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The dynamic symmetry proportional system is found in some Byzantine and Russian icons of the fourteenth to sixteenth centuries


by Karyl M. Knee
(Mrs. Knee received her B. A, (Russian Studies), Oregon State University, 1966: M. A. T. (Secondary Education), University of Alaska, Anchorage Campus, 1969. )


Table of Contents


A personal word about this paper

General Overview





I. How to develop your own dynamic symmetry composition
"Root" rectangles obtained outside a square
"Root" rectangles obtained inside a square
The development of "root-five" rectangle themes
The rectangle of the whirling squares

II. The recognition of dynamic symmetry in Byzantine and Russian icons
Analysis of The Entombment icon with dynamic symmetry

III. Iconographic reverse perspective
How iconographic reverse perspective works
How iconographic perspective came to be
Further discussion of iconographic composition

IV. Continuing analysis of dynamic symmetry in Byzantine and Russian icons

Analysis of the Descent into Hell icon with dynamic symmetry
Analysis of the Baptism of Christ icon with dynamic symmetry
Analysis of St. Simeon Stylites icon with dynamic symmetry
Analysis of St. John the Evangelist icon with dynamic symmetry

V. An overview of the history of dynamic symmetry
Iconography: A review of the Pre-Christian Period
Iconography: A review of Early Byzantine Christian Period (330-643)
Iconography: A review of the Mid-Byzantine Christian Period (643-1204)
Iconography: A review of a period of transition (1204-1500)

Map: Proposed probable spread of dynamic symmetry: c3000 B. C. to cl500 A. D.

Closing remarks


Selected references
Cited time-line



I-1 to I-9. How to develop your own dynamic symmetry composition
I-10. "Root" rectangles obtained outside a square
I-11. "Root" rectangles obtained inside a square
I-12. "Root-five" rectangle theme repeated
I-13. "Root-five" rectangle theme, halved
I-14. "Root-five" rectangle theme, triad
I-15. Construction of whirling square rectangle
I-16. Development of rectangle of whirling squares
I-17. Development of spiral within whirling square rectangle
I-16. Compound "root" rectangle

II-l. The Entombment icon, main forms
II-2. Establishment of "root-two" rectangle base for The Entombment icon
II-3. Horizontal triad position of dynamic symmetry analysis of The Entombment icon
II-4. Vertical asymmetry of icon-mountains in dynamic symmetry analysis of The Entombment icon

III-l. Schematic of Santa Sophia Cathedral, Kiev, Russia
III-2. Normal perspective; Schematic of the side view
III-3. Normal perspective: Schematic of the frontal view
III-4. Christ among the doctors, perspective analysis
III-5. Dormition of the Virgin icon, multiple vanishing points
III-6. Dormition of the Virgin icon, multiple vanishing points
III-7. St. John the Forerunner icon, icon-mountain perspective
III-8. The Transfiguration icon, icon-mountain perspective
III-9. Numbering the people icon, reverse perspective analysis
III-10. Christ the Giver of Life icon. Gospel Book perspective

IV-1. Descent into hell icon, dynamic symmetry analysis
IV-2. Baptism of Christ icon, dynamic symmetry analysis
IV-3. Simeon Stylites icon, dynamic symmetry analysis
IV-4. St. John the Evangelist icon, dynamic symmetry analysis

V-l. Egyptian "rope-stretcher"
V-2. The 3, 4, 5 right-angle triangle
V-3. Ancient Egyptian wall painting and analysis
V-4. Ancient Egyptian knotted rope
V-5. Ancient Egyptian 3, 4, 5 right-angle triangle analysis
V-6. Method for laying the Egyptian knotted rope
V-7. Schematic of the Great Pyramid at Giza
V-8. Schematic of Greek vase
V-9. Schematic of the Parthenon at Athens


I have spent a hectic, wonderful five years with this research on dynamic symmetry and its fascinating appearance in Byzantine iconography. It is incredible - I merely wanted to understand the construction of icon-mountains and I eventually was surrounded with ghosts of ancient Egyptians, ancient Greeks, eighteenth century artists and ecclesiastics (who hoarded the secret of Plato's "Golden Rectangle" in Germany); and then there were the fiery artists of the late nineteenth and early twentieth centuries who repulsed the previous art forms!

All the above so I could understand icon-mountains!! But - I did find the understanding. I discovered that Jay Hambidge did discover the old formula that the eighteenth and nineteenth century artists were seeking and gave the world the means to comprehend the work of the ancient artisans.

Although Hambidge had his critics - the same ones who also disputed the eighteenth and nineteenth century seekers - the discovery was and is valid, for then and for now
Karyl M. Knee
Portland, Oregon
March 1988



A search for understanding the construction of icon-mountains brought knowledge of the principles and applications of dynamic symmetry as found in ancient icons. For example, dynamic symmetry "fit" the design composition of the fifteenth century icon, The Entombment, and also demonstrated the "reverse" perspective of not only the icon-mountains but the entire composition.

Further searching and analysis of Byzantine and Russian icons disclosed that others, too, appeared to be designed with the dynamic symmetry proportional system.

How could this be? Jay Hambidge (to be introduced in part II) discovered the formula for dynamic symmetry in the early twentieth century and subsequently traced its use back to the ancient Egyptians of the First Dynasty.

This paper attempts to show that it was possible and probable for the dynamic symmetry proportional system to have travelled from ancient Egypt, to Greece, to Christian Byzantium and on to the far reaches of Northern Russia and elsewhere in the world of that time.

This paper will demonstrate that this system of dynamic symmetry is also a useful tool for the modern iconographer as it guarantees a pleasing composition.





The purpose of this paper is not to simply impart information about dynamic symmetry and its possible relationship to icons of the Middle Ages. It also shows that it is a valid tool for the modern icon-writer. Its use insures that the composition will be of pleasing proportions and it is simple to use.

Several years ago I read a Russian article by Zhyegin (See Selected References) about the dynamic character of Russian icons of the Middle Ages, with illustrations and diagrams. I was particularly interested in the way in which the author diagrammed icon-mountains. The author used the terms "dynamic point of sight" and "dynamic visual position. " My translation of this article led me to research the term "dynamic" for a better understanding of the iconographic composition involved. I thus discovered the term and concept of "dynamic symmetry. " This, most interestingly, was the principle espoused by Jay Hambidge in the early 1920's, and discussed in detail later.

Using this "dynamic symmetry" system, I analysed several Russian and Byzantine icons dating from the fourteenth to the sixteenth centuries, and discovered that they appeared to have been designed by this very system. I then began to trace the history of this dynamic symmetry, and I found that it is possible for this ancient proportional measuring system to have survived through a very long time. It had come to be used by the Byzantine icon-writer monks, and then had been taken by them throughout the Balkan area to Northern Russia. The pre-Christian use of this system is recorded by contemporary Egyptian wall pictures and by writer-travellers throughout the long history of the Near East, the Balkans, and Russia.

The proportional measuring system was known originally by its descriptive Egyptian name, "rope-stretchers;" then the Greek name for the system, also meaning rope-stretchers, was "harpendonapate. '' The East Indian Hindu name for the system was "Sulvasutras," meaning "rules of the cord. "

Interestingly, many of today's popular icon compositions can be traced to their origin in the Byzantine Era, which we continue to admire for their lasting aesthetic beauty.

Most of us are keenly aware of the timeless beauty of Greek vases, temples and sculpture, but we may not be aware of the precise, mathematical system that was used to achieve these unique, beautiful results. Hambidge discovered that the dynamic symmetry proportional system was used in the construction (not decoration) of many Greek vases from the sixth century B. C. to about 323 B. C. , when Alexander the Great died and the Hellenistic period began.

Hambidge termed this system "dynamic symmetry" because of its built-in movement and dynamic character. He determined that the reason that the Greek vases had remained so famous was not only because of their decoration, which he saw as minimally artistic, but also because of the actual design structure of the vases themselves, which have a dynamic symmetry and are psychologically pleasing to the viewer.

The following paragraphs discuss the drawing and composition of dynamic symmetry for use in the analysis and construction of icons. After this section I will describe dynamic symmetry in its discovery and passage through time. At the end you will find comprehensive Selected References, and a Cited Time-Line encompassing the subject of dynamic symmetry from the beginning, c3000 B. C. , to the present time. Preceding the Cited Time-Line is a Matrix showing the applications and relationships among the various aspects of this fascinating subject.