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DYNAMIC SYMMETRY CITED TIMELINE:
c3000 B.C. TO DATE
[The numerals in parantheses represent the Selected References.
The first numeral refers to the reference and the numerals after
the colon refer the the page number(s).]
c3000 BC
First Dynasty Egyptians used a knotted rope for land measure,
temple architecture, wall painting and sculpture. To do this
required knowledge of the 3, 4, 5 right angle triangle (the basis
of dynamic symmetry). The Temple of Amon Re at Karnak is a prime
example. (1:89)(36:489, 61) (43:145, Note II)(54:44)(93:Part
3)
21601090 BC
The Egyptian "New Empire" is still using the "knotted
rope" measure. It is now the 18th Dynasty, the greatest
period of temple building. (23:596)(36:56)
21001800 BC
A period when Egyptian coffins had "diagonal calenders"
on their lids. (82:88)
c1850 BC
The reign of Sesostris III (12th Dynasty). The history surrounding
Sesostris is given in the history by Herodotus, c490 B.C. (50:139142)(56:14)
16741558 BC
The Egyptian "Rhind" papyrus states that the Egyptians
used constellations of the "Bull's Thigh," "Great
Bear," "Meskhetier," "Alphe Draconis"
(the Big Dipper) and the "Ship" (Pegasus) to plot their
measurements. (1:89) (43:160161)(80:88)(57:11)
15801069 BC
Some designate this period as the New Empire in Egypt. The Egyptian
ceilings in tombs often have a constellation painted on them.
(82:8889)
15581303 BC
The Temple of Amon Re at Karnak was constructed in the 18th Dynasty.
By this time the Egyptian system of measurement was known all
over the ancient world and commented upon by contemporary travellers.
(36:4849)(43:167)(45:xiiixv) (67:20)
15201085 BC
An artisan village, DeiralMedina, nestled between the Valley
of the Kings and the Valley of the Queens, was where "knotted
ropes" for measuring were found to have been used. Three
principal Egyptologists have worked there: the Czech, Jaroslav
Corny; the Frenchman, Bernard Bruyere; and the Englishman. John
Romer. (56:87)(93:Part 3)
In Sesostris III's reign, his inspectors measured flooded
land: the land was divided into equal squares and doled out;
geometry was known and Herodotus states that its knowledge passed
into Greece. He also states that the Egyptians had knowledge
of the sundial and the gnomon. They also divided the day into
twelve parts  a practice they had learned from Babylon. (50:141142)(56:14)
In the Egyptian 15th Dynasty, the RMP51 papyrus gives the
area of a triangle of land to find the area. (38:138)
c1500 BC
Egyptian geometry was at the same level as "Old Babylonian"
geometry. An Old Babylonian clay tablet (Plimpton 322) has the
"Pythagorian Theorum" on it. This theorem was known
and understood a thousand years before Pythagorus' time. There
is the 3, 4, 5, right angle triangle on the clay tablet. (28:1)(82:36,
7880, Plate 7)
14001300 BC
In Egypt the statue of Amenophis, with its Egyptian proportional
system, was made which was closely copied by the Greeks later
in their statue of Apollo. (45:xiii)
c1400 BC
Greek travellers were aware of the Egyptian form of measurement.
The Greeks accumulated knowledge from all over the Mediterranean
area (36:4849)(45:xiiixv)(57:20)
600480 BC
This is the period of the Greek "Archiac" style. (36:118)
569500 BC
The Greek philosopher Pythagorus lived during this time and his
work with the 1.618 ratio system spread throughout his world.
(43:145, Note II)(54:26)
c500 BC
The Hindus in India were using dynamic symmetry up to the "rootsix''
rectangle. They termed this system Kalpasutra ("rules
of the cord") and this is also found in their Sulvasutras.
(43:144145)(45:xv)
500523 BC
Greek trade with Egypt greatly increased at this time and geometry
began. Pythagorus brought to Greece the Egyptian use of geometry
and the use of odd numbers. (39:78)
The period of the use of the Egyptian measuring system we
know today as dynamic symmetry, called harpedonoptae, (''ropestretchers'')
by the Greeks. This was also the period of the Greeks "Golden
Section," "Golden Mean," and the "Golden
Rectangle." (43:145, Note II)(45:xivxv)(42:2531)
It was during this period that Homer's Illiad and Odyssey
were passed from the oral to the written language. (108:12)
c500 BC
The Greek sculptor Rhoesus of the island of Samos, had two sons,
Theodorus and Telecles. Each son sculpted onehalf of a statue,
one in Ephesus on the coast and one on Samos using their father's
Egyptian measuring system. When they were placed together, the
two sides fit perfectly and appeared to be of one piece. Rhoesus
brought the knowledge of geometry and the rightangled triangle
from Egypt to Samos, and hence to Greece. (23:1670)(43:145, Note
II) (45:xiv)
Greek sanctuary buildings improved through Greek inventiveness
and experiments with the Egyptian system of measurement. Egyptian
temples were built to be experienced from the inside while Greek
temples were built to be experienced from the outside. (23:22)(57:1213)(36:6263)
c490425 BC
The Greek traveler and historian Herodotus, born c490 in Halicarnassus,
in Asia Minor, commented on the Egyptians in his writings. He
died in 425 B.C. (49:141142, 200) (56:9)
c400 BC
Greek building activity centered itself outside of the Greek
mainland, particularly in Asia Minor. The Greeks had much influence
during this time. (36:166)
c481 BC
The Greek "Classical Period" was during these times.
(55:2021)
448c427 BC
The Parthenon in Athens was built by Greek architects Ictinus
and Callicrates. It is a perfect example of dynamic symmetry's
"rootfive" rectangle composition and also a prime
example of the "Golden Rectangle," when measured by
a similar means. The meander (Greek key design) design over the
panathenaic frieze is a 1.618 ratio rectangle. The cornice meander
design is a 1.472 ratio rectangle (16/19). (31:77)(36:118)(43:160.
Note XIII) Sg (46:86)(54:6265)(57:2526)(99:148)
430427 BC
A great plague swept over Athens and decimated its population,
leaving it greatly reduced. The population loss was so great
that it changed Greek civilization itself. (7:xiii)(47:C4)
427347 BC
In Plato's Theaetatus, his students used the Egyptian
measuring system and are known to have calculated it up to the
''rootseventeen'' rectangle. (46:24)
356323 BC
Alexander the Great spread Hellenistic culture over a large area
of the East. His death brought the beginning of the Greek Hellenistic
Period. (36:156) :
c200 BC
The "Golden Section" proportional system comes from
Euclid's Book XIV written between 200 and 100 B.C. The Greek
mathematician Euclid flourished during this time. He wrote his
Elements which is the basis of modern geometry. Euclid's
five solids are to be found in dynamic symmetry composition.
(23:638)(43:152153)(45:xivxv)
The Egyptian priest, Manetho, wrote the first reliable history
of Egypt. (56:10)
c100 BC
The dynamic symmetry system in Greek design, sculpture and architecture
disappeared from their works. From this time on the Greek human
figures were in a static form. (43:157158)(45:xivxv)
21 BC
Diodorus Siculus, of Sicily, wrote about how the Greeks obtained
their knowledge of sculpture from Egypt. (23:542)(43:xiv)
c200 AD
Clement of Alexandria (d.215) quoted Democritus, who lived in
Egypt five years, on the use of the Egyptian harpedonoptae
(Greek for ropestretchers). He tried to synthesize Platonic
and Christian thought. (23:406)
There are two red vases from the island of Samos (the island
where glassmaking is reputed to have been invented), and two
Sidonian glass cups in the collection of Edward E. Edwards that
are designed with dynamic symmetry. This demonstrates that artisans
were still using this measuring system during a time and place
when its general use had died out in Greece itself. (31:ix)
The Coptic coffins at Newart and Fayum had encaustic (wax)
portraits on them. The Coptic Christians are the last of the
ancient people of Egypt. (9:4)
205270
Plotinus, a Greek philosopher on art and religion, lived during
this time. He proposed that art should be a metaphysical experience.
(9:2)
330630
Constantinople was built beginning in 330. This began the Early
Christian Period of the Byzantine Empire. (27:xi)
402
Ravenna, Italy, was the Western seat of the Byzantine Empire.
(85:13, 30)
350
This is the Coptic Period in Egyptian history, ending with the
Arab conquest. (17:9)
c300
The Silver Chalice of Antioch (c4th5th century), excavated in
1910, was designed with the dynamic symmetry system. (23:353)(31:ix)
600c500 [?]
The Golden Age of Byzantine Art came into being. Hagia Sophia
church in Constantinople is an excellent example of this art.
(22:10)
The Parthenon in Athens became a Christian church. (23:1492)
There was a decline in Pharaonic art. Hellenistic, Roman,
Alexandrian and Pharaonic art all merged in Egypt. (17:51)
543552
The Christian Topography, a work by Cosmos Indicoplenstes,
was written and it identified the Church with the Cosmos. (10:68)
641
The time of the Muslim conquest of Egypt. (17:286)
725843
The Iconoclasm period in Early Christian history when the depiction
of images was forbidden. (22:6)
732
The Battle of Tours (France) and the Mediterranean area was lost
to the East. There was no more EastWest travel and the source
of papyrus was lost to the West. (55:58)
c800900
The period of the "Macedonian" Dynasty in the Byzantine
Empire. (22:6)
843
The end of the Iconoclastic period and the meeting of the seventh
Oecumenical Council of the Christian Church. The beginnings of
the Second Golden Age of Byzantine Art came with its use of gold
in the backgrounds, in both mosaic tiles and painting. (22:15)(27:xiii)(36:266267)(85:51)
8431204
The Crusades came from Europe to the Byzantine Empire. (22:8)
1080
Greek mosaicists mere sent from the Monastery of Blachernai in
Constantinople, to Kiev, Russia, to the Lavra of the Kievian
Caves, to decorate it. (10:254)
10811185
The Comnene Age in the Byzantine Empire. Iconpainting on panels
came into prominance due to a new merchant class of patron. Byzantine
art was characterized by brilliant decoration. (10:284)(90:128)
1114
The Hindu Indian mathematician, Bhaskara, used the Pythagorian
theorum although he "proofed" it a different way. (54:85)
11401200
Regional styles developed in the Byzantine Empire but still were
connected by Byzantine influence, and the "dampfold"
appeared in sculpture and painting. (78:243)
1175
In Italy, Fibonacci was born, Filius Bonacci, son of Bonacci,
called Fibonacci. He wrote Liber Abaci. He discovered
the mathematical series that bears his name which explains the
mathematical growth pattern in biology. The ratio 1.618 is paramount
to this mathematical series as it also is to dynamic symmetry,
the Pythagorian Theory, the "Golden Mean," the "Golden
Rectangle," and the "Phi" theory. (54:157158)(91:149)
12001400
This is the Palaeologue Age in the Byzantine Empire. In Russia
art was the main form of expression. There was an important art
center at Salonika. (3:1415)(10:297298)(112:63)
12041261
In Italy, Giotto was realizing true perspective and realism in
his art. In Constantinople, these were years of exile due to
the Crusades, followed by the Turkish takeover of the Byzantine
Empire. (90:223, 229)(91:149)
1261
A new style of icon developed, that of multiple figures and scenes
and a return to tenth century models. (27:123)(77:243)
1262
The Crusaders were ousted from Constantinople. (112:144)
c1300
During this Palaeologue Dynasty, artists began to sign their
icons in Mistra. In Italy, many individual artists began to be
recognized. (10:328)
1321
The last church decoration signed by Michael and Eutychinos was
the St. Elijah Church in Gracanica, with a strange, stylized
landscape which shows the way to the development of art at Mistra.
(10:322)
1345
Iconpainters returned to the eleventh century style of severe,
withdrawn images. Serbian icons are an excellent example. (10:284)
13581389
Prince Dimitri Donskoi, of Moscow, resisted the Ottoman turks
at the Battle of Kuilovo in 1380. (10:324)
1370
A painting of The Nativity by W. des Rudolf von Ems was
designed with the "rootfive" rectangle of dynamic
symetry (16:66)
13701430
Andrei Rublev, the great Russian iconpainter lived during this
time. (3:Plate 199)(36:282)
Theophanes the Greek worked with Andrei Rublev, in Moscow,
decorating churches. Theophanes had come from Novgorod where
he painted and taught. Especially great icons were painted in
this period of time. (10:324)(22:27)
1380
The Greek icon, Baptism of Christ, was painted and falls
within two "rooteight" rectangles in its design composition.
(112:113, 135)
13951405
Theophanes the Greek and Andrei Rublev decorated three churches
in Moscow. (10:324)
14351450
Roger van der Weyden's Descent from the Cross painting,
in the Prado Museum, Spain, is designed with the use of a "rootthree"
rectangle plus three pentagons which incorporate the use of the
"Golden Section" and "Golden Mean." (10:340)(16:6768)
1420
The first use of the vanishing point in art was in Florence,
Italy, by Masaccio. (49:327)
1421
The artistic center of iconpainting shifted to the island of
Crete. (112:83)
1480
The Northern Russia icon, The Entombment, was designed
on "root two" rectangle. (122:208214)
The Northern Russia icon, The Descent into Hell, is
based on a "rootthree'' rectangle scheme. (67:39)
1550
The Cretean iconographer, M. Damaskina, was a great iconpainter
during this time. (85:83)
15711630
This is the time of the great mathematician Kepler. (54:23)
1580
The Moscow School icon, Simeon Stylites, was designed
with two "rootfive" rectangles. (83: Plate 125)
1600
Iconography began a rapid decline in Russia. (3:1415) (67:Plate
201)(122:182)
1637
During this time E. Tzane was a great iconpainter. (85:83)
1653
Pascal's "triangle" was written (Traité du
Triangle Arithmetique, 16231662). (54:87, 131)
1780
The icon, St. John the Evangelist with St. Prochorus,
was designed using two "rootsix" rectangles. (67:Plate
146)
1792
The first measured drawings of the Parthenon in Athens were made.
(23:1492)
1800
The revival of the "Sacred Measure'' of antiquity was begun
by the Germans. This was equivalent to Hambidge's Whirling Square
rectangle and Plato's "Golden Rectangle." (16:244)
The NeoClassical School of Cornelius and Overbeck in Germany,
rediscovered dynamic symmetry by tracing it back to ancient Egypt,
but they did not realize it was the "root" rectangle
system. They called it the "Golden Number." (16:244)
1850
Zeysing showed the presence of the "Golden Section"
in his frontal view of the Parthenon, in Athens (38:124)
1876
Gustav Fechner's experiments with the "Golden Rectangle"
and its influence on human aesthetics was during this time. He
was a German psychologist and he studied Greek architecture.
(54:52, 64)
1877
Edward Lucas gave the name to the Fibonacci Series. The Series
originated in a puzzle problem in 1202 by Fibonacci. (54:47.
158)
1880
Moritz Cantor, a mathematician and historian, flourished during
this time in Leipzig, Germany. (38:2)
1884
Adolf Zeising, a German, wrote Der golden Schmitt. He
influenced Gustav Fechner in regard to the "Golden Rectangle"
and its aesthetics. (54:62)
1894, 1908, 1917
Witmar (1894), Lalo (1908) and Thorndike (1917), all repeated
Gustav Fechner's 1876 experiments with the "Golden Rectangle''
and its aesthetics. (54:64)
1897
Sérusier obtained, from his friend Verkade (who was a
novice at the Benedictine Monastery of Beuron, in southern Germany),
the secret "Sacred Measure" when he saw him in Prague.
Father Didier (Lenz) gave this "Secret Measure" to
France. (16:244)
1903
Jay Hambidge (18671924) studied phyllotaxis for 25 years
before turning to the study of proportion in art. He gave a talk
in London on this. (43:xi)
1903
Kepler wrote about division of a line into "extreme and
mean." This is the basis of the ratio proportioning in dynamic
symmetry and in the "Golden Section" and the "Golden
Rectangle." (43:151153)
1906
Jay Hambidge based his dynamic symmetry research on Francis Cranmer
Penrose's (18171903) work, Investigations of Principles of
Athenian Architecture. (132:)
Hambidge began to study the symmetry in art and rediscovered
dynamic symmetry. (48:xii)
1908
From this date onward, Sérusier was one of the principal
teachers at the Academie Ranson who taught "dynamic symmetry''
[though he didn't use the term] and wrote a book about it in
1921. (16:244)
1917
In the Autumn, Hambidge's students in New York, were: George
H. Whittle, Miss Christine Herter, Miss Frances Morris, Miss
Eugenie Shonnard, Wilford S. Conrow, Chester Beach, Louis P.
Skidmore, Sergent Kendall, and Edward B. Edwards. (23:1950)(31:viiviii)(51:
ix)
At this time Hambidge was primarily an illustrator.(31:ix)
Hambidge was giving lectures on dynamic symmetry in New York
in the office of George H. Whittle, 70, 5th Ave. Whittle was
the former assistant editor of Century Magazine. Among
those attending were: George Bellows, George Lukas, Robert Henri,
Leon Kroll and Howard Giles. (51:ix)
Professor H. B. Mitchell, a mathematician at Columbia University,
was a friend of Edward B. Edwards and helped Edwards with the
mathematics of dynamic symmetry ratios. (31:viii)
c191718
Edward B. Edwards, a designer, offered Hambidge the use of his
studio, and Hambidge gave lectures there on dynamic symmetry.
(31:x)
191819
Hambidge gave a series of ten lectures at the Architectural League
rooms in New York. Horace Moran was Chairman of the League. (31:xi)(37:1617)
191920
Hambidge began writing monthly lessons on dynamic symmetry in
the Yale monthly magazine, The Diagonal. The lessons were
entitled, "Elements." (45:v)
1920
Hambidge's book, The Greek Vase, was published by Yale
University Press. (43:24, 32)
1921
Professor Rhys Carpenter of Bryn Mawr College, published a highly
critical article about Hambidge's dynamic symmety system and
questioned Hambidge's personal qualifications to scholarship.
(74:3, 1116)
1922
J.D. Beazley, of Oxford University, was critical of Hambidge's
dynamic symmetry theory and influenced Dr. L.D. Caskey away from
espousing it. Dr. Caskey was a curator at the Boston Museum of
Fine Art. (128:2)
1923
Christine Herter was one of the first artists to use Hambidge's
dynamic symmetry in her art. She did three pieces. (31:vii)(44:1721)(51:xixii)
Artist George Bellows used dynamic symmetry in his art compositions
throughout his life and when he began he won several prizes.
(32:815)(44:2238)(79:12, 218, 238279)
1924
Hambidge designed a dynamic symmetry ad for Chrysler company
which appeared in the Saturday Evening Post, January 19,
1924. (30:57)(132:)
Hambidge died of a cerebral hemmorage while giving a lecture
on stage in New York and he died apologizing for the interruption.
(132:)
1926
Bretano's published a reprint of Hambidge's 191920 lectures
and entitled it Elements. (45:iv)
1927
Mitila Ghyka, a German, had a thorough and direct knowledge of
the German works on "dynamic symmetry" and she expanded
the "Golden Number'' a few years after Sérusier died
in 1927. (16:244)
1932
Seashell diagrams and illustrations of sunflowers demonstrating
phyllotaxis in an article. (46:8, Plate V)
1946
William Ivins, Jr., Harvard University, wrote Art and Geometry,
and stated that the Greeks introduced linear subtleties to architecture.
(55:16)
194752
The French architect, Le Corbusier, used dynamic symmetry in
his "L'Habitation" decorations. (14:Plate 208)(23:1110)(59:118)(65:32)
Real name: Edouard Jeanneret, born Swiss (18871965) built planned
village, Vaucrisson, near Paris, 1923.
1948
Yale University Press reprinted Brentano's 1926 reprint of Hambidge's
Elements.
1949
Oto Meugebauer gave six lectures on dynamic symmetry at Cornell
University. In 1969 Dover Publications reprinted the 1957 2d
edition of the Brown University book of these lectures. (82:viii)
1959
The historian, Cantor, believed the Egyptians knew a 3, 4, 5
triangle was a right angled triangle and that they used it in
their constructions. (38:242)
c1962
E. Wigginton wrote a senior high school research paper on Hambidge's
theory of dynamic symmetry. (117:41)
1964
Dover Publications reprinted William Ivins, Jr.'s 1946 book,
Art and Geometry. (55:iv)
Zhegin, A Russian, wrote an article on Russian iconographic
proportions in which he talked about the painters, "alloting
the space within the border," and said "how is no matter,
they simple did not notice, that it was the habitual method of
representation....'' (122:175192)
1966
Greek development, based on dynamic symmetry and the "Golden
Section," was what Le Corbusier based his Modular on in
his architectural work. (38:119)
It is believed that the Greeks originally evolved an efficient
dimensional basis for construction and then rationalized it in
mythology. (38:122)(65:32)
1967
Dover Publications reprinted Brentano's 1926 Elements
by Hambidge. (45:iv)
1969
A National Geographic Magazine article about seashells
with diagrams and illustrations explaning phyllotaxis. (118:386429)
1970
Professor H. E. Huntley, an Englishman who had taught mathematics
and physics since 1940, wrote a book The Divine Proportion.
(54:vi)
1985
An article in the St. John's Review about dynamic symmetry by
Howard J. Fisher. (133:4055)
1986
An article about the dynamic symmetry and phyllotaxis in botany,
illustrating its use with a sunflower center. (18:6364)
1987
The ratio of our visual perception is 1.618.
