticelli was atleast aware that a tondo has a middle center, and that architectural and perspectival forms within it could use verticals and horizontals. The center surely is used to place the Madonna and Child figures with considerable balance.

But Botticelli did not rely on this compositional form too closely, and certainly many shapes and figures do not fit the form – this is, in my oh-so-humble opinion, one of the marks of a truly great composition (and that Bouleau’s too-firm reliance on 20th century ideals really overstates his case): the artists uses and relates to rigorous symmetries throughout the image, but with flexibility and selective use of the form. Not everything has to fit for the painting to be great, and in fact, if it did all fit, it might lose a sense of the dynamic, of the messiness of real life. It would be too perfect to speak to real life.

To illustrate this point about mastery, here’s a funny thing to consider with this composition: why is it open in the sky on the upper right? Clearly Botticelli was very interested in symmetries, and if we repeat the circular pattern of the arches, then we see quickly that the painting is missing the upper right circle:

And in fact you can find good graphic reasons reflecting these four circles in the lower half of the painting, from the arcs of figures, their poses, or even the strange curve of a horse’s neck (lower right). Such devotion to symmetry seems to suggest that the painting is incomplete. So why not place a circular form in the upper right?

One response would be that keeping the sky open on the upper right helps to bring emphasis down to the amazing peacock in the middle right, who by the way, does have a long curvature to his tail that arcs upwards. A closer look reveals that the peacock is standing on a piece of a broken archway, there are hints of their circular format…

As a character in the scene, the peacock, by the way, has special significance in the history of European paintings and Christian symbolism. I’ve read many times that long ago the sky-goddess Juno had a chariot flown by peacocks, and as Mary became the new goddess, the peacock symbolism was coopted by Christian thinkers in her honor. There’s also the common hypothesis of the medieval belief that the peacock would never rot, thus symbolizing the eternal or immortal, allowing the image to be associated with the resurrection or eternal life of Jesus.  It might be that such imagery hints less at a literal circular visual pattern, and more at the idea of the circle of life, or at least the cycles of the well-known biblical stories.

Circles abound.  Around the peacock the branches also arc, as do the long tail feathers, and throughout the painting there are many instances of small circles made from hats, people’s heads, etc.  And actually another favorite detail from the painting is this little fellow, from the lower left foreground:

It’s a monkey, or baboon, or monkey-thing, quite human in pose, squatting/sitting/fetal curl – circle body with circular head and angled snout… more repeated curvatures. It’s not too much to assume, I think, that Botticelli was thinking about symmetries in both the story cycle as well as what could be observed in life and nature.

Doubt it? Next time you go the National Gallery I think you should spend a fair bit of time looking at this feature, which is the sexiest horse ass every painted!

That’s too obvious to be Freudian; and in any case, it is such an unnatural combination of legs and muscles that we must conclude the artist has made the image subservient to ideals of symmetry rather than to ideals of what horses actually look like.

None of this firmly answers the question, however, of why isn’t there some sort of circular pattern in the sky in the upper right?

I don’t have a firm answer. There probably isn’t one, and the easiest response is that that’s just the way Botticelli made the image: he felt like it. Maybe the ruins fell down? Standard art historical interpretations of the ruins in the background of the painting suggest that the motif of ancient ruins, common in Florentine art, reflected how the myths of the past have fallen into disregard and disrepair, to be supplanted by the universal ideals of the new Christianity, which were believed egalitarian and humanist, indeed applicable to all of nature including animals, and trees, and the distant sky. A new era is beginning, built on top of the old.

This strikes me as particularly powerful a metaphor in Italy, where there are countless ruins to be observed all over the countryside – indeed in Rome it is possible to look down the side of many buildings, whenever there’s some construction and some of the ground is dug away, to see layer after layer of changing stonework patterns that indicate how the building was placed one top of older culture’s constructions.

Bouleau contrasts Botticelli’s masterpiece with the work of a lesser-known artist, Botticini, who also created a tondo of the Adoration of the Magi, about twenty years later than Botticelli. Bouleau opines that:

“In the imitator we find a strictness that is more dry, and at the same time a greater quantity of decorative detail; everything is traced with the compass point, and the lines of perspective follow the diameters and intersect at the centre of the circle, realizing in a striking fashion that identification of perspective with the composition which is so frequent at this period… The figures have been made very small so as to fit into this complicated network – the scene has lost its ease.”  (PSG, p39)

This is the Botticini, and, well, I guess I agree with Bouleau’s assessment that the painting is a lot stiffer and less interesting than Botticelli’s:


There is, however, still a peacock in the upper right. So of course the painting is at least partially good. (The definition of a good painting is that it has a bird in it!) You can see right away, I think, a too-strict reliance on the circles in the square pattern. It’s quite a quote of the Botticelli, but with a fanciful boat on the left, thank goodness. Bouleau, so involved with his own geometric inventions, like many abstract painters of the 20th Century doesn’t really talk much about subject matter in the paintings. This is, I think, a compositional mistake: in the Renaissance the symbolism of every narrative painting was very well-established by religious traditions, and required. And why not paint a boat, if you can? It’s entertaining!

And just for the sake of variety, and evidencing a different compositional form for the circle, here is another tondo Adoration, from Fra Angelico and Lippi, around the same time period as the Botticini:

Compositional form = spiral pattern, not squared-circle. And, more peacocks, of course! Such art as this is profoundly beautiful, but foreign to the contemporary eye because it doesn’t rely on linear perspective or camera-like lensing to depict form.

Within fifty years of these early Renaissance circular-format compositions, the art of painting moves towards a much heavier emphasis on perspective and optics. To see this new optical, reflective look, consider Parmigianino’s Self Portrait in a Convex Mirror:

(Parmiginanino (c. 1524); Oil on wood, diameter 24.4 cm; Kunsthistorisches Museum, Vienna)

Parmiginanino’s name was actually Girolamo Francesco Maria Mazzola, from Parma. He chose to push far beyond the ideals of classicism and its geometric symmetries of number and form, and innovate the new style of Mannerism, which was part optical image, and part distorted, stretched and altered away from the stricter geometric formats for Classical imagery. In Parmiginanino’s work we can no longer rely on geometric compositional forms within the circle, and instead, must begin to consider idiosyncratic new uses of perspective, bent and reflected by a mirror – moving beyond confines and borders, out of the measures handed down to Renaissance artists from Pythagorus.

But Parmiginanino still chose to use the circle, which still had a centering, symmetrical general perimeter or frame, and a great honor and place within Italian art of his day – perhaps by choosing it he was showing just how different art could be when it broke with inner conventions of how a picture should be arranged within the overall frame, while still conforming to outer conventions, that is, the unavoidable dynamics and cultures of the tondo.

That he was aware of the many dynamics of circles, spheres and eggs is clearly evident in drawings such as this:

(Two studies for a Holy Family, Pen and brown ink with brown wash, over red chalk, heightened with white gouache, 5 7/8 x 5 5/16 in., Getty Museum)

Looking at each set of figures separately, it’s fairly clear that Parmigianino constructed an overall egg-like format for the group, and then each figure’s head and body flow into egg-like forms of their own. I don’t know if Parmigianino placed these two sketches together like this, but supposing he did, then perhaps we might start to consider the overall circular arrangement of heads and arms pushing us into the center together as a reflection of the older, more geometric circular patterns of composition – not a copy of the patterns, but more like a jazz musician improvising within the general structure of the pattern.

My larger point here is that some artists rely on geometric patterns with intensive rigor, and others use them as a counterpoint against more distorted forms, or within the forms themselves (the pattern becomes the ‘form sense’ of the figure) and others still as a way to react against dominant theories, beliefs, or even politics of a culture. Composition when understood as part of the larger dynamic of an artwork’s provocation of our thoughts, can indeed reflect profound aspects of our lives. And it can do so today at the level of the larger cultural contexts surrounding the image, at the level of choice and manner of perimeter-frame of the artwork, and of courses unavoidably at the level of the images made within the perimeter-frame. All three levels of construction are available for artists to compose.

If you’ve read this far: I thank you! You should know that while I’ve quoted diagrams from Charles Bouleau’s book Painter’s Secret Geometry, that his ideas and extensions very much are 20th Century modern interpretations of composition. Other art historians, writing on the topic of composition, point to quite different conclusions, and some (most notably Thomas Puttfarken), very rigorously argue that Renaissance artists didn’t specifically rely on these types of geometric patterns for the establishment of the whole composition, but rather, more closely only within the sense of form of individual figures within a composition. Indeed Alberti and other early theorists spoke only rarely of ‘composition’ (in our modern sense of organizing the whole picture), and made distinctions between composition (of arranging the parts an individual figure) versus disposition (the arrangement of everything in a picture in service of telling the picture’s narrative). It’s always critical to remember that to the Renaissance eye, the interpretation of the image was quite different than the values we pre-suppose when we look at pictures today. I’ll write more about this distinction later. :)

2 thoughts on “The Circle, the Square, and Botticelli with Parmigianino

  1. i noticed that the magic square of venus
    may be embedded in the face of venus painted by botticelli: it aligns fairly well with intersections at the eyes and nose, parallel lines to the neck, mouth, and nose, and a point at the chin.
    do you think this was intentional?

    • Thanks for the comment and observations.

      I’ve been meaning to update this post and strengthen its link with 20 Century geometrical ideas… the source you cite, and my reference to geometry from Bouleau applied to Botticelli, are contemporary ideas, and there is no evidence at all (such as supporting notes, drawings, texts, etc.) from Botticelli’s studio that he would’ve composed with any secret religious number games.

      I think you’d also see, given the symmetry of the magic square diagram that you cited, that you could draw many different diagonals through it, as well as superimpose it in many different ways over the face of any of the characters… it has enough edges and diagonals that it could seem to fit more or less any face.

      There is a lot of evidence that Botticelli used and helped develop what was then the new linear perspective, as did so many artists of his time. Perspective is a fantastic and wonderful system for creating a rigorous sense of depth, as well as a set of symbolisms.

      If you’re interested in skeptical and engaging stories regarding numbers in architecture, art, and nature, I recommend Mario Livio’s book “The Golden Ratio” (Broadway Books: 2002) as a fascinating read.

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