Sacred Geometry- God in Numbers

Since the beginning of man’s perpetual quest to ideate, create, and construct- beauty was not in the eye of the beholder. It was in the hands and minds the artists, scribes, mathematicians and craftsmen. Those who Illuminated Manuscripts, applied Scientific perspective in paintings, and designed the lucent Rose Windows of Gothic Cathedrals. These hands and minds were determined to create a permanent and resplendent creation that would radiate through into the world of the transient. What was their secret, what is their connection? The beauty of their success in producing the most intricate and beautiful works of art is linked by the very laws that govern nature. They all employed patterns and exact proportions, sacred geometries: the underlying structure of our Universe. Within this report, I will explore the use of sacred ratios, pattern and proportions in Medieval Illumination Transcripts and Early Renaissance paintings.

Sacred Geometry: The Book of Kells

Bridging our temporal existence, the idea of replicating this “Divine” structure of proportions and applying it to art/sculpture and architecture- was and is an epic concept. Let’s first begin discussing what sacred geometry is and how it was used within the Illuminated manuscript of The Book of Kells (Decorated by Irish monks, in Scotland ca. 800) sacred geometry is used to describe the geometrical laws that create everything in existence. Patterns found in nature, structures of light waves, the vibration of music notes, and cosmology. Looking back in prehistory, the cultural context of this sacred geometry was used in foundational construction of temples, cathedrals, megaliths and mosques. During the Middle Ages, as religious art goes, one of the most famous of Illuminated Manuscripts (The Book of Kells) was decorated using the traditional Celtic & Anglo-Saxon design principles of pattern, grids and geometry. This illuminated manuscript contains the four Gospels of the New Testament written in Latin, along with various masterworks of calligraphy and design. The main tools that were used for planning out the complex conception were compasses and “straight-edges”, a tool similar to our modern day ruler. These two simple instruments, combined with the knowledge of Egyptian, Greek and Roman architecture and art allowed the monastics to decorate these pages with the most unbelievable detail of ornaments, human and pattern wise, that interlace in a labyrinthine of complexity.

In analysing one of the carpet pages (Trinity College Dublin MS 58 (the Book of Kells) f. 33r ), this carpet page is placed within a 4x3 rectangle. According to the sacred geometry and number theory used by Christians, this geometry was used as a “building foundation”, a foundation that might only be apparent to those knowledgeable enough, or associated with the scribe or scholar. Called the “Squared Circle” this proportion of form is scared in that the rectangles, circles and squares contain measurements of the numbers 3,4 & 5 (based on complex bisecting of triangles and hypotenuse formulas) , all of which were very important to the early Christian scribes. The number 3, symbolises the Trinity. The number 4, represents the 4 points on Christ’s cross, a symbol of the Tetramorph. The number 5, calls upon the 5 books of Jewish Law ( Genesis, Exodus, Leviticus, Numbers & Deuteronomy) and also the five wounds that Christ bore on the Cross. As you can see, there are 8 circles within the Squared Circle, and are founded on the sacred geometry of “Vesica Pisics”. The word Vesica Picis, means “fish bladder” in Latin, and is an intersection of two circles who’s centers distance is equal to the circles radius. Circle one: God, Circle two: Humanity, the Intersection: Jesus Christ. This underlying sacred element further reminded the reader that Christ was the foundation of the design. The eight circles that again, create another Vesica Picis within the image, was no accidental pattern. In early Christianity, the number 8 symbolized immortality, and the covenant between God and his worshipers. Christ also rose from the dead on the 8th day of the week, a renewal of birth, victory over death. All these manifestations symbolized through the sacred geometry of the Vesica Picis and the Squared Circle, embed an even deeper meaning. With the use of geometric forms and number theories, the artist was able to connect with God, the original “compass”, the ultimate mathematician. The scribes were completely aware of this spirituality expressed in physical form, and this was their “pyramid”, this would stand the test of time, just as the foundations of the universe is never swayed, so did the scribes consider their artwork, as beyond velum and ink, was now a part of God’s infinite sacred web of geometry.

Trinity College Dublin MS 58 (the Book of Kells) f. 33r

God in Nature, God in Numbers: Early Renaissance

Let’s fast forward from the Illuminated folios of medieval manuscripts of the early 9th century to the dawn of the early Renaissance in the 15th century Italy. The artists of the Early Renaissance were fascinated with numbers and ratios. Luca Pacioli had published a booked called “On the divine proportion” in 1509, describing one ratio that he found almost everywhere in nature- now known as the “golden ratio”. The idea that like God himself is the Trinity,3, and cannot be described in words, this divine number can only be described within the Divine Proportion. In sharing his mathematical idea’s with Renaissance artists such as Leonardo da Vinci and Peiro della Francesca, his geometrical theories would pave the way for numerous Renaissance artists who would use this ratio hidden within their art and architecture.

Portrait of Luca Pacioli

Piero della Francesca (1415-1492) was one of the most avant-garde artists of the early Renaissance. With his passions, art & geometry- he integrated the two in hopes of bridging the organic beauty to the geometric foundation of it. Within the Flagellation of Christ (c.1460), Piero sought to create perfection within geometry, which he had. With even today’s computer analysis, the vanishing point is accurate, right down to the nearest millimetre. Sacred geometry from the tiles, suggests an octagonal pattern, yet again the number 8- symbolizing the 8 days after Christ entered Jerusalem, and his resurrection. The use of the “Golden Rule”, which was the Renaissance mathematical tool of the Rule of Three, and scientific one point perspective, anchors the composition into a realm as mathematical and precise as the very nature of the wing of a butterfly.

Piero del Pollaiuolo ( 1441-1496 ) was an Italian painter that used perspective, and an exploration of sacred geometry, contributing to the humanistic movement of the Italian Renaissance. Along with his brother Antonio del Pollaiuolo, they composed one of the greatest achievements of the Early Renaissance. This particular painting: The Martyrdom of St. Sebastian (ca. 1475) we will make note to the intricate geometrical placement of the figures. Working around the “golden triangle”, and the use of rotational symmetry, Francesca’s composition shows three of the archers in same position as each, but at different angles. The figures are highly realistic, with obvious knowledge of the human form and anatomy. You can see the muscle, bone, tendons and veins beneath the skin and drapery. There is atmospheric perspective within the landscape, yet the arrangement of the figures in the middle and foreground, seem not as convincing. The use of a new technique of aerial perspective highly idealizes the martyr’s story. They are arranged in a pyramidal composition, in a very specific triangle, one that forms what would be the base of the pentagon. This triangle the “golden triangle” contains the golden ratio found in snail shells, the nautilus and all around nature. So here we have again, the incorporation of the Holy Trinity, the very presence of God and his divinity.

The use of pattern, geometry and mathematics within art and architecture was and is more than just creating visual harmony and aesthetics. The artists of the Renaissance sought to create a “mirror of the soul” and used the spiritual ratio of the Golden Rule, the square root of 3 to express the deepest connection to God’s creation- more than words could express. During the Medieval era, there was spiritually and creativity bubbling through the air. Mysticism, alchemy and Neoplatonic philosophy was on the raise and artists explored the sacred geometry and applied it to their illuminated manuscripts and explored its applications to music. Details only fathomable today by aid of a magnifying glass, were delicately and meticulous planed by aid of sacred geometry. Just in analysing the layers upon layers of sacred symbolism and geometry of all these works, we can see the significance. It interacts with the viewer without their knowledge, and just as the sacred foundations of temples, pyramids and cathedrals- their fortitude to withstand the sands of change, they remain timeless and universal. Engineered with the smallest of details in mind, these patterns are just as infinite as they are beautiful.