ORIGINAL QUERY: 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?
NNJ READERS'
RESPONSES: 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>
Of COURSE!
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:
http://www.geomancy.org/sacred_geometry/sacgeo-5.html
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:
http://www.enpc.fr/enseignements/Picon/Architechnique.html
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)
www.owlnet.rice.edu/~hart205/Lectures/lecture33.htm
www.arch.ced.berkeley.edu/courses/arch170/past/95fall/euro.html
2. pointed arches in Morienval
www.newadvent.org/cathen/06665b.htm (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.
Copyright ©2001 Kim Williams
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