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The important relationship of mathematics to art cannot be understated when discussing Leonardo’s later work, and in numerous documents, letters and notes, the relevance of this is well documented. At times, he seems obsessed with these issues: while working on Mona Lisa for example, Leonardo is reported by Fra’ da Novellara to be concentrating intensely on geometry.
“Non mi legga chi non e matematico.”
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“Let no one read me who is not a mathematician.”
Leonardo da Vinci
Certainly the instruction of Luca Pacioli in Milan was revealing to Leonardo, and this was manifested particularly in the ‘Last Supper’. There exists in mathematics a unique number, 0.618, which is the only one when divided into unity (1.0) yields its own reciprocal – 1.618. It is referred to as the ‘Golden Section’: also known as the ‘Golden Rule’, ‘Golden Cut’, ‘Golden Number’, ’Golden Proportion’, ‘Golden Ratio’. The formula was first recorded by Euclid, c. 300 B.C. In the fifth attribute of God, functional comparison, Pacioli sets the ‘Divine Proportion’ in relation to the Platonic quintessence.
‘Portrait of Fra’ Luca Bartolomeo de Pacioli’, by Jacopo de Barbari, c.1495 (attribution unconfirmed). Table is filled with geometrical tools: slate, chalk, compass, a dodecahedron model. A rhombicuboctahedron half-filed with water is suspended from the ceiling. Pacioli is demonstrating a theorem by Euclid.
The letter ‘A’, illustration and design, for the De Divina Proportione by Luca Pacioli.
“As God confers being to the celestial virtue, called by the other name ‘fifth essence’, and through that one to the other four simple bodies, that is, to the four earthly elements … and so through these to every other thing in nature. Thus this our proportion is the formal being of (according to Timaeus) heaven, attributing to it the figure of the solid called Dodecahedron, otherwise known as the solid of twelve pentagons.” Luca Pacioli, De Divina Proportione
Why is this important? To Leonardo, and other Renaissance masters, the ‘Golden Ratio’ became a critical instrument in the matter of accurate proportionality. Fra’ Luca expounds the theory in 1498, while teaching in Milan, and later, in 1509, he and Leonardo collaborate to publish De Divina Proportione, in which is seen one of the most famous drawings associated with Leonardo: ‘Proportion Man’, also known as ‘Vitruvian Man’, which has become one of the world’s most iconic images. In the meantime, when the French finally re-occupy Milan in 1500, they take from Leonardo’s circle the Ferrarese architect, Giacomo Andrea, who had interpreted and translated some of Vitruvius’ work for Leonardo, and subsequently have him publicly beheaded and quartered on May 12, silencing a vital voice of science and independent thought. The message is not lost on Leonardo, who loses little time in diverting his loyalties to the French. At the same time, one can sense Leonardo disguising his own new-found knowledge in painting techniques that manifest themselves in his later works.
When Fra’ Pietro da Novellara and others write to Isabella d’Este in the early years of the 16th Century, there is significant reference that Leonardo has no patience to paint because of his constant studies of geometry. When Leonardo returned to Florence in 1500 he did so in the company of his mathematics tutor, Fra’ Luca Pacioli, and from an educational point of view this relationship cannot be underestimated. While Leonardo himself writes in general terms of the importance of mathematics, it is unlikely that this refers to the disciplines of algebra, trigonometry and calculus, common in today’s classrooms. Rather it is geometry that interests him most and that is most relevant to his art. Leonardo sees in geometry the precision through which he can construct unique compositions in perfect harmony within its setting. The two versions of Mona Lisa are suffused with mathematical similarities as well as the divine proportion.
Just after the publication of De Divina Proportione, Raphael painted his massive and extraordinary fresco, ‘The School of Athens’, in the Vatican. This incorporates many of the mathematical theories of Luca and Leonardo; in addition, most of the historically famous characters from ancient Greece are represented. It is also an homage to the master. Raphael himself is Apelles, the great painter; Bramante, the architect of St. Peter’s Basilica, is Euclid; and perfectly centered in the work is Plato, as represented by Leonardo.
Kenneth Clark writes: “If man was the measure of all things, physically perfect man was surely the measure of all beauty, and his proportion must in some way be reducible to mathematical terms and correspond to those abstract perfections, the square, the circle, and the golden section.” Clark goes on to remind us that “This union of art and mathematics is far from our own way of thinking, but it was fundamental to the Renaissance. It was the basis of perspective,” i.e. “scientific representation of receding figures in space …”
Leonardo never tired of the intense relationship between art and visual mathematics. His fascination with the sense of infinity, as depicted in his knot designs, was perhaps also an unwitting precursor to theories of Fractal Geometry and their relationship, in turn, to nature. Though these mathematical theories have been refined only as recently as the 1980s, Leonardo was working on their practical application 500 years earlier.
A beautiful example is the intricate and subtle pattern on Mona Lisa’s blouse. The design may initially appear innocuous, but the brain that conceived it, and the genius that created it was dedicated to the belief that a deep understanding of mathematics was fundamental to the creation of great art. One of the things that makes the ‘Earlier Mona Lisa’ such an extraordinary work, is that not only does it display a full range of knowledge of geometry often used by Leonardo, but that these innovative elements can be seen throughout the painting.
THE ‘GOLDEN RATIO’ IN THE ARTS
True Golden Spiral: the length of the side of a larger square to the next smaller square is in the ‘Golden Ratio’.
Many books claim that if a rectangle is drawn around the face of the Louvre ‘Mona Lisa’, the ratio of the height to width of that rectangle is equal to the ‘Golden Ratio’. No documentation exists to indicate that Leonardo consciously used the ‘Golden Ratio’ in the composition of the Louvre ‘Mona Lisa’, nor to where precisely the rectangle should be drawn. Nevertheless, one has to acknowledge the fact that Leonardo was a close personal friend of Luca Pacioli, who published a three-volume treatise on the ‘Golden Ratio’ in 1509 entitled De Divina Proportione (On Divine Proportion). Leonardo’s illustrations of polyhedra for that publication, and his views that some bodily proportions exhibit the ‘Golden Ratio’ have led some scholars to speculate that he incorporated the ‘Golden Ratio’ in (some of) his paintings.
Much has been written by scholars about the opinion that Leonardo built his portraits on the basis of a triangular construction, therefore implying that this idea was Leonardo’s innovation; something that made his work unique. Realistically, the human body posing for a portrait would naturally take a triangular shape. In addition, the number of degrees in the critical angle of any triangle might also be arbitrary. There is no hard and fast rule.
In the case of the ‘Earlier Mona Lisa’, the legs of the (blue) triangle are shown correctly placed in the lower corners, and the peak bisects the width of the painting at the top. Now, that ‘Golden Ratio’ diagram is applied. It nestles against the edge of the left column, and, coming across the top of her head, exactly meets the leg of the triangle. At the same time, the spiral beautifully frames her face, with the rounded side on the right, and the vertical side on the left. Also, the spiral winds from the tip of her nose, grazing the bottom of her chin, and all the way around to her right arm, from elbow to thumb.
The same set of diagrams was applied to the Louvre ‘Mona Lisa’. In theory, if Leonardo painted or designed both pictures, then the application of diagrams should work equally well on both. As is known, the wood panel of the Louvre ‘Mona Lisa’ is somewhat smaller than the canvas of the earlier painting, and, to complicate matters, the figure of the Louvre ‘Mona Lisa’ is slightly larger than that in the ‘Earlier Mona Lisa’. The theories of both the triangular construction, as well as the ‘Golden Ratio’ as depicted in the diagram, work equally well.
However, because of the size of this picture, some of the diagram’s edges and starting points are outside the plane of the panel. This is not a problem. In scaling drawings, not all equations have to be on the same page. Often, vanishing points and horizon lines are unseen on a painting by the viewer; but that does not mean that they are not there. The construction of the work has to fall within the limitations imposed by the size and shape of the support. At first it may look restrictive; but a qualified draughtsman will be able to apply the critical information, more or less as it is shown here.
The vertical red dotted line is an arbitrary addition. In the case of both portraits it extends the vertical line that starts at the lower point of the chin, and perfectly bisects the face to the parting of the hairline.
The Geometry Of Beauty In The Paintings By Leonardo da Vinci
by Alfonso Rubino
Works of Leonardo are interconnected through an invisible geometric-harmonious fabric. The discovery was made by studying the drawing, the ‘Vitruvian Man‘. Leonardo gives primary importance to the external dimensions of the paintings inviting us to consider not only the content but also the support of his works. By support I mean the external dimensions of the work. In the case of the Vitruvian Man, the sheet was, according to my hypothesis, originally 34.52 cm high and 24.66 cm wide.
Art historians, following the tradition of Vitruvius, define the possible presence of a geometric fabric on the basis of a Work of Art: an iconogram.
In Leonardo’s work, inconograms are connected to each other both typologically and dimensionally. The geo-seed that produces them is the geometric model found in the Vitruvian man.
It is the harmonious universal code which is based on Archimedes’ quadrature of 22/7.
The harmonic code of the Vitruvian Man is also, undoubtedly, found in His other important works:
‘The Annunciation‘, the ‘Virgin of the Rocks‘ in the Louvre, the ‘Baptism of Christ‘ and the ‘Last Supper‘.
And in Leonardo’s work, one can reconstruct a sequence of iconograms depending on the level of complexity.
- The Annunciation – Level 1
- Baptism of Christ – Level 2
- Virgin of the Rocks, Louvre – Level 3
- Vitruvian sheet – Level 1
- Vitruvian Man – Level 3
- Earlier Mona Lisa- Level 2
- Louvre Mona Lisa – Level 3b
The analysis of Verrocchio’s ‘Baptism of Christ‘ (painted with the help of Leonardo) allows to understand that the code was transmitted to Leonardo by His Masters. He was not the only artist to use it at that time. For example, the code can be found the ‘Spring‘ by Botticelli.
In this document you will find the geometric sequence between the ‘Vitruvian Man‘, the Louvre and the earlier Mona Lisas. He is the logical and deductive order.
The Geometric-harmonic fabric suggests that the author of the ‘Earlier Mona Lisa‘ is the same as the author of the Louvre Version. Given the geometric data presented, it would seem impossible that the earlier version could have been executed by any artist other than Leonardo.
Geometric construction for the establishment of the circle / square of the human figure.
In the link below, you will find a comparative table with the various iconographic models of Leonardo
http://alfonsorubino.altervista.org/
http://alfonsorubino.altervista.org/
In the table below, you will find both the theoretical and effective dimensions of the Leonardo works. (The theoretical dimensions of the support of the ‘Vitruvian Man‘ are fixed before the fact).
Actual | Theoretical | |||
Annunciation | 98 | 217 | 97,81 | 216,47 |
Baptism of Christ | 151 | 177 | 152,04 | 177,37 |
‘Virgin of the Rocks‘ | 122 | 199 | 122,26 | 199,13 |
Vitruvian man | 34,4 | 24,5 | 34,52 | 24,66 |
Louvre Mona Lisa | 53 | 76,8 | 53,14 | 76,77 |
Earlier Mona Lisa | 64 | 86 | 64,11 | 85,51 |
Through the link below, you will find a comparative table between the Louvre ‘Mona Lisa‘ and the ‘Earlier Mona Lisa‘
http://alfonsorubino.altervista.org/
Related bibliography by the author:
a- La Triplice Cinta –Roberto Mosca & Alfonso Rubino
La geometria della bellezza nelle opere dei maestri di ogni tempo-Terra Nuova Edizioni – Firenze
b- Il Segreto dell’Uomo Vitruviano di Leonardo –libro elettronico
Casa Editrice – Liberfaber – Principato di Monaco
http://www.liberfaber.com/
http://alfonsorubino.altervista.org/
Related bibliography by the author:
a- La Triplice Cinta –Roberto Mosca & Alfonso Rubino
La geometria della bellezza nelle opere dei maestri di ogni tempo-Terra Nuova Edizioni – Firenze
b- Il Segreto dell’Uomo Vitruviano di Leonardo –libro elettronico
Casa Editrice – Liberfaber – Principato di Monaco
http://www.liberfaber.com/
A slideshow of the essential elements is available here:
http://www.slideshare.net/alfonsorubino/dall-uomo-vitruviano-alle-donne-vitruviane-di-leonardo2
http://www.slideshare.net/alfonsorubino/dall-uomo-vitruviano-alle-donne-vitruviane-di-leonardo2
Mona Lisa
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Alternative Title: “La Gioconda”
Mona Lisa, also called Portrait of Lisa Gherardini, wife of Francesco del Giocondo, Italian La Gioconda, or French La Joconde, oil painting on a poplar wood panel by Leonardo da Vinci, probably the world’s most famous painting. It was painted sometime between 1503 and 1519, when Leonardo was living in Florence, and it now hangs in the Louvre Museum, in Paris, where it remained an object of pilgrimage in the 21st century. The sitter’s mysterious smile and her unproven identity have made the painting a source of ongoing investigation and fascination.
Who was the Mona Lisa in real life?
There has been much speculation and debate regarding the identity of the Mona Lisa’s sitter. Scholars and historians have posited numerous possibilities, including that she is Lisa del Giocondo (née Gherardini), wife of the Florentine merchant Francesco di Bartolomeo del Giocondo—hence the alternative title to the work, La Gioconda. That identity was first suggested in 1550 by artist biographer Giorgio Vasari.
How many years did it take to paint the Mona Lisa?
Leonardo da Vinci began painting the Mona Lisa in 1503, and it was in his studio when he died in 1519. He likely worked on it intermittently over several years, adding multiple layers of thin oil glazes at different times. Small cracks in the paint, called craquelure, appear throughout the whole piece, but they are finer on the hands, where the thinner glazes correspond to Leonardo’s late period.
Where is the real Mona Lisa kept?
The Mona Lisa hangs behind bulletproof glass in a gallery of the Louvre Museum in Paris, where it has been a part of the museum’s collection since 1804. It was part of the royal collection before becoming the property of the French people during the Revolution (1787–99).
What is the value of the Mona Lisa?
The Mona Lisa is priceless. Any speculative price (some say over a billion dollars!) would probably be so high that not one person would be able or willing to purchase and maintain the painting. Moreover, the Louvre Museum would probably never sell it. The museum attracts millions of visitors each year, most of whom come for the Mona Lisa, so a steady stream of revenue may be more lucrative in the long run than a single payment. Indeed, the museum considers the Mona Lisa irreplaceable and thus spends its resources on preventive measures to maintain the portrait rather than on expensive insurance that can only offer mere money as a replacement.
Why is the Mona Lisa so famous?
Many theories have attempted to pinpoint one reason for the art piece’s celebrity, including its theft from the Louvre in 1911 and its tour to the U.S. in 1963, but the most compelling arguments insist that there is no one explanation. The Mona Lisa’s fame is the result of many chance circumstances combined with the painting’s inherent appeal.
Subject
The painting presents a woman in half-body portrait, which has as a backdrop a distant landscape. Yet this simple description of a seemingly standard composition gives little sense of Leonardo’s achievement. The three-quarter view, in which the sitter’s position mostly turns toward the viewer, broke from the standard profile pose used in Italian art and quickly became the convention for all portraits, one used well into the 21st century. The subject’s softly sculptural face shows Leonardo’s skillful handling of sfumato (use of fine shading) and reveals his understanding of the musculature and the skull beneath the skin. The delicately painted veil, the finely wrought tresses, and the careful rendering of folded fabric demonstrate Leonardo’s studied observations and inexhaustible patience. Moreover, the sensuous curves of the sitter’s hair and clothing are echoed in the shapes of the valleys and rivers behind her. The sense of overall harmony achieved in the painting—especially apparent in the sitter’s faint smile—reflects Leonardo’s idea of the cosmic link connecting humanity and nature, making this painting an enduring record of Leonardo’s vision. In its exquisite synthesis of sitter and landscape, the Mona Lisa set the standard for all future portraits.
There has been much speculation and debate regarding the identity of the portrait’s sitter. Scholars and historians have posited numerous interpretations, including that she is Lisa del Giocondo (née Gherardini), the wife of the Florentine merchant Francesco di Bartolomeo del Giocondo, hence the alternative title to the work, La Gioconda. That identity was first suggested in 1550 by artist biographer Giorgio Vasari. Another theory was that the model may have been Leonardo’s mother, Caterina. That interpretation was put forth by, among others, Sigmund Freud, who seemed to think that the Mona Lisa’s mysterious smile emerged from a—perhaps unconscious—memory of Caterina’s smile. A third suggestion was that the painting was, in fact, Leonardo’s self-portrait, given the resemblance between the sitter’s and the artist’s facial features. Some scholars suggested that disguising himself as a woman was the artist’s riddle. The sitter’s identity has not been definitively proven. Numerous attempts in the 21st century to settle the debate by seeking Lisa del Giocondo’s remains to test her DNA and recreate an image of her face were inconclusive.
History
Leonardo da Vinci began painting the Mona Lisa about 1503, and it was in his studio when he died in 1519. He likely worked on it intermittently over several years, adding multiple layers of thin oil glazes at different times. Small cracks in the paint, called craquelure, appear throughout the whole piece, but they are finer on the hands, where the thinner glazes correspond to Leonardo’s late period.
Picture Of Mona Lisa Smile
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Mona Lisa Secret Message
Best video poker sites. French King Francis I, in whose court Leonardo spent the last years of his life, acquired the work after the artist’s death, and it became part of the royal collection. For centuries the portrait was secluded in French palaces, until insurgents claimed the royal collection as the property of the people during the French Revolution (1787–99). Following a period hanging in Napoleon’s bedroom, the Mona Lisa was installed in the Louvre Museum at the turn of the 19th century.
In 1911 the painting was stolen, causing an immediate media sensation. People flocked to the Louvre to view the empty space where the painting had once hung, the museum’s director of paintings resigned, and the poet Guillaume Apollinaire and artist Pablo Picasso were even arrested as suspects. Two years later an art dealer in Florence alerted local authorities that a man had tried to sell him the painting. Police found the portrait stashed in the false bottom of a trunk belonging to Vincenzo Peruggia, an Italian immigrant who had briefly worked at the Louvre fitting glass on a selection of paintings, including the Mona Lisa. He and two other workers had taken the portrait from the wall, hid with it in a closet overnight, and ran off with it in the morning. Peruggia was arrested, tried, and imprisoned, while the Mona Lisa took a tour of Italy before making its triumphant return to France.
During World War II the Mona Lisa, singled out as the most-endangered artwork in the Louvre, was evacuated to various locations in France’s countryside, returning to the museum in 1945 after peace had been declared. It later traveled to the United States in 1963, drawing about 40,000 people per day during its six-week stay at the Metropolitan Museum of Art in New York City and at the National Gallery of Art in Washington, D.C. It also toured to Tokyo and Moscow in 1974.
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Condition
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Scholars have noted that the Mona Lisa is in fairly good condition for its age. The poplar panel shows some evidence of warping from resistance to its original frame and to braces added by early restorers. To prevent the widening of a small crack, visible near the centre of the upper edge of the painting, dovetails were added to the back of the painting. Restorers later pasted heavy canvas over the crack and replaced the top dovetail.
The glass protecting the Mona Lisa was replaced with a bulletproof case after several attacks in 1956, one of which damaged an area near the subject’s left elbow. The Mona Lisa thus escaped harm from acts of vandalism in 1974 during the work’s visit to Tokyo and in 2009 when a museumgoer threw a ceramic mug at it.