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The Painter's Secret Geometry: A Study of Composition in Art
Bouleau's classic illustrated work examines the essential reliance of European painting tradition on the golden mean and other geometrical patterns. From antiquity to the present, expert painters-including abstract modern masters such as Paul Klee and Jackson Pollock-have conveyed harmony through the mathematics of spatial division, ultimately giving geometry a crucial role as the foundation upon which these classics were built.
268 pages, Hardcover
First published June 1, 1980
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Displaying 1 - 14 of 14 reviews
April 14, 2019
Did you ever wonder why Botticelli's Venus in “the birth of Venus”, is not at the center of the painting but slightly centered to the right? Did you ever think about the connection between painting and geometry and music? If so, this book is for you.
Reading this book, one might wonder if all the great artists were actually secretly undercover mathematicians. It can’t be random. The connection between the algebra and the painting subject in the overall composition. Yet I still do wonder how many of them actually meant it to be so scientifically composed, or maybe the author of this book just found a way to suggest why we’re attracted to certain artworks, and what’s the secret harmony that makes them work. I do believe though that yes, a large number of those artists did actually pay a lot of attention to the composition, and as I’ve said, it can’t be random. Maybe its a mix of both.
This book gets sometimes too scientific, it’s not an easy read for the average art lover but an actual deep study of a somewhat esoteric aspect, even mystical at times. It’s highly academic, but nonetheless, it’s a breathtaking lesson, and I’m sure going to look even deeper at the composition of artworks from now on.
Reading this book, one might wonder if all the great artists were actually secretly undercover mathematicians. It can’t be random. The connection between the algebra and the painting subject in the overall composition. Yet I still do wonder how many of them actually meant it to be so scientifically composed, or maybe the author of this book just found a way to suggest why we’re attracted to certain artworks, and what’s the secret harmony that makes them work. I do believe though that yes, a large number of those artists did actually pay a lot of attention to the composition, and as I’ve said, it can’t be random. Maybe its a mix of both.
This book gets sometimes too scientific, it’s not an easy read for the average art lover but an actual deep study of a somewhat esoteric aspect, even mystical at times. It’s highly academic, but nonetheless, it’s a breathtaking lesson, and I’m sure going to look even deeper at the composition of artworks from now on.
October 8, 2020
The Painter’s Secret Geometry: A Study of Composition in Art by Charles Bouleau is a reprint of the 1963 edition of the book. The author makes it clear that this is not an art history book or comprehensive study of art, but a narrowly themed book on how geometry played a role in earlier works of art.
To start with I do know a little about art, but nowhere enough to be considered an expert or scholar on the subject. I have a masters degree in liberal arts and was lucky enough to visit plenty of museums while stationed in Europe. I know a Monet from a Picasso and a Dali from a Rembrandt. I have an appreciation for art and for mathematics too. I am one of those people who think mathematics is the key to understanding the world around us. There is symmetry in nature. Leaves, shells, pollen, crystals, rivers can be shown mathematically through fractals. Might there be something that makes some art more pleasing to the eyes than others? Might that be based on geometry?
Bouleau starts with an easy enough topic of scale. In very early works of art scale was used to express importance. The pharaoh dwarfed his subjects in size in Egyptian art. Gods likewise, when in human form, were drawn well taller than the people they addressed. It wasn’t until the Greeks that gods were scaled down to man size. Other early works show the subject bent or with a curved back symbolizing the frame of the picture was too small to contain the subject. In Bronzino’s Allegory of Love, the subjects bend and allow their bodies to conform to the frame. They form almost a perfect rectangle against the borders of the canvas. Heads were drawn proportionally smaller on show a subject of greater size. The explanations in these early works were interesting. The real focus of the book came with medieval and later painters.
I always found Medieval art interesting for a number of reasons. One reason is that the complete painting looks pleasing to the eye, but on closer examination individual objects or people in the painting seem off. There is a tree that looks like an asparagus stem or a child that seems disproportionate in size when singled out in the painting. One wonders why these oddly shaped objects do not attract attention when viewed in the entire painting. The answer seems to be it is because they are oddly shaped or placed that they work in the painting. The human mind looks for patterns. Optical illusions delight us. We enjoy music with rhythm and a beat. We can tell when something is out of place or out of sequence. We may not know what is out of place, but something is just not quite right. The same works with art.
There is a geometry in art. In some works, it is Euclidian geometry. In others, addition of musical tones is added the geometry. Botticelli’s Primavera is used as one example. Bouleau superimposes the geometric lines and patterns over the works of art. In many of the cases, the results are stunning. There is more than a causal relationship between positioning and the subjects to the geometry of the canvas. Piero della Francesca’s The Virgin and Child with Saints is mind blowing, the subjects and the background fit perfectly. It seems that Francesca drew his subjects over a visually pleasing geometric pattern right down to the angle that the child lies across the Virgin. Perhaps my favorite painting, School of Athens by Raphael, in the foreground Pythagoras is explaining the musical consonances where the ratio of 4/6/9 is derived from. This ratio became known as the golden ratio and is used in much of the painting of the time.
Poussin’s Rape of Sabines is used as another example of ratios The painting is overlayed with lines in a ratio of 9/16. This moves the vanishing point to the left of center and the horizon above the center of the canvas, but visually it appears in the center of the painting. The people on the right are larger and the buildings on the right seem to move out to the viewer. The viewer placed in the lower right of the painting viewing as a member of the crowd in a seemingly three dimensional experience.
Many paintings are covered and some modern work is also shown. Works where the geometry plays an important role as in modern art where there may not be a subject or a traditional subject. When we look at anything there are two things we see what is on the surface and the mind sees something more. Much like the ideal of a subliminal message, the conscious sees one thing and the mind sees another. The overlays over the paintings used by Bouleau show us what our minds see when looking at art -- pattern, symmetry, ratios, vanishing points. The use of modern art near the end of the book may go on to support the idea that we are attracted to the patterns and symmetry much more than we may be attracted to the subject of the painting. What makes the art great may boil down to not what we see, but what our mind sees.
To start with I do know a little about art, but nowhere enough to be considered an expert or scholar on the subject. I have a masters degree in liberal arts and was lucky enough to visit plenty of museums while stationed in Europe. I know a Monet from a Picasso and a Dali from a Rembrandt. I have an appreciation for art and for mathematics too. I am one of those people who think mathematics is the key to understanding the world around us. There is symmetry in nature. Leaves, shells, pollen, crystals, rivers can be shown mathematically through fractals. Might there be something that makes some art more pleasing to the eyes than others? Might that be based on geometry?
Bouleau starts with an easy enough topic of scale. In very early works of art scale was used to express importance. The pharaoh dwarfed his subjects in size in Egyptian art. Gods likewise, when in human form, were drawn well taller than the people they addressed. It wasn’t until the Greeks that gods were scaled down to man size. Other early works show the subject bent or with a curved back symbolizing the frame of the picture was too small to contain the subject. In Bronzino’s Allegory of Love, the subjects bend and allow their bodies to conform to the frame. They form almost a perfect rectangle against the borders of the canvas. Heads were drawn proportionally smaller on show a subject of greater size. The explanations in these early works were interesting. The real focus of the book came with medieval and later painters.
I always found Medieval art interesting for a number of reasons. One reason is that the complete painting looks pleasing to the eye, but on closer examination individual objects or people in the painting seem off. There is a tree that looks like an asparagus stem or a child that seems disproportionate in size when singled out in the painting. One wonders why these oddly shaped objects do not attract attention when viewed in the entire painting. The answer seems to be it is because they are oddly shaped or placed that they work in the painting. The human mind looks for patterns. Optical illusions delight us. We enjoy music with rhythm and a beat. We can tell when something is out of place or out of sequence. We may not know what is out of place, but something is just not quite right. The same works with art.
There is a geometry in art. In some works, it is Euclidian geometry. In others, addition of musical tones is added the geometry. Botticelli’s Primavera is used as one example. Bouleau superimposes the geometric lines and patterns over the works of art. In many of the cases, the results are stunning. There is more than a causal relationship between positioning and the subjects to the geometry of the canvas. Piero della Francesca’s The Virgin and Child with Saints is mind blowing, the subjects and the background fit perfectly. It seems that Francesca drew his subjects over a visually pleasing geometric pattern right down to the angle that the child lies across the Virgin. Perhaps my favorite painting, School of Athens by Raphael, in the foreground Pythagoras is explaining the musical consonances where the ratio of 4/6/9 is derived from. This ratio became known as the golden ratio and is used in much of the painting of the time.
Poussin’s Rape of Sabines is used as another example of ratios The painting is overlayed with lines in a ratio of 9/16. This moves the vanishing point to the left of center and the horizon above the center of the canvas, but visually it appears in the center of the painting. The people on the right are larger and the buildings on the right seem to move out to the viewer. The viewer placed in the lower right of the painting viewing as a member of the crowd in a seemingly three dimensional experience.
Many paintings are covered and some modern work is also shown. Works where the geometry plays an important role as in modern art where there may not be a subject or a traditional subject. When we look at anything there are two things we see what is on the surface and the mind sees something more. Much like the ideal of a subliminal message, the conscious sees one thing and the mind sees another. The overlays over the paintings used by Bouleau show us what our minds see when looking at art -- pattern, symmetry, ratios, vanishing points. The use of modern art near the end of the book may go on to support the idea that we are attracted to the patterns and symmetry much more than we may be attracted to the subject of the painting. What makes the art great may boil down to not what we see, but what our mind sees.
December 2, 2014
More reviews (and no fluff) on the blog http://surrealtalvi.wordpress.com/
Although written in 1964, this is a very thorough and well referenced/researched analysis of (mostly) pre-renaissance era paintings and the often geometric basis of those compositions. As with cubism, pre-raphaelite, even ancient Egyptian art: each era has its own style and influences and this book describes the core of middle ages period art. The book goes into detail of many paintings and statues to dissect and understand the placement of people, objects, and backgrounds in the composition. As a photographer, I found this book incredibly useful for inspiration and understanding of deeper compositional options I can use within my own art.
Chapters in the book include: Monumental art, The frame, Geometrical compositions in the Middle Ages, Musical consonances, Geometry after the middle ages, Dynamic compositions, Compositions in space, Picture framework in the nineteenth century, and Solutions of the problem in contemporary painting.
As can be seen from the above, author Bouleau compares and contrasts many different periods of art in order to put the art of the middle ages into context. From the musical note placement of friezes in ancient Greece to Renaissance era framing, there is so much to learn about composition and placement. Although many have noted that this is a great reference for learning the golden mean, I actually found so much more to digest. The complexity of some of the paintings, like using perspective sloping architecture or tall trees in order to create endless triangles and squares within triangles and squares was very elucidating.
If I was a painter, this would be open daily for inspiration and to push me to create the most purposeful and sophisticated images possible. As a photographer, I reread the examples every few months ago to refresh and inspire.
Since this is an old text, the images are in black and white and the writing is, indeed, very academic and dry. Be prepared for an old fashioned textbook feel. It's a shame it hasn't been rewritten or updated by a more modern author to take adventure of 21st century publishing. But still, for those serious about their work, this is a must-have reference.
Reviewed from a ecopy provided by the publisher.
September 8, 2017
I don't understand this book at all and it definitely is not what I expected it to be. It is so dense and theoretical/philosophical/what the fuck even that I just skimmed through it,honestly. So idk if I can say I actually read it.
February 14, 2023
THIS BOOK WOULD BE GREAT FOR USE IN A COLLEGE COURSE
Although this book was very well written, it reads more like a college textbook. It goes into a of of theory behind the composition of art and history of art composition. This book does not go into how to compose art.
Although this book was very well written, it reads more like a college textbook. It goes into a of of theory behind the composition of art and history of art composition. This book does not go into how to compose art.
Read
June 18, 2022Avoid the Allegro Editions, the images are blur.
January 21, 2024
Some good tidbits here. The book didn’t keep my interest long but there were some beautiful images and some of the geometric elements were interesting.
November 25, 2024
this book is great and all but it's crazy how many old paintings were in black and white. I thought that was only a TV thing.
May 10, 2025
It was long, but it had the secrets.
I don't know, I enjoyed it. It took me a while to read, mostly because of its density. I enjoyed the words and diagrams, though.
I don't know, I enjoyed it. It took me a while to read, mostly because of its density. I enjoyed the words and diagrams, though.
June 5, 2015
This review originally published in Looking For a Good Book. Rated 4.25 of 5
The arts are vastly under-respected. For so many people, you go to a play and you maybe think that the acting was good or the music was nice, or the costumes were pretty. You look at a painting and typically you might think it looks nice or it doesn't.
But do you ever stop to think about what goes in to the work? Aristotle once wrote something to the effect that in order to fully appreciate a work of art, one must have first-hand experience in that art. That becomes very clear to me after reading through a book like this.
This is not an art book. This is not a book that you will want to pick up to look through and admire the pictures (though you may end up doing just that). This is not a simple book. This is an advanced, academic study and at times it can be tough reading. I randomly picked a paragraph as example:
There's no context here, of course, but this is to give the potential reader an idea of the language being used.
Author Charles Bouleau goes in to depth with his studies and shares just how much geometry has gone in to the composition of paintings. Mostly he focuses on a number of old masters, but he does touch on some slightly more recent artists.
I'll have to be honest and say that at times, despite Bouleau's rather convincing arguments, I didn't always see the geometry in the pictures. But I trust his assessments and his reasoning is sound, even if I couldn't see it myself. And I like what Bouleau has to say in his conclusion:
This is a great summation and definitely captures my own feelings about the geometry in art and the appreciation of the work itself.
Looking for a good book? If you are serious about art, either creating it yourself, or studying it, or just like to be in the know about things, The Painter's Secret Geometry is well worth studying.
I received a digital copy of this book from the publisher, through Netgalley, in exchange for an honest review.
The arts are vastly under-respected. For so many people, you go to a play and you maybe think that the acting was good or the music was nice, or the costumes were pretty. You look at a painting and typically you might think it looks nice or it doesn't.
But do you ever stop to think about what goes in to the work? Aristotle once wrote something to the effect that in order to fully appreciate a work of art, one must have first-hand experience in that art. That becomes very clear to me after reading through a book like this.
This is not an art book. This is not a book that you will want to pick up to look through and admire the pictures (though you may end up doing just that). This is not a simple book. This is an advanced, academic study and at times it can be tough reading. I randomly picked a paragraph as example:
"To return to the altarpieces: it is the central part of the triptych that acts as the axis of symmetry, sometimes as a whole if it represents one subject only, such as a Madonna adored with identical gestures by the saints on the wing pieces, and sometimes by means of its own axial figure if the center itself represents several people. But the altarpiece-composition is the naivest and poorest expression of symmetry -- poor because lacking in creative force. No force binds together the parts of this purely static whole to make of them a new work." (~p. 46)
There's no context here, of course, but this is to give the potential reader an idea of the language being used.
Author Charles Bouleau goes in to depth with his studies and shares just how much geometry has gone in to the composition of paintings. Mostly he focuses on a number of old masters, but he does touch on some slightly more recent artists.
I'll have to be honest and say that at times, despite Bouleau's rather convincing arguments, I didn't always see the geometry in the pictures. But I trust his assessments and his reasoning is sound, even if I couldn't see it myself. And I like what Bouleau has to say in his conclusion:
I should add that, as a partisan of geometrical construction, I am delighted when I see it become, sometimes, the actual form which the picture presents to the view, but this does not make me think that geometry is everything in painting. The work of art draws its enrichment from the tension between its various components.
This is a great summation and definitely captures my own feelings about the geometry in art and the appreciation of the work itself.
Looking for a good book? If you are serious about art, either creating it yourself, or studying it, or just like to be in the know about things, The Painter's Secret Geometry is well worth studying.
I received a digital copy of this book from the publisher, through Netgalley, in exchange for an honest review.
August 13, 2016
'The Painter's Secret Geometry' by Charles Bouleau is a reprint of a book first published in 1963. I'm glad Dover republished it, because I really enjoyed reading it.
The book is all about the composition of art and how geometry came to claim a big part in how pictures were composed. The books chapters build on concepts like paintings on monuments, how pictures are framed within things like friezes and altar pieces. We move into geometry in the Middle Ages, then learn about the musical consonances that inform paintings. Eventually we see how modern painting tries to move away from geometry and how, even with those attemps, there are examples.
The book is full of paintings showing overlays of the geometrical lines. I've known some of this but to see how completely pervasive it is was just amazing. The planned orderliness of the figures is something you sense, but when you see it laid out, it's grand and a bit breathtaking. It gave me a whole new appreciation for the amount of planning went in to these works of art.
I received a review copy of this ebook from Dover Publications and NetGalley in exchange for an honest review. Thank you for allowing me to review this ebook.
The book is all about the composition of art and how geometry came to claim a big part in how pictures were composed. The books chapters build on concepts like paintings on monuments, how pictures are framed within things like friezes and altar pieces. We move into geometry in the Middle Ages, then learn about the musical consonances that inform paintings. Eventually we see how modern painting tries to move away from geometry and how, even with those attemps, there are examples.
The book is full of paintings showing overlays of the geometrical lines. I've known some of this but to see how completely pervasive it is was just amazing. The planned orderliness of the figures is something you sense, but when you see it laid out, it's grand and a bit breathtaking. It gave me a whole new appreciation for the amount of planning went in to these works of art.
I received a review copy of this ebook from Dover Publications and NetGalley in exchange for an honest review. Thank you for allowing me to review this ebook.
May 20, 2015
A very scholarly work with lots of interesting information on how earlier western artists composed there paintings. Many early artists used their compasses and rulers as freely as masons and other craftsmen did. I'm a bit skeptical of the later periods, the formal schools were breaking down and I'm not as sure about the composition techniques. I don't think this will make you a better painter, but may help supplement your knowledge of art history.
March 25, 2015
I regret that I didn't spend more time on this in order to write a lengthy fair and honest review for netgalley. (It's now on my amazon wishlist.) There is so much that I want to understand here, and it's going to take more concentrated effort on my part to see and learn what Bouleau offers. This is an excellent study for those who are truly interested in mastering the fine arts.
February 6, 2017
Absolutely fascinating. A must-read for anyone interested in art history and especially European painting from the Middles Ages on.
Displaying 1 - 14 of 14 reviews