Composite Results for Seurat's La Parade de Cirque

Composite Results for Seurat's La Parade de Cirque

Here is a collection of all the places where those people who have done Project 3 this term and the last several terms found evidence of the Golden Ratio in Seurat's La Parade de Cirque.

I only included those that I could verify with measurements on my version of the image, and which use features of the picture to determine placement of lines or cuts.

I also added in some that I found as I put this together.

Is my image in the same proportions as the original?

	Original	My image
Measurements:	99.7 cm x 149.9 cm	775 px x 514 px
Ratio:	1.504	1.508

If we look at the ratio of the two width-to-height ratios, ^1.508⁄_1.504=1.0027, we see that my image is within 0.27% of the original -- very close. The two width-to-height ratios can be considered to be equal.

Notice: Looking at the width-height ratios, it is clear the painting as a whole is not a Golden Rectangle

Acceptance range for the Golden Ratio:

On the one hand, I can get the computer to give me extremely accurate measurements. On the other hand, they'renot perfectly accurate since (a) I have to be able to see where to place the cursor and (b) the edges are of course not completely sharp. Furthermore, there's the question of how accurately Seurat might have been measuring, assuming he was measuring at all.

Balancing all of this, and taking into account the range of ranges that students used, I will choose to allow for a 3% error in the ratio, or in other words, roughly 1.5% error in each measurement.

This leads to the range:

1.569 ≤ measured ratio ≤ 1.667.

Cuts into Extreme and Mean Ratio (within our margin of error)

Vertical Cuts:

Total height, cut by line on railing dividing light and dark

Height from line below gaslights, cut by bottom or railing

Tall man on left, cut by top of railing

Tall man on left, cut by lower line

Shorter men on left, cut by bottom of railing

Height of trombonist, cut by line between light and dark on the railing

Height of trombonist, cut by middle finger of hand

Length of trombone, cut by middle finger

Total height, cut by change in shading of red block

Red block, cut by change in shading

Far man on right, cut by edge of sleeve

Near man on right, cut by cane

Height

514 px

251 px

333 px

308 px

365 px

182 px

514 px

255 px

242 px

253 px

Long length

314 px

288 px

208 px

212 px

187 px

226 px

115 px

321 px

153 px

146 px

157 px

Ratio

1.632

1.642

1.601

1.571

1.647

1.615

1.583

1.601

1.667

1.658

1.611

% of φ

100.8%

101.5%

98.9%

97.1%

101.8%

99.8%

97.8%

99.0%

103.0%

102.4%

99.6%

Horizontal Cuts:

	Total width, cut by right side of stage	Length from left edge to right side of stage, cut by left side of stage	Railing, cut by left side of center back-up musician
Width	775 px	479 px	357 px
Long length	479 px	301 px	220 px
Ratio	1.618	1.591	1.623
% of &phi	99.995%	98.4%	100.3&

Golden Rectangles (within our margin of error)

Series 1:

	Whole width, height up to line below gaslights	Vertical along right side of stage	Low man's shoulders; top of right man's hands	Low man's lower leg	Elbows	Shirt-front	Lower edge of hand
Longer side	775 px	473 px	296 px	183 px	110 px	69 px	42 px
Shorter side	473 px	296 px	183 px	110 px	69 px	42 px	26 px
Ratio	1.638	1.598	1.617	1.664	1.594	1.643	1.615
% of φ	101.3%	98.8%	99.97%	102.8%	98.5%	101.5%	99.8%

Spiral:

(I added one more rectangle that had no guidelines within the rectangle, although it does follow the man's hand, because I wanted to to see if the spiral followed the man's elbow.)

Series 2:

Consider the rectangle formed by the following lines: On the top, the line below the gaslights; on the bottom, the bottom of the rail; on the left, the left edge of the painting; on the right, the dividing line between colors to the right of the central trombonist.

This rectangle turns out to be (nearly) golden. Since it has numerous features within it, I decided to borrow your classmate's idea and look for features that might again subdivide this into numerous nested golden rectangles.

	Largest rectangle	Vertical along 3rd musician's clarinet and placket	Pink line in white rectangle	Right side of trombone	Top of 0
Longer side	468 px	286 px	176 px	109 px	67 px
Shorter side	286 px	176 px	109 px	67 px	41 px
Ratio	1.636	1.625	1.615	1.627	1.634
% of φ	101.1%	100.4%	99.8%	100.5%	101.0%

(These measurements are quite close to those we found for innermost 5 of the rectangles in the previous series.)

Two Identical Rectangles on the left, plus a clarinetist:

Two of these rectangles use the same top and bottom lines as we started with in our previous series:

	From left edge of tree to color-change	From color-change to next color-change	clarinetist's body
Longer side	286 px	286 px	129 px
Shorter side	179 px	179 px	80 px
Ratio	1.598	1.598	1.613
% of φ	98.7%	98.7%	99.7%

Three more on the left:

	Over to left side of podium; down to bottom of oval	Over to color change line	Over to left side of podium; up to bottom of railing
Longer side	302 px	222 px	302 px
Shorter side	190 px	139 px	185 px
Ratio	1.589	1.597	1.632
% of φ	98.2%	98.7%	100.9%

(note: the right-most rectangle in the middle is not golden; I just left the right edge in to remind you where the right edge of the top rectangle came from.)

Golden Triangles (within our margin of error)

	Sides of hat, extended up to point; base formed by bottom of trombone bell and pink line	top vertex is center of where forehead meets hat; drew lines out to two edges of the podium
Left side	161 px	344 px
Right side	160 px	345 px
Base	102 px	215
Ratios	1.578, 1.569	1.600, 1.605
% of φ	97.6%, 96.9%	98.9%, 99.2%

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