While often overlooked, there is abundant evidence of the intentional use of geometry in the composition of traditional arts, crafts and architecture. This was often accomplished through the use of regular polygons -frequently concentric- to establish proportional systems within a composition.
These associations can create a feeling of unity within the work by harmonizing its disparate elements of form, decoration and purpose. Polygonal composition also allowed the incorporation of number and shape symbolism associated with religion, mythology, culture and the organization of society, within a work of art.
This presentation will reveal the appearance of regular polygons found within round (tondo) creations from across the ancient world. Through many examples we’ll see how polygonal shapes, patterns and proportions have been applied to harmonize the elements of great painting, jewelry, ceramics, sculpture, architecture and more across a variety of cultures and centuries.
Michael S. Schneider is an American author, educator, and speaker who has written several books on sacred geometry, including “The Beginner’s Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science”. He has also given many talks and workshops on the subject, and is considered an expert in the field. Schneider’s work explores the mathematical and geometric principles that underlie the structure of the universe, and how these principles are expressed in art, architecture, and other areas of human creativity. His approach is interdisciplinary, drawing on insights from science, mathematics, art, and spirituality to provide a holistic understanding of the role of geometry in human culture.
Here he has deconstructed illustrations in ancient art through the use of polygonal geometry.
“It’s almost impossible to find art from the ancient world that is not done with intentional harmonious proportion” – Michael Schneider
Polygons are used to determine the groundlines of illustrations of art found in the ancient world.
The inscribed hexagon in red reveals a circle in which a square is formed that encodes not only the groundline, but the pillar behind him too.
A timeline for some of the art we’re looking at here..
Two triangles within this bowl reveal the circle in the middle. A pentagon is then inscribed within it to show the groundline.
Speaking of triangles within circles…
And while we’re on the topic of shapes within circles, let’s check out what’s hiding in the square within the circle..
Most kitchen plates are designed this way. If you have children, fill the inner circle of a your plate with food then have them spread it to the outer rim. They will quickly learn that the outer rim and inner circle have equal area.
Above, the inner circle is defined by a heptagon. A pentagram reveals the placement for the bow behind his right arm.
An upside down pentagon reveals the groundline in this talisman from around 800 B.C. Notice how the circle is squashed. That is on purpose to mimic the Sun when it nears the horizon. This squashed circle was found in artwork all over ancient Egypt.
The odd shape of this ancient stone is baffling until we think geometrically.
Here we have a bowl from Greece, likely from a wealthy land owner. Notice how the inner circle with the profile of the man is formed by two interlocking squares.
This old ceramic jug’s design seems random until until we overlay a pentagon (red) and pentagram (blue).
A dome from the Byzantine displays Christ in concentric circles. The yellow ring has the same area as the yellow circle. This is something that square root 2 geometry does.
I can highly recommend Michael’s book. I’ll never forget the first time I read it, almost a decade ago. Really awesome stuff!!!
If you enjoyed this article you’d be a fool not to watch the whole presentation below.
Composing in the Round: Polygons in Traditional Art (Michael Schneider via The Prince’s Foundation School of Traditional Arts)