Here is Gauguin’s "D'où Venons Nous?”. A geometrical analysis will show the origins of the composition and the underlying structure.
The red lines create diagonals across the whole painting. Note that the reclining woman at left leans on the rising diagonal, which also defines the lighter colored ground at left of center, the hand of the central nude with the turned back, and the branching of the tree at top right. The falling diagonal defines the changing ground color at left of center and the small child’s leg and loincloth at the lower right.
A circle filling the picture’s full height at its center sweeps around the sleeve of the larger child in the foreground, past the rear and elbow of the central nude with the turned back, and through the fruit being grabbed by the main figure near the top.
Starting from the left, two squares are made, each inscribed with the “X” of its diagonals. The figures in the middle ground, walking from the left, stop in front of the vertical margins of these squares.
Next, in orange, the same step with the squares is applied, moving from the right this time. In this case, it is the idol that abuts the margin of the square. The outer pair of red and orange verticals divide the composition into a triptych of sorts, particularly in the upper half of the painting. (Note that the steps in this analysis proceed in the spectral order of the rainbow: first red, then orange, and in subsequent slides yellow, green, blue, and violet.)
In the left wing of the “triptych,” the steeply falling yellow diagonal passes through the head and body of the reclining woman, whose bracing arm is defined by the yellow vertical halfway across the left “wing.”
In the upper left half of the painting, the yellow horizontal defining the horizon line passes through the intersection of the red and orange diagonals near the idol.
In the middle panel of the “triptych,” the yellow diagonal falling to the orange vertical defines the sloping feet of the idol, the pink feet of the woman in the middle ground, and the ankle joint of the main figure.
In the right panel of the “triptych,” the dog at right leans its paws on the falling diagonal, while the second woman of the seated group rests her elbow on the rising diagonal.
The navel of the idol can be found by drawing a short green horizontal from the intersection of the orange vertical and the falling red diagonal of the painting until it hits the rising red diagonal of the first square. The green vertical descending from the navel subdivides the idol’s legs, but not its head, which is displaced left.
The bright green vertical stands .707 of the way from the left margin of the painting to the right; this is the ratio of a square’s side to its diagonal, which is an interesting relationship to invoke, since the painting is not square.
A green “X” through the bright green vertical defines a green vertical against which the large child in the foreground reclines. The cats climb the rising diagonal of the “X,” while the falling diagonal defines the tilt of the second woman’s head at right, the placement of her hand, and the head/torso junction of the small child.
In blue, a circle is drawn at the center of the painting, so that it is tangent to the green vertical against which the older child leans. This circle intersects the diagonals reaching out from the painting center in points that define the blue vertical axis of the main figure, which passes through his navel and along the line separating his thighs.
The blue vertical further to the right, tangent to the original red circle, forms a bookend of sorts for the rear of the first woman in the group at right.
In the left half of the painting, the rising violet diagonal to the top center of the painting intersects the descending red diagonal at a point 2/3 of the way up the painting, defining the height of the brown land at left, and 1/3 of the way across the painting, defining the back of the figure near the idol.
In the middle of the painting, violet lines of 60-degree slope descend from the top of the main figure’s axis. The left line passes along his forearm, arriving at a prominent crease in the sleeve of the large child by the cats. The right line passes along the main figure’s other forearm, along the back of the central seated nude, and along the arm and leg of the first woman in the right-hand group.
A violet line ascending from the base of the blue vertical defines the elbow, wrist, and face, respectively, of the three right-hand women. Voila…