Islamic Geometric Ornament: Jules Bourgoin

How Did the 19th Century Artist Jules Bourgoin Construct Islamic Patterns? Alan D. Adams, Holland, New York, 2015.

It is generally agreed that it cannot be determined with certainty how most Islamic Geometric designs were drawn by the original artists. The compass and straight edge method of their construction is not generally clear by inspection of the final product.

It is surprising that it is also not very clear how the artists who collected and cataloged these in the 19th century constructed their patterns. Ernst Herzfeld, James Wild and Jules Bourgoin published drawings but it is remarkably difficult to work backwards from their layouts to see how they define proportions and construction. The evidence does exist in their publications, but it is not always obvious.

The best known English language catalog of Islamic pattern, mostly due to a Dover publication Arabic Geometrical Pattern & Design, 1973,1 is Bourgoins collection from, Les Elements de l'Art Arabe Trait des Entrelacs of 1879.2 This collection of over 200 patterns covers many of the basic types of the art. It has probably started thousands down the road of learning the art.

It is frequently said that the text of Les lments de l'Art Arabe Trait des Entrelacs does not teach much about how most of the patterns are drawn. The text was not even included in the Dover publication. The basic layout circles of the patterns appear in the plates but it is not clear how the sizes or spacings of these layout elements are determined. The information is in the text of the original publication and earlier work by

Bourgoin and it is possible to see how he laid out most of his patterns.

Bourgoins Trait des Entrelacs is in fact his third publication on the art of the Arabs. The first major publication is Les Arts Arabes; Architecture, Mensuirie, Bronzes, Plafonds, Revtements, Marbres, Pavements, Vitraux, etc. Le Trait Gnral de lArt Arabe of 1867, 1873.3 This publication certainly does contain enough information in some of the drawings to determine exactly how he constructed his patterns. He uses a general and common method which leads to the best symmetry patterns. The layouts for the classic parallel arm 10 point and twelve point stars appear in the early chapters and sufficient evidence appears in the drawings to define the exact method used for layout.4

Bourgoin gives a complete course on the geometry needed to draw the figures in the 1867 publication. He introduces the divisions of the circle, the Regular Polygons and Derived Polygons followed by the regular and Archimedean tilings he will use later. Finally he shows the complete layout of the ten point star in Deuxime Partie, Part Two; The Interlacing Line.

A set of divided circles are drawn inside a grid of 72 rhombi (rhombuses). The

Creative Commons -Attribution 3.0 Unported !1 (CC BY 3.0) Text, photos and drawings.

divisions required to draw the decagon are drawn, the radii. The inter-radii, to divide the star into 20 parts are also drawn. He does not include any construction of the rhombus or pentagons used to do these divisions. Bourgoin always assumes that angles are measured.

There is a single extra layout line on this drawing, drawn as a dotted line. It is indicated in pink.

This is the only layout line required to complete this pattern, beyond the divided circle. It connects two 10 fold divisions, radii, of the circle, divisions 1 and 4.

Where that line crosses the inter-radii, the 20 fold division, a layout circle is drawn, shown in red. Inside that circle, a star polygon is drawn by connecting the vertices, radii, 1 to 5, in blue. To be confusing, mathematicians call this 0 to 4, a 10/4 star polygon.

Extending the star polygon to intersect the decagon drawn inside the circles completes this star. Where the pattern lines meet the edge of the circle, lines are extended until they intersect a line from a neighboring star, where they terminate. These rules and a single layout line completely define the star. The text description is sketchy, but consistent.

Bourgoins layout is a short cut and it is only general for parallel sided, even number stars. The general case appears below

The two points used by Bourgoin are defined by a small minor layout circle. It is drawn at the intersection of the inter-radii. The radius of this minor circle is defined by the line perpendicular to the radius from the major circle, to the point indicated in black. If the correct tiling polygon is drawn, in blue, this is easy to draw.

If the star polygon in the center is extended out, it defines a new star polygon inside the minor layout circle, a perfect five point star.

This completely defines the pattern, and it is completely general for 10 point symmetry with any star polygon in the center, not just the 10/4 polygon.

The figure on the next page shows the result for a different star polygon, resulting in a tapered 10 point star. Technically, this is a 20/7 star, drawn as a ten point star. The minor star is in turn now drawn from a 10/7 star polygon.


There is good evidence to say that Bourgoin understood this completely. A layout for a 12 point pattern in his third publication Prcis de l'art arabe of 1892,5 Plate 94 of part III shown at left, shows the correct and complete method.

The exact layout is drawn in full. The minor layout circle, in red, lies on the tiling boundary, drawn in blue, at the inter-radius. This minor layout circle defines the required second circle to draw the star polygon. No further layout is required to complete this pattern.

Many but not all of Bourgoins star rosette patterns can be drawn without any additional layout rules.

The results for the smaller star are not predictable with this method.

The figure in the center of the layout will always be a regular star polygon. The figure in the smaller, minor layout circle is unpredictable. The five point star at

left for the twelve fold figure is irregular. All rays have the same length, but the angles are not equal. Angles are only equal for six and ten fold stars. Using this layout method gives a minor star with the least possible distortion.

It is entirely possible that Bourgoin discovered this independently, but he is not the first person to understand this correctly. A completely correct description appears as a sketch with in the unpublished notebooks of James William Wild from about 1845.

Wild served as recording architect in 1842 travels with Karl Richard Lepsius and then stayed on in Egypt to study Arabic architecture. Wild made extensive written and sketched records of Mosque construction, decoration and residential decorative pattern.6 His material was later used for the four Arabic plates of his brother in law Owen Jones famous Grammar of Ornament of 1856. After serving as curator at Sir John


Soanes Museum, he left his collection of notes to various libraries and these notes are now at the Victoria and Albert Museum.7

Figure 1. James William Wilds Notebooks. Victoria and Albert Museum, London. 2011EP3581

The text in Wilds notebook reads: A Star of 12 points inscribed within 12 gons which touch each other in four points. The constructive lines are squares. The small circle at A shows the manner of setting out the thickness of the 12 petals so that the

little stars B left by the intersections of the figure may have equal rays.

Wilds construction is exactly the same construction shown above from Bourgoins later 1892 publication.

Ernst Herzfeld was another later major contributor to the recording of the monuments of the near east. He published principally on the monuments and architecture of the area but he did include carefully drawn


depictions of their geometric ornament. It is clear from his surviving preliminary sketches that he used the same method of construction as Wild and Bourgoin.

Bourgoin Pattern Instructions from Les lments de l'Art Arabe

It is interesting that Bourgoin did not use this general and precise method in many of his patterns where it would have given the best symmetry result. There are text notes for each of the plates in Les lments de l'Art Arabe. They are brief and need the to be read together with the layout lines sketched in the plates to read sensibly, but they are clear in most cases. A classic, extremely common star serves as an example. Plate 48 is the classic 8 point star rosette. From page 19:

PL 48 Vertices and the center: 1st with a radius equal to half of the side of the square, describe a regular octagon on the tangent circumference; 2nd with a radius almost arbitrary (according to the proportion that we want to give the arms of the rosette; Here radius equal to half the side of inscribed square is used) describe a concentric circumference and construct the diagonal 6 into 6 divisions; a star is thus obtained where long sides, extended to meet the sides of the octagon, determine the rosette mesh. Extended sides of the octagon determine small octagons that separate rosettes.

Following Bourgoins text instructions with an eye on his plate gives exactly the figure he has drawn in plate 48. On the left; 1st with a radius equal to half of the side of the square, describe a regular octagon on the tangent circumference. The tangent circumference is the inscribed circle of the square tiling polygon. The radius of that circle is of a side. On the right; 2nd with a

radius almost arbitrary (according to the proportion that we want to give the arms of the rosette; Here radius equal to half the side of inscribed square is used) describe a concentric circumference. An inscribed square is drawn in blue and it inscribed circle is drawn in turn. construct the diagonal 6 into 6 divisions; a star is thus obtained where long sides, extended to meet the sides of the octagon, determine the rosette mesh. Extended sides of the octagon determine small octagons that separate rosettes. The term 6 into 6 divisions sounds odd but it simply means the construction of the star


polygon by connecting each sixth intersections of the divisions of the pattern at the inscribed circle. Note that Bourgoin also counts from zero, 0 to 6.

Extending the sides of the layout octagon forms the sides of the small octagons of the pattern and it is complete. It is not the best symmetry pattern. If he had used the same layout which he used for his 12 point

star, he would have used the inner circle shown in the figure to the right. The small layout circle at the right of the layout should define equal length arms for the small 5 point star. This is doomed to be a poor symmetry star due to the 8/4 fold symmetry of the pattern. Even so, Bourgoins layout could have been more symmetric if he had used the layout method he had used for 10 and 12 stars.

Later 12 point star rosette pattern constructions use similar arbitrary radii. This is particularly surprising since he had used the best construction in his earlier or contemporary publication, shown above.


The pattern which should show perfect symmetry in all its elements is the ten point rosette tiling. The layout described by Bourgoin in Les lments de l'Art Arabe is correct, but it is completely unrelated to the layout shown from his earlier work above. It is rigorously correct, but rather strange. It teaches no general lesson.

As a final impression, Bourgoins Les lments de l'Art Arabe is an inconsistent collection of constructions. Some are geometrically correct but not general, some are unsuccessful with poor proportions and some are simply trial and error. Almost all of them rely on construction of angles with a protractor and are therefore unrelated to any possible historical method. It is safe to say that the constructions described do work to give the patterns shown. They do not teach anything useful to approach new patterns or understand the structure of those presented.

References and Notes

Note: The translations from the French originals are mine. I do not read French, these were laboriously translated and doubtless contain errors. Geometry, however, is universal. I believe that the sense is correct.

Note on copyright: The last copyright on Bourgoins works expired in 1978. Born December 12, 1838 died February 4, 1908. James William Wilds notebook extract is copyright to Victoria and Albert Museum, used under their conditions; Content in which the V&A owns copyright (or related rights) may be downloaded and used free of charge but subject always to these Terms of Use. The permission granted by these Terms of Use is for "non-commercial" use of the Content only (meaning any use that is not intended for or directed towards commercial advantage or private monetary compensation). http://www.vam.ac.uk/content/articles/t/terms-and-conditions/

1) Bourgoin, Jules. Arabic Geometrical Pattern & Design, Dover Publications, 1973.

2) Bourgoin, J. Les lments de l'Art Arabe Trait des Entrelacs, Librairie de Firmin-Didot et Cie, Paris, 1879.

3) Bourgoin, J. Les Arts Arabes; Architecture, Mensuirie, Bronzes, Plafonds, Revtements, Marbres, Pavements, Vitraux, etc. Avec une table descriptive et explicative, et le Trait Gnral de lArt Arabe, V. A. Morel et Cie, Paris, 1867, 1873. p 25. Originally issued in 40 parts, explaining the publication dates.

5) Page 25 Ref 3.

5) Bourgoin, J. Prcis de l'art arabe et matriaux pour servir l'histoire, la thorie et la technique des arts de l'Orient musulman, (Summary of Arab Art.) Ernest Leroux, Paris, 1892.

6) The Art Journal: New Series, 1893 J.S. Virtue London, p 120 - 121. Obituary. Stanley Lane-Poole Art of the Saracens in Egypt Chapman and Hall, London, 1886. p 115 and other sources mention Wilds stay.

7) Notebooks of James William Wild, Victoria and Albert Museum, Accession number 2011EP3581


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Islamic Geometric Ornament: Jules Bourgoin