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| Albrecht Durer, Salvatur Mundi |
Saviour of the World was a common motif in 15th and at the beginning of the 16th century as a response to the apocalyptic predictions that were in fashion at the end of old century. Artists like Jan van Eyck and Hans Memling, Leonardo da Vinci, Andrea Previta, Pedro Berruguete, all painted Saviour of the World. Art historians suggest that Durer painted his version of Salvator Mundi around year 1503. There is a strange relationship between this painting and ten years later engraving Melencolia I. It appears that the main character of both artworks is the same, but in case of Salvator Mundi he is holding the sphere firmly, while in Melencolia I the Christ -like figure this time even more resembling Durer, is timidly sitting, gazing in an unknown direction with the sphere laying on the floor. This sphere in the lower left corner proves to be the module of the engraving since it's perimeter fits exactly 11-times in the breadth, and 14-times in the height of the engraving, encoding the approximation 22/7 for the value of π. Durer used this two numbers, approximating infinity, many times in his compositions and he was not alone, many artists and architects encoded these two numbers in their compositions, beginning with the Great Pyramid whose main features are derived from the ratio of 22/7, which closely approximates the value of π.
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| 22 modules needed for π approximation |
An interesting example of such a compositional 'story of π' told by means of measures is Albrecht Durer's Salvator Mundi. It represents Christ dressed in blue and red clothes holding a sphere in his left hand and making a gesture of the second coming with his right hand. The colors are typically gothic: bkue and red for Christ's clothes and green background represent the basic trinity of colors so often used by gothic artists. A reader is reminded that if these three colors are mixed together, a radiant white light is obtained.
The sphere that Christ holds in his left hand proves to be the module of composition. It's perimeter fits 7-times in the breath and 8.5-times in the height, giving the ratio of 14:17 if expressed in round numbers. The interesting part of this composition is the diagonal of 22 modules, which together with 7 modules of the breadth reveals the ratio 22:7. A width, a height and a diagonal of the painting can also be considered as a √2, √3, and √5 respectively.
√2 = 1.414 = width
√3 = 1.732 = height
√5 = 2.236 = diagonal
This is also an uncanny reference to a similar manipulation of square roots - the Giza plateau floor plan expressed in royal cubits reveals the same proportions as Durer's canvas. Surely just a coincidence..
Another peculiar feature of √2 and √3 is that added together, a value close to π is obtained: √2 + √3 = 3.146...
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| 22 perimeters of sphere |
Albrecht Durer even further enhanced the importance of π in the underlying structure of the composition. If the sphere that Christ holds is applied to the circumference of the circle aligned to the top of the painting, we get 22 divisions for the circumference of the circle with the diameter of 7 modules. It is surprising that Durer repeats the 'story of π' so many times, though in different ways - like variations on a theme. The modules of main dimensions are all factors of the popular Fibonacci series widely used by the artists throughout the period of Renaissance. The fifth of Fibonacci series contains the main dimensions expressed in modules:
| 1 |
5 |
6 |
11 |
17 |
28 |
45 |
73 |
118 |
... |
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22 |
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14 |
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Both main dimensions, 14 and 17 modules, also encrypt by means of simple Masonic gematria the title of the painting, and a variant of Albrecht Durer's signature.
SALVATOR MVNDI = (19+1+12+22+1+20+15+18)+(13+22+14+4+9) = 170
ALBRECHT DUERER = (1+12+2+18+5+3+8+20)+(4+21+5+18+5+18) = 140
The surface area of the rectangle 14 x 17 modules is 485, which is a gematric value of the Greek word ΙΕΟΥ, IEOU, a Gnostic name of God as revealed by Clement of Alexandria.
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