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I think the pointed arch came from the east going to the west, i.e. came from Islamic sources.

I believe that Spain too (not only Sicily and Palestine) may have been one of the medieval "communication zones" for inspiration of Gothic architecture. Additionally, the commercial contacts within the Mediterrean, e.g. between Pisa and Algeria (like Fibonacci) should not be underestimated. (Fibonacci lived as a son of a Pisa wholesaler in Bougie (Algeria), spoke therefore perfectly Arabic and learnt a lot of Greek-Arabic geometry.

Dr. Heinz Götze (+ 02.03.01) was interested in these issues, and I discussed some with him. There may be some discussion in his last English version of his "Castel del Monte" book (NY: Prestel, 1998, German ISBN 3-7913-1930-2). I have forwarded him some communications of specialists in Islamic architecture I received shortly before (after discussion on a website), but I pity that this all lies on my former computer (it would take some time to find this communication on the other computer); Dr Götze showed high interest in these ideas expressed on Islamic geometry and architecture. If I have more time, I will search this communication once again, including his letters.

Also between 1120 and 1130, Athelard (Adelard fo Bath (1070/1080-1146?) travelled to Sicily and later probably to Spain, also to produce two Latin translations of Eucllid's Elements based of Arabic texts (an antique Roman translation of this still perfect textbook has not been found up to now); similarly acted Gerardo di Cremona (sometimes written: Gherardo, 1114-1187, + in Toledo) and Herman of Carinthia (Hermannus Dalmata, in German "Hermann von Kärnten, 12 c). This gave inspiration of the static qualities of the equilateral triangle, well tested in Muslim architecture, and inspired the practical geometry (construction geometry) of Gothic Europe.

Of course, these are only assumptions. The Gothic style may "multi-rooted", but the inspiration has come from Islam Math & Geometic Science & Architecture (including architectural decoration).

It appears to be sure, of course, that Villard de Honnecourt - around 1125 - was well acquainted with the pointed arch and its overwhelming static possibilities of the "built equilateral triangle" realized in ogive arches, ribs, vaults etc., huge cathedrals (see Prof. G. Binding's recent books on Gothic architecture!), which enabled not only a wonderful new world of architectural proportions, but also an "architecture of light" (as admired by Abbot Suger and Bernard de Clairvaux). The Arabic Euclidian architecture was able to show all 17 of the 17 planar symmetry groups (as idfentified by Dr. Götze's author in
Granada; personal letter of Nov. 18, 1998); it is still unknown how many of 230 3D symmetry groups (space groups) may have been "realized" by Gothic master builders in their masterworks.

This was possible on base of a "compass only" geometry (the Danish Georg Mohr 1672 & 1673 and the Italian Lorenzo Mascheroni 1797 (french 1798, 1828) have shown that Euclid's Elements could be fully drawn with "compass only". This way surely part of the so-called secret of Gothic master builders. Of course, they used measuring chords, rulers, straightedge, too).

I've always been told it began at Durham Cathedral, England at 1080 but not to change the planning of the church, then it really began at St Denis, France in 1143 when it changed planning. But these countries warred ofr things of less importance over the years.

With regards to this mornings query on pointed arches, another NNJ reader has asked a further question about them: Does anyone know of any symbolism in the shape or mathematics that produces a pointed arch?

You already know my answer. A pointed arch is simply the top half of a vesica piscis, and "the" vesica piscis is prominent in the very first proposition of Euclid's elements, showing how to construct an equilateral triangle. This construction (which uses only the top half of the vesica piscis, as well) must have been known quite early on in prehistoric times. This is all speculation, of course, which is why you didn't include it in your Mathematical Intelligencer article, much to my chagrin.

I'd be interested in learning how many others mention this possibility.

I think that many pointed arches are just formed from pairs of circular arcs meeting abruptly (discontinuously).