Historical Use

“… I beg you to consider me not as a mathematician but as a painter writing of these things.”Leon Battista Alberti, On Painting.


What makes art meaningful?

The character in the painting “Allegory of Geometry”, 1649 by Laurent de la Hire holds a paper and compass that allude to the configurations typically used when forming Orthogons—specifically the Auron or Golden Section. 

The Parthenon and Pantheon were constructed using this series of relationships to make a unified structure related to religious beliefs.  Many familiar artists in this and previous eras have also incorporated design structures such as the Orthogons (the term “Orthogon” is used on this website according to information from a text by Wolfgan Von Wersin Die Orthogon-scheibe published by Otto Maier Verlag Ravensburg 1956). 

Calligraphers have likely been consistently using the Orthogons in the manner Of the Just Shaping of Letters by Albrecht Durer.  Information and diagrams appear in the book: Calligraphy, Modern Masters—Art, Inspiration and Technique; by David Harris, 1991, Crescent Publishers, NY, NY.

Quilters have also used the Golden Section to create their patterns.

The Orthogons surface in the works of: Brunelleschi, Mondrian, Braque, Degas, and Georgio Morandi (whose University collegues chuckled at his constant “measuring”).  Walter Valentini, a contemporary Italian artist, defines the Orthogons in molded paper with touches of color and gold leaf.  Samples of his art can be found at: http://www.arsmedia.it/valentini/f4e.htm


Maestro’s quick footsteps echo through San Lorenzo’s marble hall—summoning a group from the guild analyzing the play of light filtering through the dome’s little round windows.  Spreading his cloak on the cold floor, he abruptly kneels down and begins loosening the strings of his leather pack.  Gently pulling out a precise drawing (carefully crafted on yesterday’s wooden table), his finger begins to trace the charcoal-drawn squares and arcs derived from Greek temple designs.  Maesto’s gaze shifts from the diagrams up towards Brunelleschi’s incredibly graceful series of arches (carved from the grey stone Florentines call pietra serena) set against white stucco walls.  Lifting his arm, he outlines each elegant shape.  In an instant, concept is transformed from parchment into reality.  Maestro’s intense gaze surveys the group to determine who realizes why Brunelleschi’s revolutionary architecture actually reverberates with the sound of eternity.

          A movement from the corner of the parchment escapes notice.  Long fingers reach straight through the years, defying the impossibility of traveling backwards in time, to tug at the designs in maestro’s grasp.


* * *

“Begin with a square,” Professor explains, his hint of German accenting the tones.  Students lean closer as north light glowing from a snow-covered mountain high in the Rockies fills the room with a shadowy blue.  Some are skeptical of what appears to be a tedious process for making art.  Professor’s stiletto-sharp pencil, honed to a point on sandpaper, skillfully extends precise lines of a square to the grey arcs made with a little metal compass.  No one speaks during this process as much from respect for the Professor’s Bauhaus/European heritage as from fascination with the composition that magically emerges.   


“Is all this measuring necessary?”  A particularly intense young man asks for the group.  “If you do not do it with purpose, you will be doing it from instinct,” comes the patient answer.  “Things ‘feel right’ because everywhere you look, centuries of designers and painters have followed the same order.” 


Professor’s large hand makes a characteristic sweeping gesture that summons up images from past lectures, “Lay out anything from nature: pine cones, seed pods, leaves and begin to draw.  You will automatically set them within an orthogon, you can’t help it because their form follows a design that is already an orthogon—the golden section.”  The student then joins the procession of previous skeptics and answers the challenge.  By semester’s end, in the process of attempting to prove Professor wrong, he, too, will become an ardent believer.  He will decode Professor’s subtle meanderings, learning the answers to: “What did the Masters gain from so many hours in the guild?  What information was so valuable, they were sworn to secrecy to protect?”


“More, Art, faster!”  Another class with the German maestro has ended and a long day in the studio gets underway confidently addressing the familiar challenges:

Where to begin a design


How to organize a work


How to make art meaninful


About Orthogons  Orthogon Instructions  Design Application  Historical Use  References  Links  Artist