Of interest is to any other instances of the tiling outside of Egypt in other countries, with what I term as 'foreign Cairos'. Indeed, although not widely known, there are others, likely arising independently, best described as a variation of the theme, specifically in Japan, Germany, Switzerland, United Kingdom and United States, of a like street paving in style, but not reflecting the Cairo collinearity model. Furthermore, there are also other instances used in an architectural capacity, all of which I detail below. Likely, given that the tiling is intrinsically simple to compose, there are indeed other instances, of which I would be delighted to receive details from any reader of this page.
It would appear that the paving is also common in Japan, although actual pictures in publications are extremely rare, with just a single instance in a book, described below. However, despite this lack of documented sightings, it would indeed appear, relatively speaking, to be ‘frequent’:
A photograph appears in Symmetry A Unifying Concept by István Hargittai and Magdolna Hargittai, page 174. Upon correspondence, Hargittai told me that it is ‘very frequent’, and the photograph dates from approximately 1984. However, he has no other pictures, and the exact location, scale and extent remain unresolved.
Another instance (upon correspondence with the Japanese mathematician Toshi Sunada), is at a school/college in Hamamatsu, with a picture on Jun Nishiseko’s blog (this reflecting his interests in ‘interesting’ pavements). The date here is uncertain, but approximately 1970s.
© Jun Nishiseko
Another instance, courtesy of Yoshiaki Araki, is at Tokyo, with a paving in front of the Higashi-Koganei station of Japan Railway Chuo line. This is quite extensive, although the age is unknown, but appears relatively modern.
© Yoshiaki Araki. 1 Extreme detail 2. Overall detail 3. Street Scene
Also see Google Street view: https://maps.google.com/maps?ll=35.70119,139.5247&z=22&t=k
Just drag the little man to the pavement, and the pentagons will then appear.
Hamburg Music Hall
Apparently three isolated instances have also arisen in Germany, although again, pictures are rare, but are perhaps of even greater significance, due to all being of a possible old age, in one instance possibly many centuries old! (But I stress possibly here). However, there is only one sighting here so far confirmed, detailed below:
The first, and only confirmed sighting, by Harald Riege, is in the foyer at the Laeiszhalle Musikhalle (music hall), at Hamburg. Riege is a frequent visitor to concerts there, and who, upon having been familiar with Jürgen Köller’s German mathematics website, with a page on the Cairo tiling illustrated with a line drawing, noticed the similarity, and reported this to him, and sent him an in situ picture. This sighting is of note due to the likely, in relative terms, old age of the tiling, of slightly over 100 years, likely (but not necessarily) dating from 1904-1908, when the hall was built. Riege has been visiting the hall for 50 years, and has always been familiar with it. Although this does not conclusively date this as from the turn of the 20th century (as it could have been installed close to his first visit), he tells me that he is convinced that this is indeed the date of installation. Support for this conjecture is that the music hall was not damaged (and so not needed repairs) during World War 2. If so, then this sighting is of significance; this is the earliest date I have of the tiling, as either a mathematical entity or a physical structure. As can be seen, the tiles here are noticeably of a small scale, compare Riege’s shoes with the tiles.
A stunning 3D virtual tour panorama video of it is at:http://www.3d-top-event.com/musikhalle-hamburg2/3D%20Virtual%20Tour_3d-tour_16x9.html
On the opening page, scroll a little to the right, and the tiling comes into view. Also, there’s a drop down box, selecting ‘30 Klassenhalle’ gives an apparent different location from the foyer here.
© Harald Riege: 1. Detail, 2. Extreme detail, 3. Wider view, 4. The Musikhalle, Hamburg exterior 5. Reverse side of tile, with Villeroy & Boch insignia
Upon further research by Harald Riege as to the tiles background, the company and location of the manufacturer has been found, namely Villeroy & Boch, at Mettlach, near Saarbrucken. Upon visiting the company website for further background information there can be seen to be a pattern book:
© Villeroy & Boch, Unternehmensarchiv, Catalogue, Villeroy & Boch Logo
Upon contacting the company archivist, Agnes Mueller, to see if the tiling was included there, it indeed was! However, there is no person credited with the design or any further background details. Agnes told me that the tiles were especially designed for places such as entrances, as at the Music Hall, being unvarnished, and therefore skid proof. And so for now at least my inquiries here have come to an end. However, this is not to say that the tiles may not have been manufactured considerably earlier, as the Villeroy & Boch company has a long history, dating from 1748, and so perhaps there may yet be more findings.
As ever, an open invitation to readers of this page to inform me of any relevant details. Would anyone care to visit the company and have a general look for this?
'German School Sighting'
Another (old) German sighting which has recently come to light is in a mathematics journal, in conjunction with an article on pentagon tiling by (indirectly) A. P. Rollett: ‘A Pentagonal Tessellation’, in The Mathematical Gazette, Vol 39, No. 329 (Sep. 1955) page 209, note 2530, with a line drawing. However, this is of a somewhat vague nature as to specifics:
‘My colleague Mr. R. C. Lyness noticed this [Cairo tiling] pattern on the floor of a school in Germany’. No other detail was given. Needless to say, given the paucity of detail, searching for this sighting is fraught with difficulty. Upon research, R. C. Lyness, a distinguished mathematician, was a notable school inspector in the UK, and so it is possible that he did indeed see this at a school in connection with his role as an inspector, rather than a university post, as I originally thought this might refer to. Although it’s decidedly a long shot with the passage of time, to say the least, does anyone know which school in Germany Lyness is referring to here? Or indeed, have anything to add, no matter how small, that might aid the inquiry?
Heidelberg Castle Sighting?
A third sighting, by Leon van den Broek of the Netherlands in Germany, at Heidelberg castle, is possibly even more exciting, on account of a mooted even greater age, possibly dating from as early as c.1650 (sic), when the castle was rebuilt. If indeed so, this would be quite sensational, predating the instance above by over 250 years! However, for now at least, this remains speculation. This also appeared on a home mathematical web page, on pentagon tiles (link below), but without the association of Cairo. However, it is of a more tentative nature, although almost certainly to have existed at some time, although exactly when it was installed is unclear. Although the veracity of the sighting is almost certain, I have no pictures of this. The report is slightly vague. Here he states ‘...the tiles have been there for ages…’ but are shown as a line drawing rather than an in situ picture. Upon correspondence, he could add little to this account. However, much that was on the website was inexact is terms of specifics. The tiles are not necessarily equilateral, nor coloured as shown. Therefore, the dating of this instance thus remains highly speculative; it could be old as the castle, but this is speculation; it may very well be of more modern times. An initial in situ investigation March 2012 revealed nothing. In due course, from my investigators, I hope to have pictures from the castle if it is still in place.
United Kingdom - Leicester Cathedral
(2014) installation of a Cairo tiling is at Leicester Cathedral
gardens (and were featured on the news in conjunction with King Richard III reburial in March 2015, which is
how this sighting came to my attention). The cathedral gardens were officially
opened on 5 July 2014 as part of a celebratory weekend, of a general
renovation/refurbishment of the surroundings.
United States - Bellingham Arts District
A substantial and significance ‘foreign’ sighting is at Bellingham, Washington state (near Seattle), in the Bellingham Arts District. Jared Williams of the Arris Stoneworks Company, in association with Ellen Sollod (a local artist) and Nakano Design Associates designed these. The pavers are in Obsidian (black) and Brindle (grey). Each pentagon’s geometry is of 90° (2), 108° (2) and 144° (1) and they were installed in 2008.
© Jared Williams. Bellingham Arts District, left, and Detail, right.
Welford, for photographing the Leicester Cathedral pavement sighting upon my request
Created: 22 March 2012. Updated 15 June 2012.
30 September 2015. Added United States, Bellingham Arts District sighting.
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