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[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)(36:48-9, 61) (43:145, Note II)(54:44)(93:Part 3)

2160-1090 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)

2100-1800 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. (50:139-142)(56:14)

1674-1558 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) (43:160-161)(80:88)(57:11)

1580-1069 BC
Some designate this period as the New Empire in Egypt. The Egyptian ceilings in tombs often have a constellation painted on them. (82:88-89)

1558-1303 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. (36:48-49)(43:167)(45:xiii-xv) (67:20)

1520-1085 BC
An artisan village, Deir-al-Medina, 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 know-ledge 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. (50:141-142)(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, 78-80, Plate 7)

1400-1300 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 (36:48-49)(45:xiii-xv)(57:20)

600-480 BC
This is the period of the Greek "Archiac" style. (36:118)

569-500 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 "root-six'' rectangle. They termed this system Kalpasutra ("rules of the cord") and this is also found in their Sulvasutras. (43:144-145)(45:xv)

500-523 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. (39:7-8)

The period of the use of the Egyptian measuring system we know today as dynamic symmetry, called harpedonoptae, (''rope-stretchers'') by the Greeks. This was also the period of the Greeks "Golden Section," "Golden Mean," and the "Golden Rectangle." (43:145, Note II)(45:xiv-xv)(42:25-31)

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 one-half 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 right-angled 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)(57:12-13)(36:62-63)

c490-425 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. (49:141-142, 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. (55:20-21)

448-c427 BC
The Parthenon in Athens was built by Greek architects Ictinus and Callicrates. It is a perfect example of dynamic symmetry's "root-five" 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)(54:62-65)(57:25-26)(99:148)

430-427 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)

427-347 BC
In Plato's Theaetatus, his students used the Egyptian measuring system and are known to have calculated it up to the ''root-seventeen'' rectangle. (46:24)

356-323 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)(43:152-153)(45:xiv-xv)

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. (43:157-158)(45:xiv-xv)

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 rope-stretchers). He tried to synthesize Platonic and Christian thought. (23:406)

There are two red vases from the island of Samos (the island where glass-making 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)

Plotinus, a Greek philosopher on art and religion, lived during this time. He proposed that art should be a metaphysical experience. (9:2)

Constantinople was built beginning in 330. This began the Early Christian Period of the Byzantine Empire. (27:xi)

Ravenna, Italy, was the Western seat of the Byzantine Empire. (85:13, 30)

This is the Coptic Period in Egyptian history, ending with the Arab conquest. (17:9)

The Silver Chalice of Antioch (c4th-5th century), excavated in 1910, was designed with the dynamic symmetry system. (23:353)(31:ix)

600-c500 [?]
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)

The Christian Topography, a work by Cosmos Indicoplenstes, was written and it identified the Church with the Cosmos. (10:68)

The time of the Muslim conquest of Egypt. (17:286)

The Iconoclasm period in Early Christian history when the depiction of images was forbidden. (22:6)

The Battle of Tours (France) and the Mediterranean area was lost to the East. There was no more East-West travel and the source of papyrus was lost to the West. (55:58)

The period of the "Macedonian" Dynasty in the Byzantine Empire. (22:6)

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)(36:266-267)(85:51)

The Crusades came from Europe to the Byzantine Empire. (22:8)

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)

The Comnene Age in the Byzantine Empire. Icon-painting on panels came into prominance due to a new merchant class of patron. Byzantine art was characterized by brilliant decoration. (10:284)(90:128)

The Hindu Indian mathematician, Bhaskara, used the Pythagorian theorum although he "proofed" it a different way. (54:85)

Regional styles developed in the Byzantine Empire but still were connected by Byzantine influence, and the "damp-fold" appeared in sculpture and painting. (78:243)

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. (54:157-158)(91:149)

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. (3:14-15)(10:297-298)(112:63)

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)

A new style of icon developed, that of multiple figures and scenes and a return to tenth century models. (27:123)(77:243)

The Crusaders were ousted from Constantinople. (112:144)

During this Palaeologue Dynasty, artists began to sign their icons in Mistra. In Italy, many individual artists began to be recognized. (10:328)

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)

Icon-painters returned to the eleventh century style of severe, withdrawn images. Serbian icons are an excellent example. (10:284)

Prince Dimitri Donskoi, of Moscow, resisted the Ottoman turks at the Battle of Kuilovo in 1380. (10:324)

A painting of The Nativity by W. des Rudolf von Ems was designed with the "root-five" rectangle of dynamic symetry (16:66)

Andrei Rublev, the great Russian icon-painter 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)

The Greek icon, Baptism of Christ, was painted and falls within two "root-eight" rectangles in its design composition. (112:113, 135)

Theophanes the Greek and Andrei Rublev decorated three churches in Moscow. (10:324)

Roger van der Weyden's Descent from the Cross painting, in the Prado Museum, Spain, is designed with the use of a "root-three" rectangle plus three pentagons which incorporate the use of the "Golden Section" and "Golden Mean." (10:340)(16:67-68)

The first use of the vanishing point in art was in Florence, Italy, by Masaccio. (49:327)

The artistic center of icon-painting shifted to the island of Crete. (112:83)

The Northern Russia icon, The Entombment, was designed on "root two" rectangle. (122:208-214)

The Northern Russia icon, The Descent into Hell, is based on a "root-three'' rectangle scheme. (67:39)

The Cretean iconographer, M. Damaskina, was a great icon-painter during this time. (85:83)

This is the time of the great mathematician Kepler. (54:23)

The Moscow School icon, Simeon Stylites, was designed with two "root-five" rectangles. (83: Plate 125)

Iconography began a rapid decline in Russia. (3:14-15) (67:Plate 201)(122:182)

During this time E. Tzane was a great icon-painter. (85:83)

Pascal's "triangle" was written (Traité du Triangle Arithmetique, 1623-1662). (54:87, 131)

The icon, St. John the Evangelist with St. Prochorus, was designed using two "root-six" rectangles. (67:Plate 146)

The first measured drawings of the Parthenon in Athens were made. (23:1492)

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 Neo-Classical 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)

Zeysing showed the presence of the "Golden Section" in his frontal view of the Parthenon, in Athens (38:124)

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)

Edward Lucas gave the name to the Fibonacci Series. The Series originated in a puzzle problem in 1202 by Fibonacci. (54:47. 158)

Moritz Cantor, a mathematician and historian, flourished during this time in Leipzig, Germany. (38:2)

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)

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)

Jay Hambidge (1867-1924) studied phyllotaxis for 25 years before turning to the study of proportion in art. He gave a talk in London on this. (43:xi)

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." (43:151-153)

Jay Hambidge based his dynamic symmetry research on Francis Cranmer Penrose's (1817-1903) work, Investigations of Principles of Athenian Architecture. (132:-)

Hambidge began to study the symmetry in art and rediscovered dynamic symmetry. (48:xii)

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)

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:vii-viii)(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)

Edward B. Edwards, a designer, offered Hambidge the use of his studio, and Hambidge gave lectures there on dynamic symmetry. (31:x)

Hambidge gave a series of ten lectures at the Architectural League rooms in New York. Horace Moran was Chairman of the League. (31:xi)(37:16-17)

Hambidge began writing monthly lessons on dynamic symmetry in the Yale monthly magazine, The Diagonal. The lessons were entitled, "Elements." (45:v)

Hambidge's book, The Greek Vase, was published by Yale University Press. (43:24, 32)

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, 11-16)

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)

Christine Herter was one of the first artists to use Hambidge's dynamic symmetry in her art. She did three pieces. (31:vii)(44:17-21)(51:xi-xii)

Artist George Bellows used dynamic symmetry in his art compositions throughout his life and when he began he won several prizes. (32:8-15)(44:22-38)(79:12, 218, 238-279)

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:-)

Bretano's published a reprint of Hambidge's 1919-20 lectures and entitled it Elements. (45:iv)

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)

Seashell diagrams and illustrations of sunflowers demonstrating phyllotaxis in an article. (46:8, Plate V)

William Ivins, Jr., Harvard University, wrote Art and Geometry, and stated that the Greeks introduced linear subtleties to architecture. (55:16)

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 (1887-1965) built planned village, Vaucrisson, near Paris, 1923.

Yale University Press reprinted Brentano's 1926 reprint of Hambidge's Elements.

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)

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)

E. Wigginton wrote a senior high school research paper on Hambidge's theory of dynamic symmetry. (117:41)

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....'' (122:175-192)

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)

Dover Publications reprinted Brentano's 1926 Elements by Hambidge. (45:iv)

A National Geographic Magazine article about seashells with diagrams and illustrations explaning phyllotaxis. (118:386-429)

Professor H. E. Huntley, an Englishman who had taught mathematics and physics since 1940, wrote a book The Divine Proportion. (54:vi)

An article in the St. John's Review about dynamic symmetry by Howard J. Fisher. (133:40-55)

An article about the dynamic symmetry and phyllotaxis in botany, illustrating its use with a sunflower center. (18:63-64)

The ratio of our visual perception is 1.618.