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 B.C.E. Experts agree Babylonian mathematics dates to between 5000 - 3000 B.C.E 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. Egyptians used maths for surveying & building, taxing the public for cooking oil & astronomy. Geometry in Greece came later (300 B.C.E) 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 B.C.E (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
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. 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 B.C.E. 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 B.C.E – 700 B.C.E during the greek dark ages (geometric period) and Greece's cultural epicentre was Athens.
Greek Decorative Geometric Art: Funeral urns (750-720 B.C.E)
Geometric art was originally created as decorative abstract patterns and used basic geometric shapes (triangles and rectangular forms) and in some cases used symbolism. Later in the Classical period 510-323 B.C.E 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 B.C.E) 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
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. This is why geometric symbols, motifs (patterns) were used to create beautiful art and design.
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 B.C.E 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 B.C.E Uruk (Sumer) Hassuna, modern Iraq, once 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 B.C.E) during Picasso's famous cubist period (1909 to 1912).
Cycladic Sculpture (Aegean Cyclades, Greek Islands - Early Greek Pre-history)
Pablo Picasso Pictured with Cubist Geometric Artwork
Gutenberg Printing Press
The first type of printing was the Chinese woodblock (601 - 700 C.E) 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 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.
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 (18th Century) whereby each paper size increase is half 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 in A-format sizes due to the ratio used (1:4142), there are slight adjustments used between A format paper sizes. 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.
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 use 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)