How does Brunelleschi’s dome manage to support itself? History, explanation and VIDEO

Brunelleschi’s dome is   the roof of the  cruise  of  the Florence Cathedral ; at the time of construction it was the largest dome in the world and still remains the largest  masonry dome  ever built (the maximum diameter of the internal dome is 45.5 meters, while that of the external one is 54.8 and is 116 high meters). [1]  Thanks to the fundamental importance it had for the subsequent development of architecture and the modern conception of building, it is still considered by some to be the most important architectural work ever built in  Europe  since Roman times ^[1]. Its size prevented the traditional construction method through the aid of  ribs , causing many hypotheses to be formulated on the construction technique used. Below is a long in-depth analysis that will help us understand how it was possible to build such an unusual dome as resistant to time:

History

The problem of its construction had been troubling the workers of the Cathedral for some time. In fact, it was not an easy task to build and identify where to place the enormous  wooden ribs that should have supported it until its final closure with the keystone, nor was it certain that a wooden support structure could support the weight of the vault or even collapse on itself:

Most likely the first architect of the new Cathedral,  Arnolfo di Cambio , must have foreseen a domed roof of the presbytery, as in the cathedrals of Siena and Pisa. The fact that a smaller dome was still thought of in the fourteenth century seems to be proved by the well-known fresco by  Andrea Bonaiuti  in one of the walls of the chapter house, the  Cappellone degli Spagnoli , in the Florentine basilica of  Santa Maria Novella . The fresco, dated about 1365-1367, shows a church in the background in which a Cathedral inspired by the project of  Santa Maria del Fiore is clearly recognizable , whose dome is however devoid of the drum and is round-arched (at the time impossible in masonry ). In  1418 theOpera del Duomo  announced a public competition for the construction of the dome. [2]  Following the competition, which also officially had no winners,  Filippo Brunelleschi  and  Lorenzo Ghiberti  were appointed master builders. On 7 August  1420  the construction of the dome began, [3]  which was completed up to the so-called “menagerie” at the base of  the lantern  on 1 August  1436 . [4]

The grandiose construction site opened its doors the day after the drafting of the so-called “device” of 1420, attributed to Brunelleschi himself, in which the way in which the drum should have been closed was explained and the methods of construction were specified by salient points. Basically, it was a singular “work program” which summarized the structure, shape and dimensions of the building in a few lines, but rather than expressing a programmatic intention, Brunelleschi enunciated the project by giving executive instructions. In those twelve points listed by him not only was the finished work already contained, but there were even indicated those variations, incidents and additions that should have been made.

Following ups and downs and a climate of rivalry, according to  Vasari , in  1423  Ghiberti was ousted from the works, which passed entirely into the hands of Brunelleschi. The construction site thus proceeded without appreciable interruptions, until, in August 1436,  the completion of the factory was officially celebrated with the solemn blessing of Pope Eugene IV . The consecration was solemnized by the execution of the  isorhythmic motet   by  Guillaume Dufay Nuper rosarum flores , with reference to the name and coat of arms of Florence as well as to the dedication of the basilica to Santa Maria del Fiore. Once the construction of the dome was completed, another public competition was held for the lantern, always won by Brunelleschi. However, the works began only in  1446 , a few months before the architect’s death; they then continued under the direction of his friend and follower  Michelozzo  di Bartolomeo, to be finally finished by  Antonio Manetti  on 23 April  1461 . [5]

Shape and structure

Starting from an octagonal drum, the Dome stands on eight segments, the sails, organized on two caps separated by an empty space. The space between the two canopies measures about 1.20 meters and it is through this space that the steps that allow you to go up to the Lantern pass. A wooden chain made up of 24 beams connected to each other by brackets and iron pins surrounds the whole building. Its effectiveness has been discussed for a long time. Briefly, today, we can affirm that, in principle, a dome is all the more stable the more solid its drum and its tax base are: therefore an effective hooping system is useful for stability. This ring, in fact, serves to “tighten” the construction at the base, in order to counteract the dangerous forces directed towards the outside. As for the the use of wooden or stone chains remains doubtful, if only because of the elasticity of the wood and the inability of the stone to work in traction. Among the elements that make up the Dome exist golden proportions  as it was in use at that time. The sensation that one has, in fact, when observing this masterpiece, is one of substantial balance and harmony in its parts. Its tax base is located about 55 meters above the ground, the lantern is 21 meters high, the drum measures 13 meters and the height of the Dome is, on average, 34 meters. The total elevation of the entire structure, including the golden ball and the cross that surmount it, is 116.50 meters. It should be remembered, however, that the real measurements of the Dome must be calculated in Florentine arms and not according to the metric system, therefore any suggestive rumination referring to the belonging of the numbers 13, 21, 34, 55 to the famous Fibonacci sequence is completely erroneous. and meaningless. When the Dome was consecrated in  1436, a famous Flemish musician,   of the Dome complies with very specific rules: the external angular profile is a sixth of an acute quarter, while the internal one is a sixth of an acute fifth. Each diagonal of the outer octagon, which measures approximately 54 meters, has been divided into four equal parts: hence the definition of “acute fourth”. The profile of the Dome, in any case, assumes a form of extreme importance for its stability: in fact, it is very close to that of a  catenaryGuillaume Dufay , composed for the occasion the motet  Nuper rosarum flores , a composition that reproduced the relationships of the building in music. Even the  apparent outline overturned. This name derives from the fact that its shape is the one assumed by a hanging chain, holding its two ends still. As Bernoulli would have shown only at the end of the seventeenth century, this form is the most suitable for supporting a dome that supports itself with its own weight. At the top we find the Lantern, completed with the intervention of several artists after Brunelleschi’s death in 1446. To create it, machines that the architect himself had designed were used. These machines, necessary to lift materials during the construction of the Dome, and which alone mark a formidable advance in the science of construction are generally seen by almost all authors who deal with construction, Scarperia . The Lantern also has a very important function for global statics. The ribs, in fact, converge towards the menagerie, the base of the  Lantern , whose diameter is about 6 meters. The forces acting on the Dome are such that the ribs themselves tend to bend inwards due to the loads and their own weight. The Lantern, with its enormous weight (about 750 tons) has the function of countering these dangerous forces by wedging into the structure and canceling the thrusts that are generated at its base. In  1472 ,  Verrocchio  built the bronze ball which was placed on its top used to stabilize the connecting ring of the dome. ^[2] For this too, Brunelleschi’s machines were needed. Among the workshop boys who helped Verrocchio in this difficult operation was a young da  Vinci ,  Leonardo . On April 5,  1492 ,  the ball was struck by lightning but did not fall ^[3] . On January 27, 1601 around 5 in the morning, due to lightning, the ball fell, damaging the dome in several places ^[4]  (it was repositioned on October 21,  1602 ; behind the square under the dome a marble disk still testifies to the exact point where the original sphere crashed to the ground) ^[5] .

The construction

The problem of the dome and the ribs

The drum, of imperfect octagonal shape, on which the dome was supposed to rest, measured about 45 meters wide on the largest diagonal ^[6]  and was 54 meters high. These dimensions were considerably larger than those originally anticipated. The reasons for this increase, which led the size of the building to exceed those of the dome of the  Pantheon , until then the largest dome in the world so much so that the legend considered it the work of the devil, are to be found not so much in the desire for primacy, but in the need to reinforce the dome drum as much as possible. In fact, the drum had been raised compared to the original modelthrough a plane in which eight large eyes open, which favored the illumination of the apse triconchus of the Cathedral. With this expedient the dome’s tax plane was also raised above all the vaults built up to then. The very high vaults of the  cathedral of Beauvais  in  France , which for their daring collapsed shortly after their construction, reached “only” 48 meters in height. But the irregular octagonal shaped drum ^[7]  also created the main obstacle to the erection of the dome. Brunelleschi accurately calculated every detail, from the inclination of the walls to the arrangement of the bricks in a herringbone pattern. Sothe dome was able to support itself , without resting on the traditional sulphurous wooden scaffolding. A video documentary from National Geographic:

A dome that is not a dome

A hemispherical dome (or parabolic, or ellipsoidal, as in  the cathedral of Pisa ) is a figure or place of points identified as an  arc  “rotated” around its own axis. In this case we speak of  a rotation dome . Building a rotating dome is theoretically always possible, as the dome is made up of infinite arches, each of which once completed will stand on its own. Beginning to build the dome from the edges, small arches will be created that can stand alone which in turn will be able to support larger arches leaning against the previous ones, which once complete will be self-supporting.

The concern of the master builders who succeeded one another in the construction sites of the Duomo was motivated by the fact that the project included an octagonal dome with flat faces, which is not a solid of rotation. The dome of the Florence Cathedral  is not a dome but an octagonal vault, which can be described as the 45 ° intersection of two vaults with a square plan (very similar, in fact, to the vaults of the nave of the Cathedral itself). Unlike a rotating dome, once it is not self-supporting. In this case, the use of ribs, that is wooden scaffolding to support the masonry under construction up to the setting of the mortars, was indispensable. Among other things, in Italy it was not possible to obtain the gigantic beams available in Northern Europe instead. But even the immense beams used for the cathedrals of France and  England  would not have been enough to support vaults like those that were to be built.

The concept of the dome

Filippo Brunelleschi was famous in Florence, as well as a multifaceted artist, as possessor of a temper and a slightly perverse sense of humor; one of his jokes, played against a poor  cabinetmaker  named Grasso, was famous in the world of the brigades of Florentine society: through a series of expertly orchestrated testimonies, Filippo made the poor man believe that he had become another person, a perpetually reckless bad waters named Matthew. The success of the joke was such that Grasso ended up fleeing the city, and the story of the ferocious joke, with the title of  Novella del Grasso carpenter  , was a real editorial success, reaching us in numerous versions.

Brunelleschi, the fable seems to suggest, was a master in making people believe one thing for another; not for nothing Brunelleschi is the father of  perspective , which is an illusionistic representation of a  three-dimensional reality  with two-dimensional means. Well, Philip with his dome seems to have played us a joke of this kind, even more extraordinary than the other; after years of debating what was the “magic artifice” that had allowed the result that is in front of everyone, we had not gone one step further. The octagonal dome with flat faces, to be built without ribs and with the slow-setting mortars of the time  could not stand . The use of  the herringbone pattern of the bricks, visible to all in the corridors of the cavity between the two domes, was generally indicated as a component of the “secret” but without understanding its real function.

One of the most generally accepted explanations is that expressed separately by Professor  Salvatore Di Pasquale  (former dean of the  Faculty of Architecture in Florence ) and Professor Mainstone. These and other scholars were helped by the discovery, during the removal of the tiles from one of the sectors of the dome for restoration work, that the brick laying beds were not horizontal at all, but followed an open upward curve, called  a cord. bland. This fact, never noticed before, led to examine the arrangement of the bricks, which in previous studies was always taken for granted, with obscure and generic references to Roman or even Arab masonry techniques. It was therefore possible to observe how the faces of the bricks are not parallel, but arranged along lines originating from a point located in the center of the base octagon of the dome. The conclusion was disconcerting; the bricks were arranged as if they had been arranged to construct a rotating dome. To simplify as much as possible, it was as if the flat-faced dome had been built by cutting out parts of the masonry built like a classical dome;

Not being able, however, to build the dome of such a thickness as to contain a rotation one, Brunelleschi introduced the double cap and the intermediate ribs through which the circular shape of the rotation dome could pass from the internal cap (where it reaches the intrados in the corners of the octagon) to the external one (where it reaches the extrados in the median points of the sides). The herringbone bricks were then used to measure the construction of the rotation dome, the latter had the purpose of supporting the structure during construction until it was locked, thus avoiding the use of immense ribs. Filippo thanks to the study of Roman domes, geometry but above all thanks to a meticulous design that lasted years,

A theory that differs from that of other scholars is that formulated and published by prof. Massimo Ricci ^[8] . According to this theory, the technology of the dome would not respond at all, not even in the internal structures, to a rotating dome: the bricks between two   consecutive  rows of fish herringbones would not be laid according to circular courses , but  parallel  to the surfaces of the sails. Brunelleschi, through the creation of herringbone rows, has created bricks laying surfaces that form a series of “pseudo-horizontal platbands” that give the structure of the Dome self-supporting “during construction.

In this reconstruction, the structure of the dome is in fact conceived as a succession of horizontal radial platbands, which allowed it to be built “without supporting reinforcements”. Recent checks on this constructive hypothesis, made in the intrados of the calotte, attest that the structure of the dome was developed in a radial-vertical direction and not horizontal, as the hypothesis  of rotation  would require. The use of a horizontal radial system is limited to the structure of the  herringbone bricks ; Brunelleschi would have made use of a  pseudocircular curve placed on the platform of the dome and of a center on the vertical of the monument, materialized by crossed ropes leaded on the diagonals of the base and fixed in the relative angles.

In this way it was possible to trace the corners of the dome using small movable ribs, and at the same time (with the pseudo-circular curve to which a movable cord is referred to on one side on this and passing through the center on the vertical) to offer the masons a reference at every point of the construction to lay the bricks. According to Ricci, this would be the actual role of herringbone bricks  , which would explain the soft rope masonry  seen by Di Pasquale in the famous photo of the dome sail without the tiles. This theory was put into practice in the partial masonry model (scale 1: 5) erected under the direction of prof. Massimo Ricci in the Anconella park in Florence, where the construction technologies and the aforementioned construction method were used ^[9] .

The experiment also made it possible to clarify the more refined aspects of the dome technology, such as the structural texture of the corner arches, the role of the herringbone and the possibility for Brunelleschi to control its progress as the construction developed. in elevation. The important role of herringbone masonry  had  surprised and convinced even the architect  Giovanni Michelucci  during his visit to the model in 1989.

However, this scale model does not constitute proof of the theory from the structural point of view due to the fact that the loads produced by the structures grow following the cubic progression of the volume. In this sense, the resistance of materials and the influence of frictional forces are not scalable and the theory of the pseudo-horizontal flange remains to be verified and not completely accepted by the rest of the scientific community.

Brunelleschi’s possible inspirations

In the long debate on Brunelleschi’s possible sources of inspiration in the construction of the dome, various hypotheses have been advanced, without prejudice to the absolute novelty of the final technique used:

• the Florentine precedents;
• the vaulted structures of the Roman era;
• the Persian constructive practice.

In reality, Brunelleschi had no technological reference to solve the problem of building a dome with segments (that is, an octagonal shaped barrel vault); he literally had to invent the constructive procedure in all its mechanics. All the other domes that we tried to propose as Brunelleschi’s models were either rotating domes (self-supporting) or that could be arched and armored, while that of Santa Maria del Fiore did not allow these expedients and therefore its construction was an absolute unicum in the history of ‘architecture.

There is no doubt that Brunelleschi was well aware of the geometry and construction technique of the roof of the  Baptistery of San Giovanni , built on a dome with a pointed profile from an octagonal plan. But it is not turned herringbone. As for the second source of inspiration,   the news of the most important biographer of the architect, Antonio di Tuccio Manetti, in whose work we read that Brunelleschi spent years of study there, perhaps recalled by the findings of objects and sculptures , drives us to Rome . proper to those years. At the beginning of the fifteenth century the Eternal City was an immense archaeological field. It is here that he breathed the suggestions of classical architecture and had confirmation of  Vitruvius ‘ theories, according to which all architecture is governed by a module and a geometric grid. But the most famous dome in Roman times, that of the Pantheon, is a rotating dome made of concrete with formwork. The construction technique was not reproducible and indeed had to be completely incomprehensible in early Renaissance Italy, which had lost memory of the Roman techniques of  concrete .

From the study of the exterior, Brunelleschi would have been able at most to have noticed that the stepped form rose from a circular shape and, therefore, that Roman domes generally always contain a complete circular ring at each level in their thickness. Perhaps Brunelleschi appreciated the dome of the  Domus Aurea , raised on an octagonal pavilion limited to the lower part and built with a sort of fresh concrete, requiring arching during setting.

The hypothesis of Brunelleschi’s Roman voyage is generally accepted by all critics, but recently it has been pointed out ^[10]  that, once the derivation of the dome of the cathedral from that of the Pantheon is given up (as is necessary), nothing in the work of the great architect it must necessarily be traced back to architectural elements that were visible only in Rome. The trip to Rome is therefore possible, but not essential for understanding the formation of Brunelleschi’s architectural canons.

For the Persian source, someone wants to hypothesize that the architect became aware of the construction techniques of oriental mausoleums, given the intense commercial exchanges with the Middle East. The double dome turned without ribs of the mausoleum of  Soltaniyeh , in  Iran , built between  1302  and  1312 , or the herringbone masonry of the ancient Seljuk buildings ( 10th century ) or the later mosques of Isfahan and Ardistan are comparable to the language structural and to Brunelleschi’s technique, while differing substantially in materials, masonry and dimensions.

Frescoes

Although built with revolutionary techniques, the dome was always born from the direct inspiration of the dome of the  Baptistery , to which it owed the great development, and the octagonal shape. Originally another element of reference to the venerable  Romanesque dome was envisaged ; in fact the internal decoration was planned in  mosaic . Brunelleschi created numerous views that the decorators could have resorted to to venture into the scary void to work.

But the mosaic technique was by now very little practiced, and considered extremely expensive. Moreover, the mosaic aroused concern for the great weight that the preparation necessary to sink the tesserae in it would have added to the dome; this concern does not seem very important today, knowing the enormous weight of the dome (about 25,000  tons ) and its resistance, but at the time it was considered a not secondary reason for abandoning the project in favor of a  fresco decoration .

The works began only in  1572 , in full  mannerism  and well a century after the completion of the masonry works. Grand Duke  Cosimo I de ‘Medici  chose the theme of the  Last Judgment  to fresco the enormous dome, [6]  and entrusted the task to  Giorgio Vasari , flanked by Don  Vincenzo Borghini  for the choice of the iconographic theme. On Vasari’s death, however, only the first round of the planned concentric bands was completed, the smaller one, around the oculus at the top, covered by the  lantern . He was succeeded by  Federico Zuccari, who in a few years and, according to him, almost without help, completed in  tempera  the immense figurative cycle, one of the largest in the world in terms of surface area, and one of the masterpieces of mannerism; the painter himself, in his will, recalled not without pride of having conceived and completed the work, of which he mentions above all the great Lucifer, 13 Florentine arms tall (about 8 and a half meters). He naturally made use of many helpers, including a young  Domenico Cresti .

The contents of the cycle were those that emerged from  the Council of Trent , which had revised the medieval Catholic doctrine by ordering it into a clear arrangement. The dome is thus divided into six registers and 8 segments. Each segment includes from top to bottom starting from the central false lantern surrounded by the 24 elders of the Apocalypse (three in each segment), four scenes:

• an angelic choir with instruments of the Passion (second register);
• a category of saints and elect (third register);
• a triad of personifications, depicting a  gift of the Holy Spirit , the seven virtues, and the seven beatitudes;
• a region of Hell dominated by a  capital sin .

On the eastern segment, the one in front of the central nave, the four registers become three to make room for the great Christ in Glory between the Madonna and St. John the Baptist, above the three  Theological Virtues  ( Faith, Hope and Charity ) followed below by allegorical figures of Time (character with an hourglass, and two children representing nature and the seasons) and of the triumphant Church. Among the Chosen, the painter depicted a lively gallery of contemporary characters: the Medici patrons, the emperor, the king of France, Vasari, Borghini, Giambologna and other artists, and even himself and many of his relatives and friends and also puts his signature with the date. The cycle was concluded in  1579 .

The  cricket cage

Once the construction of the dome was finished, the outer upper part of the   octagonal drum remained to be decorated. The theme, from a dimensional point of view, had already been hinted at by Brunelleschi in the wooden model attributed to him (preserved at the  Museo dell’Opera del Duomo ). This was followed by the model created by Antonio Maria Ciaccheri between  1452  and  1460 , which probably incorporates some indications from Brunelleschi himself; the one attributed to  Giuliano da Maiano also dates back to the fifteenth century . ^[11]

However, the question remained unresolved until the beginning of the sixteenth century, when a competition was held for the completion of the drum. Several architects took part in the competition, each with their own wooden models:  Andrea Sansovino  (which included a crowning with a  balcony  shielded by Ionic columns),  Giuliano  and  Antonio da Sangallo  (in which the gallery is absent),  Il Cronaca  together with Giuliano da Sangallo and  Baccio d’Agnolo , as well as  Michelangelo Buonarroti ^[12] .

In particular, in the summer  of 1507  Michelangelo was commissioned by the Workers of Santa Maria del Fiore to present, by the end of August, a drawing or a model for the drum competition. According to Giuseppe Marchini, Michelangelo would have sent some drawings to a carpenter in Florence for the construction of the model, which the same scholar recognized in the model identified with the number 143 in the series kept at the Museo dell’Opera del Duomo ^[13]. It has a substantially philological approach, aimed at maintaining a certain continuity with the pre-existence, by inserting a series of rectangular mirrors in green Prato marble aligned with the capitals of the corner pilasters; a high entablature was envisaged, closed by a cornice similar in shape to that of  Palazzo Strozzi . However this model was not accepted by the selection board.

In  1512  the decision was made to start the work for the completion of the drum according to the project prepared by Baccio d’Agnolo together with the Cronaca and Giuliano da Sangallo. Baccio d’Agnolo himself, then  master builder  of the Opera di Santa Maria del Fiore, was commissioned to supervise the construction site; the project involved the insertion of a massive gallery supported by white marble columns at the top of the tambour, with nine arches on each side (later increased to eleven during construction). However, the works were interrupted in  1515 , with the gallery completed only on the side of the dome facing  via del Proconsolo , both due to the lack of favor obtained and due to the opposition of Michelangelo ^[14] .

And here is the anecdote. Baccio decided to stop and ask the people of Florence for an opinion. Michelangelo Buonarroti stayed in the city, who was naturally called into question. Looking at the work, after a while he seems to have exclaimed:  “It looks like a cage for crickets!”  Baccio d’Agnolo, a very sensitive artist, felt offended and left the drum unfinished, just as we see it today (only the  Via del Proconsolo side remains ). Most likely the enormous weight of the entire gallery thus finished would have created stability problems for the entire dome. ^{[ without source ]}

However, around  1516  Michelangelo made some drawings for the completion of the drum (preserved at  Casa Buonarroti ) and probably had a new wooden model built, identified, albeit with ample reservations, with the number 144 in the inventory of the Museo dell’Opera di Santa Maria del Fiore ^[15] . Once again the abolition of the gallery is recorded, in favor of a greater prominence of the load-bearing elements; in particular, a drawing shows the insertion of high free coupled columns at the corners of the octagon, surmounted by a series of strongly projecting cornices (a scheme that will later be elaborated also for the  dome  of  St. Peter’s Basilica in the Vatican). Michelangelo’s ideas remained on paper and the drum was left incomplete on seven of the eight sides.

Curiosity [ edit  | edit wikitext ]

• In  Barberino Val d’Elsa , in the  Semifonte area , there is the  Chapel of San Michele Arcangelo , a 1: 8 copy of Brunelleschi’s dome, built by  Santi di Tito  in  1597 .
• Popular legend has it that  Michelangelo Buonarroti , in a letter to his father, shortly before his departure for Rome had written, referring to the dome that he would have designed for St. Peter’s Basilica shortly after, “Vo ‘a Roma to make his sister, bigger yes, but not more beautiful ” ^[16] .
• Brunelleschi’s dome weighs 37,000 tons, St. Peter’s dome 14,000 tons, although the dimensions are similar. The difference is in the thickness of the masonry.

Notes

Bibliography [ edit  | edit wikitext ]

• Rowland Mainstone,  Brunelleschi’s Dome of S. Maria del Fiore and some related Structures , «Transactions of the Newcomen Society», 42, 1969-70.
• Rowland Mainstone, Brunelleschi’s Dome, in Architectural Rewiew, September 1963.
• Salvatore Di Pasquale, Pier Luigi Bandini, Giacomo Tempesta,  Analytical and graphic representation of the dome of Santa Maria del Fiore , CLUSF Editions, Florence, 1977.
• Corrado Brogi,  On some aspects of funicular curves , «Bulletin of Engineers of Tuscany», n.10, 1972; 12, 1972; 2-3, 1977; 12, 1977; n.7-8, 1981.
• Piero Sanpaolesi,  The Dome of Santa Maria del Fiore. The project; the building , Edam, Florence, 1977.
• Paolo Alberto Rossi, Construction principles of the dome of Santa Maria del Fiore, in Art Criticism, n. 157-159, 1978.
• Howard Saalman, Filippo Brunelleschi: the cupola of Santa Maria del Fiore, in Studies in architecture, n. 20, London, Zwemmer, 1980,  ISBN  030202784X .
• Paolo Alberto Rossi,  Brunelleschi’s domes , Calderini, Bologna, 1982.
• Massimo Ricci,  The flower of Santa Maria del Fiore: hypothesis on the rule of construction of the dome ; appendix:  Mathematical verification of the rule , by Adriano Bassignana; Department of Architecture Design, University of Florence, Alinea, Florence, 1983.
• Massimo Ricci, The secret of the dome of Santa Maria del Fiore, in Le Scienze, n. 227, July 1987.
• Lando Bartoli,  Brunelleschi’s drawing of the dome , Olschki, Florence 1994.  ISBN 8822242157
• Francesco Gurrieri,  The Cathedral of Santa Maria del Fiore , first volume, Cassa di Risparmio di Firenze, Florence, 1994.
• Dome of Santa Maria del Fiore: the restoration site, 1980-1995 , by Cristina Acidini Luchinat and Riccardo Dalla Negra, Ministry for Cultural and Environmental Heritage, Superintendence for Environmental and Architectural Heritage of Florence, Superintendence for Artistic Heritage and Historians of Florence, Opificio delle Pietre Dure, Polygraphic Institute and State Mint, Rome, 1995,  ISBN 8824039561 .
• The dome of Santa Maria del Fiore , edited by Timothy Verdon, Centro Di, Florence, 1995.
• Giuseppe Rocchi Coopmans de Yoldi,  Santa Maria del Fiore. La Cupola , University of Florence, 1999.
• Catherine Le Treut,  Le Jugement Dernier de Giorgio Vasari et Federico Zuccari à Santa Maria del Fiore , étude historique et iconographique, sous la direction de Philippe Morel, Paris 1 Panthéon-Sorbonne, INHA, 2000.
• Ross King,  Brunelleschi’s Dome. The Story of the great , Penguin, 2001 (trad. It.  Brunelleschi’s dome , Rizzoli, Milan 2001).
• Massimo Ricci,  The Dome of Santa Maria del Fiore and its model , «Bulletin of Engineers of Tuscany», n.1-2, year 2001.
• Salvatore di Pasquale,  Brunelleschi. The construction of the dome of Santa Maria del Fiore , Marsilio, Venice, 2002.
• Giuseppe Conti, Roberto Corazzi,  The Dome of Santa Maria del Fiore told by its designer Filippo Brunelleschi , Le Sillabe, Livorno 2005.
• Giuseppe Conti, Roberto Corazzi, Stefania Marini,  The Dome of Santa Maria del Fiore, between hypothesis and reality , Pitagora, Bologna, 2005.
• Graduate School of Design Harvard University (with the collaboration of Massimo Ricci),  Brunelleschi’s Dome , Harvard 2006.
• Roberto Corazzi and Giuseppe Conti,  The secret of the Brunelleschi’s Dome in Florence – The Secret of the Brunelleschi’s Dome in Florence , Florence, Pontecorboli Editore, 2011.
• Massimo Ricci,  The Genius of Filippo Brunelleschi and the construction of the dome of Santa Maria del Fiore , Le Sillabe, Livorno, 2014.
• Pietro Ruschi, The project for completing the drum of the dome of Santa Maria del Fiore, in Michelangelo architect, Cinisello Balsamo, Silvana Editoriale, 2011,  ISBN  978-88-366-1973-3 .

External links

• Opera of Santa Maria del Fiore in Florence , on operaduomo.firenze.it. Retrieved April 13, 2006  (archived from the original  on April 24, 2006) .
• Site of the Duomo , on duomofirenze.it.
• The Secret of the Brunelleschi’s Dome in Florence – Pontecorboli Editore , on pontecorboli.com.
• Institute and Museum of the History of Science: Dome of Santa Maria del Fiore , on brunelleschi.imss.fi.it.
• Ancient Structural Technologies Research Unit , on filippodiserbrunellesco.org.
• Corrado Brogi – Conference on Brunelleschi’s Dome , on spazioinwind.libero.it.
• Bulletin of Engineers of Tuscany: On some aspects of the Funicular Curves – , on spazioinwind.libero.it.
• Sur les traces de Filippo Brunelleschi, the invention de la coupole de Santa Maria del Fiore in Florence , on coupoledebrunellesch.wix.com.

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