In terms of geometric prints, geometric art & design we're writing this article to give a very brief introduction to some of the history of geometric art, design and its antiquity. To write thoroughly an exhaustive 1,000+ page book could be written about the very large amount of artists, geometric art influences and large body of work pertaining to this topic. We are by no means experts and are influenced in our own work by geometry, geometric art & design and fascinated by its creation throughout cultural history spanning thousands of years.
To understand geometry applied to art, architecture, design, computer science, mosaics, fashion patterns (textiles) and the myriad of reproduced geometric prints we first need to go back to square one, Summer. The Sumerian civilisation of present-day southern Iraq (ancient Mesopotamia) dates to around 5000-4000 BCE. Experts agree Babylonian mathematics dates to between 5000 - 3000 BCE and was scribed on cuneiform clay tablets. Cuneiform is one of, if not the first written system. Mathematics and the cuneiform writing system are some of the first ancient examples of geometry in use.
Cuneiform Geometry Problems
Ancient Assyrian (Modern Cristians) Wall Relief: Winged Genius (Artefact of Babylonian & Sumerian civilisations Mesopotamia) - The Great Pyramid of Giza
Mathematics was used in Summer and one of their numeric systems was sexagesimal (base of 6). Egyptians used maths for surveying & building, taxing the public for cooking oil & astronomy. Geometry in Greece came later (300 BCE) and its maths still in use today was used by and in some cases created by well known mathematicians Euclid, phi by representing the golden ratio/mean between 325- 265 BCE (Euclidean geometry), Pythagoras (Pythagoras Theorem), Aristotle, Archimedes and others. The Fibonacci Sequence having a strong relationship to the golden mean became prominent from 1202 & it was named after Italian mathematician Leonardo of Pisa, later posthumously known as Fibonacci (1170 – 1250). It was first used by Pingala and in Indian mathematics, however Fibonacci was the first to introduce the mathematical sequence to European cultures in his book Liber Abaci. The Fibonacci sequence while being used in Mathematics was later in time more broadly applied to art, design and used for determining divine proportions.
The Fibonacci Sequence
Greece
The greeks were one of the first civilisations to broadly apply geometric principles to sculpture, textiles & in terms of this article more traditional art-forms including decorative art (vase painting) & painting. Geometric designs were also commonly created on Mesoamerican vases. While the Greeks could be generally accepted as 'one of' the first it is somewhat misleading to say they were the first to create geometric art and design. The use of geometric motifs had been used across cultures pre-dating the Greeks by thousands of years. In the Mesolithic period (Middle Stone Age 10,000-8,000 BCE) of Southern Scandinavian archaeological finds, zig zag patterns and snake symbolism on antler batons, clubs and bone daggers were discovered in sites belonging to the Maglemose, Kongemose and Ertebølle cultures. Some examples of ancient geometric art also include African art and Aboriginal Australian art. Geometric art was in the truest sense created across the world in different periods of time and multiple cultures. While individual countries can claim being the first, it is merely a source of national or cultural pride rather than factual truth. New archaeological discoveries are a common enough occurrence with sometimes fierce rivalry between archeologists, quick to claim a find as being the oldest or first in history.
Ancient Geometric Aboriginal Rock Art.
Left: Wavy lines can represent water, lightning, tracks and snakes in Aboriginal culture. 10,00 year old rock art, Walga Rock monolith, Western Australia. Right: Ancient geometric rock art "Cyclone Cave" in Wandjina, The Kimberly, Western Australia
The Greeks were well known for creating art based on the accurate representation of the human figure during the Hellenistic art period. Hellenistic art visualised the ideal, human form and expression (anatomy) which came after Alexanders death in 323 BCE. It portrayed three dimensional human figures and forms, including the creation of figurative sculpture. Prior Greek Classical art was more simplified, involved stylised human figures and movement without the accuracy of a three dimensional perspective. In ancient history geometry was applied to numeric systems, architecture (pyramids), calendars, astronomy and mathematics. Greek geometric art peaked between 900 BCE – 700 BCE during the greek dark ages (geometric period) and Greece's cultural epicentre was Athens.
Greek Decorative Geometric Art: Funeral urns (750-720 BCE)
Geometric art was originally created as decorative abstract patterns and used basic geometric shapes (triangles, circles and rectangular forms) and in some cases used symbolism. Much later than the earlier examples of geometric symbolism during the Greek Classical period 510-323 BCE motifs adjoined Greek allegories and paintings of culturally significant events which at times depicted battles and victories over kings empires. One such event was when Alexander the Great triumphed over the autocratic Persian Achaemenid empire led by King Darius III (334-330 BCE). Over many generations both empires had regularly come into conflict. It turns out the Greeks took issue with being subservient to the Persian kings. As one can tell, not a lot has changed over thousands of years of time with the rise and fall of empires and in modern times "global superpowers".
Alexander "the Great" Mosaic - Battle of Issus (333 BCE) over Darius III King of Persia
Early geometric art was however decorative and simplified. The geometric style evolved throughout Greece's rich history from basic geometric shapes into much more stylised and detailed work painted on vases and through the creation of celebratory monuments and sculptures. Similarities to early Greek geometric work can be seen within other civilisations, oceans apart in the Americas and throughout the world.
Greek Classical Art
Mesoamerica
In Mesoamerica (Olmec, Teotihuacan, Toltec, Zapotec, Maya, Aztec, Mixtec) geometry and math was also applied. Similar to parts of the east it was ingrained in their religious beliefs, pyramids (architecture), astronomical systems, rituals, calendars and people's everyday lives. The Maya were known to of tracked the planets Mercury, Venus, Mars, Jupiter & Saturn as they were visible to the eye. The outer planets at this stage were not thought to be known by the Maya. The Maya commonly had scribes prophesies their future (drought, floods, maize crops etc.) based on the planetary movements, in particular Venus. Similarly to other ancient cultures the Maya used their own numeric and calendar systems. Mayan mathematics is vigesimal, with a base of 20 compared to the modern metric system base of 10 or Sumerian base of 6. The Mayan used two calendar systems. The first a 365 day calendar and the second a 260 day calendar used to determine the time of religious and ceremonial events including the naming of a newborn child. The Códice Maya de México (Maya Codex of Mexico) is currently the oldest surviving book of the Americas dated roughly to 1100 CE along with three other Códices; the Dresden Códice, Madrid Códice & Paris Códice named after their current locations. The Spanish conquistadors (Christian conquerors) invaded parts of the Americas and much of Mesoamericas ancient books & artefacts including their contained knowledge was either destroyed, burned or in the lucky case of the surviving códices secretly hidden in caves or taken abroad to be on-sold for museum collections. In modern times this is known as an ethnic cleansing and led to a loss of cultural identity within the native Central and South Americans afflicted by the conquest. This scenario was repeated similarly in Australia when in 1788 the English invaded Australia, slaughtered natives and assimilated indigenous culture into the English ways and Christian belief system.
In recent years there has been a cultural push to return artworks to their original homes from overseas galleries and institutions (to the applause of the average person). This nascent movement is occurring with African Art, Native Aboriginal Australian art and other countries in which the injustices have occurred. Countries are seeking their culturally significant artwork and artefacts to be returned.
Persia
Early Persian pottery and artefacts have similar use of geometric motifs like Greeces decorative art. Some geometric patterned pottery from the Uruk period (Sumer) dates to roughly 7000-6000 BCE found in Hassuna. Persian or Iranian geometric art (Islamic) became more aesthetically complex over time. Persian artwork over multiple millennia used geometric patterns and symmetry within Mosques along with other art and design based mediums. Persian or Iranian art is brilliantly executed and quite incredible to look at.
Pottery 7000-6000 BCE Uruk, The cradle of civilisation (Sumer) Hassuna, modern Iraq, later part of the Persian empire.
Sheikh Lotfollah Mosque, Isfahan, Iran (1619) : Persian Geometric Art
M.C. Escher (Netherlands, 1898-1972) was known to have been inspired by Persian & Islamic geometric art/patterns and math, although not a competent mathematician or advanced in his mathematics learning. Disappointingly M.C.Escher's work was shunned by the art world and he was widely known as a graphic artist or illustrator and his work was never considered to be of great value by the art critics. Over time and during the 1950's-1960's his work became quite popular and celebrated by mathematicians and drew interest from thought leaders. M.C.Escher's work was mainly created by the means of wood cut illustrations & drawings that came as lithographic prints. M.C. Escher commonly drew congruent forms or imagery in repeated patterns, namely the large body of works "Regular Division of the Plane" visualise this geometric style. He was influenced by Italian architecture too, drawing buildings & structures abstracted from the Amalfi coast. Escher created labyrinth-like scenes which could capture anyones imagination. Escher was widely known as a printmaker. His work can also be considered op art (optical art) based on optical illusions. Although his work is quite incredible Escher never considered himself an artist and struggled with the term, he considered it a somewhat pretentious term that he didn't relate to. Escher like many artists was disciplined and hard-working but personally (differentiating him from other artists) he was self-effacing and self-deprecating, particularly in writing about his working drafts and finished work, however to the observer he is genius like in working-draft form and in final execution. (M.C.Escher Scientific American)
Day & Night - Maurits Cornelis Escher (Woodcut Print)
The time spans in which geometric artwork was created covers incredibly long periods of time across multiple civilisations, even until its present day creation. Pablo Picasso (Spain 1881-1973) once famously said "good artists copy, great artists steal" in reference to this quote there are traces of cross cultural influences & knowledge transfer during ancient and modern art periods. Included within this "great artist steal" reference Picasso and Amedeo Modigliani (Italy 1884-1920) directly were known to have been influenced and inspired by earlier Cycladic work (hand carved figures 3300 BCE) during Picasso's famous cubist period (1909 to 1912).
Cycladic Sculpture (Aegean Cyclades, Greek Islands - Early Greek Pre-history)
Pablo Picasso (Spain) Pictured with Cubist Geometric Artwork
Gutenberg Printing Press
The first type of printing was the Chinese woodblock (700-601 CE) of the Tang Dynasty and metal type was also used initially in China. In 1439 the first modern form of printing press in Europe known as "Gutenberg" printing press was created by Johannes Gutenberg. It is largely attributed as the first means of mass producing books and print media affordably in Europe. While not the first type of printing used it was the first printing press invented in Europe & used movable metal type. Compared to earlier Chinese woodblock printing it was an improved technology. Books could be created cheaply and more quickly than other printing methods. As the German Gutenberg became more widely used it allowed the Renaissance to spread across countries in Europe. The Gutenberg printing press was used to create the Gutenberg Bible. The Gutenberg printing press was incredibly important historically & in terms of modern publishing and printing. In time it was superseded by other forms of printing including industrialised offset-lithography and digital printing.
Gutenberg Bible
Paper
The history of paper would deservedly require an article in itself and dates back thousands of years used early on in Southeast Asia, China, Mesoamerica (mulberry pulp paper) and papyrus (paper like material) used by the scribes of Egypt. In the 18th century A-format paper was created (devised by George Christoph Lichtenberg, 1786). A format paper is not based on the golden ratio and is sometimes confused as being used for its design. Designers and artists tend to think this way, that our work, materials and methods are in someway divinely inspired, needless to say in the early stages of ones career it's anything but true. A format paper is based on The Lichtenberg Ratio 1: 1.4142 whereby each paper size increase is double the area of the previous paper size. eg. A0 is double A1. The standardised ISO 216 (A format) paper system is based on this ratio. The Lichtenberg Ratios use with paper format design in publishing was logical along with being economically practical. The aspect ratio is retained when scaling up or down in A-Format sized paper, however it is not 100% perfect scaling of designed artwork within an A-format sizes due to the ratio used (1:4142), there are very slight adjustments used between A format paper sized artwork. For book publishing a B, C, Royal, Trade Paperback (TPB) or Demy (pronounced deny) format can be used as some theorists believed A format wasn't an ideal size for books, being too tall and narrow.
Renaissance
During the Renaissance (french term meaning rebirth) period across Europe between 1400 - 1700 Leonardo da Vinci (1452 –1519) the world renowned Italian created artwork (some geometric) and was inspired by geometry, mathematics along with other disciplines including science and engineering. He used perspective lines in some of his preparatory sketches and in painting "The last supper". While this is true there is no scientific evidence he directly used Fibonacci or the golden ratio in his work. Leonardo da Vinci was self-made and gained knowledge through observation, analysis & study. He wasn't born into a highly schooled and expensive "Latin" education and never went to traditional schools which taught theory and wrote in the academically acceptable Latin language. He was a child born out of wedlock and unlike his brothers could not become a notary (lawyer like profession). Michelangelo also Italian born (1475 – 1564) during the same period was potentially inspired by and used the golden ratio including within his Sistine Chapel work (a new study claims - The Creation of Adam 1510). Multiple artists and architects created work using perspective and geometry not only Leonardo da Vinci and Michelangelo but others (Leon Battista Alberti, Paolo Uccello, Donatello, Masaccio, Lorenzo Ghiberti, Masolino da Panicale, and Filippo Lippi) including Filippo Brunelleschi (architect) who pioneered the use of 3D perspective within a two dimensional space. Perspective & geometric design was collegial and cultural and not done solely by one person, but through shared leaning, understanding and discovery of older written knowledge, with some cases of self-discovery through observation, applied learning and new applications of theory. While some geometric art is easily perceived to be geometric-based work, some artists like Michelangelo & Leonardo da Vinci applied geometric principles to art sometimes in much more subtle ways, not noticeable to the eye, through the structural use of grids, geometric lines and forms to create perspective, sometimes forming the base outline of their paintings and in preparatory drawings of art & architecture.
The Last Supper by Leonardo da Vinci
Preparatory study for the Adoration of the Magi - Leonardo da Vinci
The Turin Portrait (red chalk self-portrait), The Mona Lisa & Vitruvian Man - Leonardo da Vinci
Michelangelo - The Creation of Adam (1510)
The Modern Bramante Staircase by Giuseppe Momo, Vatican City 1932 (Left) Homage to the original Donato Bramante Staircase 1505 (right)
