Abstract. Answers to a reader's query about the origin and symbolic significance of pointed arches, in the Nexus Network Journal.

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Query: Pointed Arches

Date: Mon, 03 Dec 2001 11:27:42 +0100
From: Kim Williams <kwilliams@kimwilliamsbooks.com>

Here is a research query from a Nexus Network Journal reader. It appears that the first pointed arch in Europe may have appeared in Sicily around 1130. In 1090 in Sicily there are no pointed arches; in 1130 there are. The first crusade dates from 1099. It may be logical to think that pointed arches were a result of the crusade.

Does anyone know what the first pointed arches were in Europe, and if there were any earlier than the Sicilian ones of 1130?

Send an e-mail to respond to this query

From: Charles William Johnson <kawil3456@home.com>

The Greek culture at Mycenaean (BC 1500-110) shows "Circular Chamber with Pointed Corbel Vault"; (would that qualify?);

Gothic: 1160-1530AD, "Ribbed vaulting, Pointed arches, Vertical Lines; Cathedrals, castles, Coucy, Pierrefonds, Christ Church, Oxford, etc.

...and then there are the pointed vaults at Palenque; although not Europe.

From: Eugenia Victoria Ellis <eve22@drexel.edu>

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

From: Marie-Therese Zenner <marie-therese.zenner@wanadoo.fr>

I cannot look into it now but it seems to me there were pointed arches in Normandy at an earlier date.

Articles on the development of French Gothic architecture should give the response. Perhaps Jean Bony's study...

From: Joachim Langhein <DrLanghein@t-online.de>

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).

From: Steve Wassell <wassell@sbc.edu>

Trachtenberg and Hyman write of some influence from Normandy. Durham cathedral's nave vaults (1128-33) had "great double bays with pointed transverse arches and roughly semicircular cross ribs". They go on to say that "In the third decade of the twelfth century, the development of Gothic passed southeastward to the Ile-de-France." This does not refute the proposed hypothesis, of course, since there may have been influences from more than one region. It may just have been the case that the time was right for the exploitation of the pointed arch. This reminds me of the fact that Newton and Leibniz _independently_ discovered/invented calculus during the 1660s/70s;
it was simply time for it to happen!

From: Mark Keane <Keane@sarup.uwm.edu>

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.

From: Pippin Michelli <michelli@ariadne.org>

Certainly there are earlier pointed arches in Europe than 1130. Montecassino and Sant'Angelo in Formis have/had pointed arches at the centers of their vaulted facade porches.

May I add to this research query? Does anyone know of any symbolism in the shape or mathematics that produces a pointed arch?

From: Steve Wassell <wassell@sbc.edu>

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.


From: Mark Keane <Keane@sarup.uwm.edu>

The math is based on the the plan of the module that is being spanned. Semi-circular, Roman, arches can only accomodate square modules otherwise the spring points and keystones do not align on similar planes. The multi-varied nature of pointed arches solve this problem and allow for rectangles, trapezoids etc in plan.

From: Paul Rosin <Paul.Rosin@cs.cf.ac.uk>

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

From: Steve Padget <spadget@ku.edu>


Its the "Vesica" (with allusions to "eye", "mouth", "vulva", "plucked string", "fish"). Just imagine two intersecting circles. Symbolically, they can represent any of various pairs of duals. In the case of the cathedral form, they are the "spheres of Heaven/Earth" intersecting with the "intercessory" form of the vesica resulting.

If the circles have their centers touching the other's edge, a ROOT 3 vesica (the "Vesica Piscis") results. This figure has other names too ("Mandalora") and, as the intermediary between heaven and earth, is the "window" or "door" or "birth opening" of the divine making an appearance on earth. So, for Christian symbology, its the sign of Mary. If one believes in its more mystical power, it 'is' Mary. There are plenty of examples of this figure framing Christ, emerging form the heavenly realm and entering the earthly to be found in the tympanums above Gothic cathedral entries.

Within the protocols of 'sacred geometry', after the circle, this root 3 figure must be made before it is possible to make all the rest. It 'gives birth' to multiplicity of form (number in space) from 'perfect' unity.

All the examples I know of Gothic era churches dedicated to Mary are of a Root 3 geometry and openly exhibit the V.P. in the form of mandalora and doors/windows/vaults (half mandalora).

See Lawlor's Sacred Geometry, esp. ch.III for more.

From: Bernard Pietsch <bernard@sonic.net>

Perhaps there is some relevance in the Vesica picis. When you look at it the meniscus that is formed has two pointed "arches" on each end. If my memory serves me right, I saw some point arches in Chichen Itza. The form of the meniscus is in the Panto Crator on the front of the (one of them) alters at the cathedral of Burgos. I have analyzed this work and found a unique mathematical form that delivers some information that you would not belive is in there. Since is has the form of the Christos in its center, and it is a very close copy of the form over the southwest door of Chartres Cathedral, I find that it can (perhaps) be identified with the Knights Templars.

From: Peter Schneider <peter.schneider@cudenver.edu>

I remembered a reference to pointed arches and the Vesica Pisces on a web
site I'd visited. Here's the link to that:


There is quite a lot of information on symbology of the vesica pisces on the web, and I don't have time to run that down, but any search for either 'sacred geometry' or 'vesica pisces' will get your reader to more information.

From: Mark Reynolds <marart@pacbell.net>

'Tis a grand question.

Have your reader read, firstly, The Gothic Cathedral, by Otto von Simson, and, then, secondly, The Construction of Gothic Cathedrals, by John Fitchen. The order is important in understanding the Gothic builder/ing, and the period in which it evolved.

The first is socio/historical, and the second primarily technical, altho' there is historical Documentation in Fitchen's writings. Both writers are good sources for Gothic Cathedrals.

O. von Simson believes (and I agree) that the simultaneity of St Bernard and the Cistercians' changes to cathedral design to, among other things, the pointed arch and its spreading popularity throughout Europe is not a coincidence. He puts the dates about 1128-32. (J. Bilson, The Beginnings of Gothic Architecture: Norman Vaulting in England, also supports this dating.) Now whether Bernard, if he were an originator, was influenced by the Middle Easterners is another question.

I personally am unsure if there is definitive proof re. exactly where the first pointed arch was made. Most importantly, it is necessary to understand Masonic thought, tradition, and procedure. Among much else, Masons were secretive, and yet, among themselves, they spread the word on new, better, and grander ideas and techniques as quickly as an African drum, and faster, it would seem, than a horse could run... but not faster than a ship could sail. It might help in the thinking to understand that Sicily is an island and that information came and went by ship. Because we see the pointed arch at this time on the European mainland, in France, and then shortly, almost in the same breath, in England, it is doubtful that the structure originated in Sicily and yet appeared, full blown, in other parts of Europe, at the same moment, if we are to go with von Simson's and Bilson's dating. Returning visitors from the Middle East certainly went to various European locations at the same time, so tracing the origin will be a murky journey, if we are to support an Arabic influence.

As a geometer, my experienced surmise is that it was born from the vesica piscis, a Necessity of a European mason (and an even earlier Arabic mason) for a perpendicular vertical as the plumb was for the Egyptian mason (altho' the plumb was still also in the builder's tool box). It is perhaps similar enough to a circular arch to be most probably structurally sound and load bearing yet distinctly different aesthetically. It follows that it was most probably a device brought from the Middle East, quite probably around the time of 1100 your reader gives, and quickly picked up by the Europeans. We do see very early references to the ogee curve (a second cousin of the vesica) in the Byzantine as well. The exact dating and placing may prove elusive.

This is all I can muster on quick notice. Hopefully, we will have a grand master in architectural history step forward with the proof the reader requests, but for now, perhaps this will help.

I, too, would like to know of the documented proof on time and place -- and, if possible, by whom -- the first pointed arch stood upright.

From: Taha Al-Douri <T-Al-Douri@peapc.com>

Meaning in the shape of the pointed arch may better be comprehended within a context of Gothic construction rather than pondering the arch in isolation. Two properties of Gothic architecture most relevant to the character of the pointed arch are "changefulness" and "variety" in the Ruskinian sense. Having more than one centre, the pointed arch is constructed with more possibilities to vary than a standard arch; for the span of the arch is governed by the distance between the two (or more) centres in addition to the radius governing the span of a circular arch. The combination of radius and distance is exclusively a character of the pointed arch, and from that combination emerge other possibilities for variety in laying out the course-work of brick or stone to construct the arch.

The point at the centre is a point of intersection and could be thus expressed in the facade for celebration of the structure, another property of Gothic style. Such intersections can be seen in the Cordova in Spain with alteration in black and white stone that set the arch visually apart from the rest of the visual plain. Other types of pointed arches to emerge in the East (Abbasid Baghdad) were constructed with four centres such that two centred the larger radii that rose to the summit point and two centered the smaller radii that connected the larger ones to the supporting columns. The Eastern roots of the pointed arch --being those of the Gothic style, the Eastern Roman Empire, the Imperial Palace in Constantinople and Islamic Architecture of Mesopotamia, Syria and Egypt-- also relate to properties of lay-out (besides style) such as the relation between the temple and the residence of the sovereign (Cathedral of St. Mark).

From: Sandrine Germain <Sandrine-GERMAIN@ifrance.com>

I recommend you to visit this page:
about architecture, sciences and techniques.

From: Don Hanlon <Dhanlon@sarup.uwm.edu>

Of course, the pointed arch is a far more economical structural system than round arches. Loads are transmitted to the ground more directly and there is a minimum of lateral thrust. I also suspect (and I have no proof of this) that arcades composed of pointed arches were discovered to resemble, in an abstract sense, groves of sacred trees. In some species, the angles of branches from the trunk are remarkably consistent and as they converge with the limbs from adjacent trees they form spaces that are virtually identical to the shapes and proportions of the spaces between columns in the arcades of pointed arches we find in 12th and 13th century churches in France.

From: Raffaele Santillo <raffaelesantillo@libero.it>

Tomorrow I will write to you and you will receive explanations and an excellent international bibliography written " for everybody" from famous deigners and teachers.
In the meantime please observe the form (and therefore the statics), of your necklace, without and with an hanging medallion ! Qualitative answer is there (we say in Italian: lá sta il lepre).


From: Michael Ostwald <michael.ostwald@newcastle.edu.au>

This isn't my specialty but the pointed arch and its geometry is quite symbolic. The vesica pisces geometric construction which underlies some forms of pointed arch is significant for a range of religous and symbolic reasons.

I researched and wrote something short about this topic almost ten years ago. I will try to remember where. There have been sections of books on this topic published in the past. John Ruskin also wrote on closely related topics but with a more pagan, or at least intuitive, naturalistic symbolic rationale.

From: Han Vandevyvere <Han.Vandevyvere@asro.kuleuven.ac.be>

I remember reading in a book on the compagnonnage, written by the president (at that time) of the Compagnons, in which he develops a history of the emerging of the gothic style in Europe. If I remember well, he situates some important first buildings in Cyprus.
If you want, I will look up the information. The problem with this book is that it was written in a novel-like style, and that it is hard to distinguish which facts are 'hard' evidence and which facts stem from a tradition.

Anyhow I believe the Compagnons could give a valuable track towards the sources of the gothic style.

From: Dag Nilsen <dag.nilsen@ark.ntnu.no>

This is really not my speciality, and I reckon the queryer has consulted the relevant literature. I'll only mention what Grodecky (1976, English version 1977) writes about pointed arches, "first widely used in Sassanid art, the pointed arch was adopted by Islamic art, which, in turn, utilized it as a key feature from the 7th C on. [...] ..the great mosque at Cordoba, Spain, offer ample evidence of its popularity, as do certain Sicilian buildings constructed by the Christians after the Norman reconquest in 1059." He goes on mentioning Modena, and Burgundian churches, but gives no actual dates of examples.

Banister Fletcher gives the dates 1120-32 for Autun cathedral, 1088-1130 for Cluny III, both with pointed arcade arches and barrel vault, and 1105-1128 for Angoulème, with domes carried on pointed transverse arches. Fontevrault was consecrated 1119, but the nave was not completed, perhaps not even begun then.

Considering the many Islamic examples in North Africa, and even in Spain, it seems strange that this motif does not seem to have been picked up earlier, or at least not before the first crusade (Why should it before, perhaps be associated with heathen architecture, and not after, if that was the case?). When it comes to symbolism it would probably be very hard to find any explicit evidence without reading every contemporary source available (not to speak of the disappeared sources on such matters. Anyway, although some people at all times have been anxious to attach symbolic meaning to every aspect of the world, maybe some future builder or client - or several of them - participating in the first crusade simply liked the look of the pointed arch?

From: Orietta Pedemonte <pedemont@dima.unige.it>

L'ipotesi delle crociate mi sembra attendibile e che quell'arco sicilano possa essere il primo esempio in italia anche.Starei più attenta a considerarlo il primo esempio occidentale; controllerei l'Aljaferia a Saragozza (e in generale la spagna nell'undicesimo sec.) e le abbazie di Cluny e di sainte Madeleine deVezelay in Francia.

[The hypothesis of the crusades seems to me to be reliable and also that the Sicilian arch could be the first example in Italy. I would be more cautious about considering it the first example in west; I would check the Aljaferia at Saragozza (and in general eleventh-century Spain) and the abbeys of Cluny and of Sainte Madeleine de Vezelay in France.]
From: David A. Vila Domini <d.vila.domini@rgu.ac.uk>

I suppose you are regarding Europe as excluding the Iberian peninsula at that time..?

There are numerous examples in the Moslem architecture of that culture, and in Spain they begin pretty soon after 711 when the Arabs entered from the South.

Pointed arches in this context exist on their own in many cases. But sometimes they arise from the interlacing of arcades of simple semicircular arches, thus often producing a strangely compressed representation of several rows of arcades onto flat, non-tectonic plane of surface decoration. I am not entirely sure about what the symbolism may be... there are certainly stylistic (strongly formal) issues that govern their development.

Also, there are many types of pointed arch, one being the one referred to above, by intersecting semicircular arches at r (radius of the arch) centres; this means the centre for each side of the (pointed) arch is located at the springing of the other side of the arch, normally above a column. But there are countless departures from this scheme: composite curves (three and four centred arches), and the different locations of these centres; some authors speak of elliptical curves, and so on.

From: Eugene Dwyer <dwyere@kenyon.edu>

Pointed arches appear in the narthex of St. John Studion monastery in Constantinople (7th century, I think). See T. Matthews, The Early Churches of Constantinople.

From: Robert Osserman <osserman@msri.org>

John Heilbron's book Geometry Civilized describes the geometry of the pointed Gothic arch.

From: Carol Watts <cmwatts@ksu.edu>

There were pointed arches in the Romanesque style before 1130 (I assume you mean in Western Europe?). The Abbey of Cluny is an example - Bannister Fletcher dates it to 1088-1121 and says "The pointed arch, among the earliest in Europe, was employed in the nave arcades......"

From: Michael Leyton <mleyton@dimacs.rutgers.edu>

Pat Hayes and I defined the mathematics of pointed arches, and how they are created.

Let me give the following simple introduction: Consider a smooth arch. It is a curvature extremum (like the end of your finger). This corresponds to an ordinary maximum in the curvature function.
Now, if you make the arch pointed, the curvature function goes off to infinity, like a spike (Dirac delta function). Then, various grammatical operations we invented will change the curve into different types of arches, e.g., like cusped arches etc.

Here are two references:

(1) Intuitive description of the mathematics:
pp. 502-509 in book Symmetry, Causality, Mind by Michael Leyton (MIT Press).

(2) Rigorous description of the mathematics:
Hayes, P.J. & Leyton, M. (1989) "Processes at discontinuities", In Proceedings of the International Conference on Artificial Intelligence, (IJCAI), pages 1267-1272.

Available in any computer science library.

Let me explain why the curvature function becomes and infinite spike for a pointed arch:

In a pointed arc the curvature is finite at all points, except at the sharp point, where it is infinite
The reason is this: Curvature is the rate of change of tangent rotation per movement along the curve.
At the arch point, you can rotate the tangent without any movement along the curve. So the arch point has infinite curvature. However, the other points have only finite curvature.

Consequence: Plot curvature (y-axis) against distance along the curve (x-axis). You get an ordinary graph representing curvature. The graph is has finite height all along it, except at the arch point, where it will have an infinite spike.

Now the grammatical operations to generate pointed arches exploits the above fact.

From: Dag Nilsen <dag.nilsen@ark.ntnu.no>

About pointed arches - out of curiosity, I just consulted Paul Frankl (1962); he notes two, almost incidental examples from about 1100, at St. Étienne, Caen, and a wall arch at Gloucester. He also states that "the first vault built entirely on pointed arches is at Moissac" (the west porch), "probably between 1120 and 1125" (p. 21). I've never been to Moissac, but Frankl also states that the cloister there has 26 pointed arches, supposed to have been completed around 1100. K.J.Conant (1959), however has a caption to an illustration of the Moissac cloister, saying: "Cloister, c.1100, later reworked", which could mean that the arches may have been changed.

From: Robert Tavernor <absrwt@bath.ac.uk>

I'm not sure about mathematical symbolism, but Deborah Howard, in her recent book Venice & The East: The Impact of the Islamic World on Venetian Architecture 1100-1500, (Yale University Press, 2000), does talk about the migration of Islamic detail and pointed arches to Venice, and relates the relatively rare ogee pointed arch to the design of Venetian boats!

From: Simon Bialobroda <Vivekarchitect@aol.com>

A pointed arch can be constructed using the equilateral triangle. From my readings on the esoteric aspects of geometry, the equilateral triangle is symbolic of the Soul. Perhaps the master builders knew this. The pointed arch can be found in Cistercian Abbeys, medieval cathedrals and Islamic architecture. I believe that the upward lifting movement or feeling of the pointed arch is appropriate for use in sacred structures. The eye abstractly fills in the underlying triangle.

The base of the equilateral triangle in gothic tracery is normally divided into 4 equal parts and is used to generate the rest of the tracery. This base line of 4 equal divisions represents matter while the arching point can elevate one's consciousness to the soul. It is the soul that is the bridge between matter and spirit.

From: Warren Sanderson <we107@sover.net>

May I assume that by now your question to the AAH has been answered? In case it has not been, then I would point out that there were already pointed arches and tunnel vaults that were apparently pointed rather than rounded at the third church of Cluny sometime between 1088/90 and 1120.

I'm fairly certain that earlier ones could be found in Spain a century or more before that, but at the moment I can't document them.

From: Raffaele Santillo <raffaelesantillo@libero.it>

Your reader's question: Does anyone know what the first pointed arches were in Europe, and if there were any earlier than the Sicilian ones of 1130?.

My answer: if Spain, South Italy, Greece etc, was and is Europe, and he means masonry block arches, the answer is yes. In fact, the mortar masonry pointed arches were imported by the Arabs. They were the owners of the Mediterranean Sea for at least 200 years, with strongholds or bases even in Provance (Fressineto) and Maunt Blanc, in the Alps!

Along the Italian peninsula they were acting as invited warriors and free lancing pirates : they burned even Saint Paul basilica in the surroundings of Rome! To day, in south Italy, we measure cultivated land in Arabic units, and I remember when grain was measured by volume by an homonym unit. When the Normans arrived in south Italy, (battle of Civitate/Fortore, therefore before crusades), the artisans, master builders, protomagisters etc were Arabic populations : King Ruggero II (Roger) stood up when El Idrisi was entering the throne room. Roger's nephew Frederik II ( father from Germany, mamma from Palermo),spoke perfectly Arabic.

How they build before the Normans of Sicily?? By... the same methods. To-day the problem is to find examples, because Normans built churches where mosques existed (exp. San Giovanni degli Eremiti, Palermo): just to search for the bridges they left. (existing), and the problem is underlined and solved with signature.

From the "sophistic" point of view, million of pointed arches existed in antiquity, long before the Normans. Leaving out Arabic Spain (Europa!), we have many megalithic examples, in Greece, in Arpino (central Italy, home country of Cicero and Marcello Mastroianni). Not only, but all the entrance doors of the earth-mud-clay houses and "capanne" (huts) were and had to be of the pointed arch type, because this is and was the best natural form which match the statics and the pattern of the stresses transmitted in relation to that material.

The true problem is not that of the dates, numbers useful for bingo play; the reader should ask himself why the ancients build by pointed arches!

SECOND question, second reader: Does anyone know of any symbolism in the shape or mathematics that produces a pointed arch?
Answer: NO-
The pointed arch, derives from the laws of statics, which means geometry: As a concentrated load on a rope marks a cusp (a medallion along a necklace), so a concentrated load marks an inverted cusp along the "spinal column" of the arch. Hanging ropes develops tensile stresses, (and pull on the supports), and hard masonry arches develop compression stresses (and thrust on the supports). Numbers, and MODERN formulas are the same, for ropes and masonry arches; ( I mean, the basic, the 80%). An observer who turn upside down a post-card of the Brooklyn bridge, will obtain the profiles of a concrete arch bridge.

Bibliografia: two famous books, without a number, for everybody :
Salvadori, Mario, Structure in Architecture (Princeton University Press)
Torroja,de Miret, Edoardo, Philosophy of the Structures (original title: La racon y ser de los typos estructurales).

From: Raffaele Santillo <raffaelesantillo@libero.it>

La cinta muraria sel Comune di Tricarico(provincia di Matera), ha la Porta Rabatana della cinta difensiva con arco a sesto acuto, o meglio con punto a centro, alla maniera delle prime moschee del Cairo,(qui l'aggettivo rabatana dice tutto a chi ha visitato il mediterraneo).Il ponte dell'Alcantara, in Sicilia è a sesto acuto (pointed arch); anche se forse è stato rifatto chi sa quando; un ponte può solo essere rifatto allo stesso modo, perché unico è il profilo per quella impostazione: <<as hangs a flexible cable, so inverted stand the contacting voussoirs>>.

I readers devono sapere che il vero arco, quello puro(esempio Cordoba,in Spagna), è una invenzione araba; quelli cosidetti romani sono ARCHIVOLTI, e NON archi. La differenza in shorts? L'arco è piano ed instabile,come una bicicletta, mentre l'archiVOLTO è spesso, come un'automobile a quattro ruote, che resta in equilibrio anche da ferma! Ecco perché un proverbio arabo recita: "l'Arco non dorme mai".

From: Susan Alexjander <xjander@got.net>

Vesica Pisces....Flower of Life.

From: Ian Pickering <i.pickering@gsa.ac.uk>

In response to your emails about pointed arches: Pointed arches also occur in the early part of the 12C in SW France in a style of architecture known as the Byzantine Romanesque - which gives the clue as to its assumed origin.

It is extremely unlikely that it was the Crusades that imported pointed arches into Europe although it is true that the Crusades placed the relatively unsophisticated crusaders in contact with some sophisticated techniques in all areas of technology.

It is much more likely that it was trade and contact with Byzantium, the most cultured and advanced society of the time that was the source. Particularly as Byzantine culture was influenced by their contact with the architecture and civilisation of the Middle East - particularly Syria.

As far as the maths is concerned it seems that the setting out of a pointed arch can be done using rather simple geometry.The setting out of a pointed arch results from two givens.
1) that the arch height is constant (so that vaults of different widths will intersect at a constant height);
2) the springing of the arch is at right angles to the horizontal line between the base of the springings; i.e. the springing is vertical and not inclined given that:
1) The setting out of the arch would be done on a tracing floor;
2) The horizontal line of the base of the springing can be drawn at whatever angle but at the correct length of the distance between the springings. This distance could be either between the Intrados, that is the inner arc of the arch, or the extrados - the outer arc of the arch;
3) The mid point of the line can be established by intersecting arcs from each end of the line as long as each of the arcs has a radius longer than half of the line length;
4) The intersections of the arcs provide two positions along which a line can be sighted through two vertical staffs, one at each intersection. This line will be at right angles to the base line;
5)A third point can be established at the height of the arch by this sighting and by measurement;
6) The known width of the arch and the height can then be used to establish the line of one side of an equilateral triangle by forming a line between the point of the springing and the point of the arch height;
7) This line, subdivided in the same way as the base line, provides a line at right angles to, and from the mid point of, the side line of the triangle which, at the point at which it joins the base line, establishes the centre point of the radius of the arch. This is the only possible radius for an arc connecting the springing to the apex.

Where the radius lies beyond the distance between the springings the horizontal needs to be extended to the radius point but this would create no difficulty. Where the radius is less than the height of the arch (and less than half of the distance between the springings) the arch formed by the radius is half of a 'Moorish' arch, albeit turned 90°.

There is no indication of the setting out that I have suggested in any of the images of a tracing floor that I have examined but this has been entirely superficial. In any case it is possible that the setting out was done with chalk and that only the relevant and important lines were inscribed.

I have not been able to establish a simple means of geometrically dividing the arc into regular pieces but this may not have been necessary. On the other hand, the mass production of the voussoirs may have made life easier for the builders. In this case, the only stone that would have to be fitted would be the keystone.

For those who might be interested in theory about number and meaning I have just found a book called The Wise Master Builder by Nigel Hiscock, which deals with Platonic Geometry in Plans of Medieval Abbeys and Cathedrals.

From: Vesna Petresin <vesna.petresin@guest.arnes.si>

I've checked the numerous remarks at the nexus site but have also contacted my colleagues at the History of Art Department who suggested checking the following links:

1. pointed arches in Roman architecture: Cluny III (cca 1088)

2. pointed arches in Morienval
(in which it is written, "The earliest structural pointed arch recorded in France is in the ambulatory of Morienval, referred to above, and is dated 1122."


From: Tomás García-Salgado <tgsalgado@hotmail.com>

Charles Williams Johnson and Bernard Pietsch refers pointed vaults in Palenque and Chichén Itzá, respectively, but strictly speaking, there are not such Maya's arches and vaults, because its structural system does not work properly this way, that is, as arches or vaults.

The so-called Maya's false vaults do not support and transmit loads to columns or walls, instead the loads runs vertically from the top of the walls to its base. In other words, the walls stands up in parallel arraignment and from its spring line starts gradually decreasing the span until it close horizontally with the capstones. To normalize the loads some wood-crossbeams were add to the walls intrados, so, at any moment the walls stones follows any sort of curvature, they simple overlaps in order to decrees the span. This explains why the spans between walls were very short (2.75m span at the spring line in the Inscriptions Temple, in Palenque, c. 602-692 AD).

Paul Gendrop, a friend of mine, acknowledges at least nine different sections of Mayan false vaults: The E-X building in Uaxactún, the structure 1 in Tikal, the frescoes temple in Tulum, the A-V building in Uaxactún, The Labná arch, The ball court in Copán, The secret crypt in Palenque, the house A in the Palenque's Palace, and the Governor's Palace in Uxmal (my favorite one). For more see: Paul Gendrop, Arte Prehispánico en Mesoamérica (México: Trillas, 1970).

From: Carlos Calvimontes Rojas <urbtecto@hotmail.com>

It is very difficult and improbable that any architectonic work can be demonstrated with complete certainty to be, mainly on the basis of it its form and structure, the first one of its type in any part of the world. In a determined place, or simultaneously on several sites, when the man reaches new levels of maturity in his ability to construct, according to the resources available for him, he produces solutions to the main architectonic problem: cover a space. In his best achievements, man has found those solutions that meet conditions of architectonic beauty, constructive ease, conservation of materials and good structural quality, with only the geometry of the compass and by repeating the perfect forms of nature. The best pointed arch (with an inscribed equilateral triangle) has the geometry of the egg, which, being ruled by the Golden Number (accompanied by the number 3), determines a form that meets such conditions due to its being a system of great stability because of the harmony between its parts. The use in architecture of the geometric regularity of the bird's egg, in its paradigmatic form, besides satisfying aesthetical, constructive and economic conditions, allows the thrusts to be transmitted to the ground more directly and with minimal lateral efforts. See the figures below about that geometry.

From: Jan Kostenec <Jan.Kostenec@cityofprague.cz>

I have read your query concerning the first appearance of pointed arch in Europe and also the responses to it on Internet. I think nobody mentioned the great palace of the Byzantine emperors: there are pointed arches in the substructures of the so-called "paved way", intersecting the Walker Trust (mosaic) peristyle [ndr -- in the Great Palace, home to the Byzantine emperors] that could be, in my opinion, dated in the mid-sixth century. In Istanbul I know of other Byzantine building with them: Seyh Suleyman Camii (on its facade) -- it seems to me that it is also an early Byzantine structure.

From: Carlos Calvimontes Rojas <urbtecto@hotmail.com>

Of the several forms of ogee archs, which and where was the first used in Europe? It may be the moorish arch called of “loin of donkey”, based in the pointed arch? I have described the geometry of this arch as you can see in the image below.

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