Requests
Would any reader of this web page know of any additional references to the Cairo tiling in books and articles other than those here? I would indeed like to see additional references. Email me with any further details.
Also, would any reader of this web page be visiting Cairo, or know of someone who is intending to do so? Ideally, I would like more detailed measurements of the pentagons, specifically of the angles. Also, any new sightings in other locations would be warmly welcomed. Email me with any further details.
Some unanswered questions of a historical
nature concerning the Cairo pentagon tiling:
1. Has anyone seen an in situ
picture (i.e. photograph) of the tiling in Cairo in any publication?
2. Does anyone know of any recorded
first-hand sightings?
3. Can anyone antedate the
apparent first recorded reference of the 'Cairo' attribute given to the tiling in 1971, namely
that by James Dunn?
4. How old are the tilings?
5. Who or what body was
responsible for installation of the tiling?
6. It is said to appear as a
mosaic on Moorish buildings; which one?
7. Is the tiling just restricted to Cairo,
or is it found in other parts of Egypt,
the wider Islamic world, and indeed other countries?
The background to the above is
as follows:
1. Has anyone seen an in situ
picture (i.e. photograph) of the tiling in Cairo in any publication?
Amazingly, despite many
references to the tiling in the mathematical literature, it has apparently
never been shown in a book or article as an in situ picture i.e. as a
photograph! Instead, invariably, author after author will give a line drawing. (Indeed,
for many a year I thought this might just be a mathematical urban myth, given
that I had not found any first-hand references until relatively recently.)
This missing picture has long (1987) piqued my
interest, eventually resulting upon placing a request (2009) on my website for an
in situ photograph. Subsequently (2010), I have indeed received a picture, from
Helen Donnelly, an artist visiting Cairo, whose own interest in this was piqued
by an in situ observation of the tiling. Having researched it on the web, and noticed
the website request she kindly sent me a picture. Indeed, amazingly, given the
previous lack of pictures, she has found numerous other instances of the tiling
(clustered around the Dokki district). This is, I believe, is the first
recorded series of pictures, of which I and some of my correspondents in this
think that it would be appropriate to record this in a paper, if it is indeed
the first in situ picture. Therefore, before going into print with what could
be possible erroneous statement, i.e. the first (?) picture, I have decided to
throw the question open to a wider audience. Does anyone know of an in situ
picture in any publication?
2. Does anyone know of any recorded
first-hand sightings?
Perhaps somewhat surprisingly
there are the very few recorded first-hand sightings. Indeed, there are apparently
just two recorded first-hand sightings
prior to Donnelly's 2010 report. The apparent first sighting is by James Dunn
[1], although his article is not explicit in stating that this was a first-hand
sighting this. However, following personal correspondence, Dunn confirmed that
it was indeed a first-hand sighting (at Cairo airport). The apparent second sighting was by Robert
Macmillan [3], who in his article stated explicitly that he visited Cairo (and incidentally he gives a more extensive account than
Dunn). Are there any other recorded first-hand sightings?
3. Can anyone antedate the apparent
first recorded reference of the Cairo attribute given to the tiling in 1971, namely that by James Dunn?
The apparent first instance is
by James Dunn, in 1971 [3], where he
stated the tiling '...is a favourite street-tiling in Cairo'. This attribution is perhaps somewhat surprisingly late,
given the obvious age of the tilings (from Donnelly's sighting). The tilings must
surely predate Dunn's attribute by many years, if not decades, or perhaps even
centuries. Also of interest are any subsequent 1970s references to Dunn's apparent first reference. I know of just three instances:
(i) 1975, Martin Gardner [2]
(ii) 1978, Doris Schattschneider
[4]
(iii) 1979, Robert Macmillan [3]
I would be very interested in
hearing of any antedating of the 1971 reference, or any other references from
the 1970s (references from the 1980s onwards abound).
4. How old are the tilings?
The pictures clearly
show that the tilings are from different periods, as some are obviously relatively
new, with the tiles in more or less new condition, whilst others are noticeably
old, being well worn, and indeed, in places the tiling pattern is obliterated
from constant usage. Obviously, from Dunn's 1971 report, the tilings he saw are
at least now approximately forty years old. However, the obviously worn tiles
would appear to be, much, much older, speculating perhaps even centuries old? Can
anyone put an age on these?
5. Who or what body was responsible for the installation
of the tiling?
Nothing is known as to the
background to the installation. Was it from just one person, perhaps at the
behest of a municipal contract, who suddenly introduced this more or less at
whim? On the other hand, was it perhaps from an institution, rather than an
individual? Can anyone furnish further details?
6. It is said to appear as a mosaic
on Moorish buildings; but which?
Aside from being seen as a tiling, Gardner
[2], states that it is seen '…in the mosaics of Moorish
buildings', but he is not specific as to the type of building. As such, there
is no documentary evidence for this in the form of a picture. Has anyone seen
this tiling on any Moorish building?
7. Is the tiling just restricted to
Cairo, or is it found in other parts of Egypt, the wider Islamic world, and indeed other countries?
Given the now obvious popularity
of the tiling, one would think it would also be found elsewhere outside Cairo in Egypt, and possibly the wider Islamic world, but I know of no
other instances. As regards its appearance in other countries, it is also to be
found in Japan, where it is said to be quite frequent. Does anyone know
of instances elsewhere?
References
[1] Dunn, James A. 'Tessellations
with Pentagons'. The Mathematical Gazette, December 1971, 366-369.
[2] Gardner, Martin. 'On
tessellating the plane with convex polygon tiles'. Scientific American, July 1975, 112-118.
[3] Macmillan, Robert H. 'Pyramids
and pavements: some thoughts from Cairo'. The Mathematical
Gazette, December 1979, 251-255.
[4] Schattschneider, Doris. 'Tiling
the Plane with Congruent Pentagons'. Mathematics
Magazine, January 1978, 29-44.
Created: 15 March 2011