THE GOLDEN AGE OF PERICLES, 5th CENTURY BCE
The Human Hands are believed to be the origin for all Numbers and Counting Systems.
There are five (5) fingers on each hand and ten (10) fingers for both hands. Four (4) fingers make the Palm. (image 7)
Protagoras, a friend of Pericles, believed “Man is the Measure”.
The proportional height of the idealized Human body was the canon of “measure and proportion” that was used in the design of the Parthenon.
Pythagoras and the Tetraktys: The Perfect Sacred Numbers Five, Seven, and Ten (images 8,9)
The Tetraktys is a triangle consisting of one (1) dot, over two (2) dots, over three (3) dots, over four (4) dots. Pythagoras believed it could be used to geometrically represent everything in Nature, The Human, and the Cosmos.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 = the Ten Individual Units.
The numbers 1 and 2 to the Pythagoreans were not numbers.
2 + 3 = 5 (five), the numbers of fingers on one hand.
3 + 4 = 7 (seven), the Number of Wisdom: the first triangular number (3) plus the first square number (4).
1 + 2 + 3 + 4 = 10 (ten), the Perfect Number.
The Tetraktys and the Golden Mean Series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144, …
The Golden Mean Series is believed to have been used by the Hindus, but it was only rediscovered in the 1200s CE in North Africa by Fibonacci.
1 + 2 + 3 + 4 + 5 + 6 = 21 a Fibonacci Number
7 + 8 + 9 +10 = 34 a Fibonacci Number
1 + 2 + 3 + 4 + 5 + 6 +7 + 8 + 9 +10 = 55 a Fibonacci Number
Pythagoras understood that adding the Ten Individual Units of natural numbers to total 55 manifested a Golden Mean Series number. This fractal series is directly related to the Golden Rectangle and its inscribed Spiral. By dividing the smaller of two adjacent numbers into the larger, one approaches the idealized Golden Mean proportion of 1.618, e.g., 8/5 = 1.600; 13/8 = 1.625; 21/13 = 1.615…; 89/55 = 1.618 18 18…
Another Proportional Series (similar to Fibonacci numbers) is in decimal equivalents: …. .090, .146, .236, .382, .618, 1.000, 1.618, 2.618 …(irrational numbers rounded back to three decimal places). These, too, express the Golden Mean proportion by dividing the smaller of two adjacent numbers into the larger, e.g., 1.000/.618 = 1.618.
Pythagoras initially believed that only Natural numbers were numbers. Eventually though, Irrational numbers were accepted as being Real numbers by him before his death around 500 BCE.
The Greeks believed that everything in Nature, the Human, and the Cosmos (not just certain major numbers, proportions, measurements, rectangles, or selected elements) was in Unity.
A few of the most important numbers and proportions used to organize the architectural elements:
· The ground plan, elevation and form are related to the numbers 5, 7, and 10. The pre-Greeks could only calculate the diagonal of a 1x1 square to be 1.4. Hence, the diagonal of a 5x5 square was believed to be 7. (15)
The Triglyph Pattern of the frieze, the organizing pattern for the entire building, is a 1000 by 1000 grid, subdivided into a 500 by 500 grid. (14)
· Fractal modules of Root Five Rectangles and Golden Rectangles are used to organize the most significant architectural elements. (images 16,17,18,19,20)
· The primary rectangular proportion is the column diameter (human height) to the column spacing, 447.2 to 1000. Large to small reciprocal subdivisions of this module regulate all shapes and details. (images 6,20)
· The primary rectangular proportion is the column diameter (human height) to the column spacing, 447.2 to 1000. Large to small reciprocal subdivisions of this module regulate all shapes and details. (images 6,20)
· Multiplying the Perfect Number 10 times Athena’s Number of Wisdom 7 creates the proportional foot dimension, the Sacred Foot of 70 units.
· The most important proportional module and measurement used in the Temple is the Hekatompedon, the one hundred foot measure. As the Sacred Foot is 70 units long, the Hekatompedon can be expressed as having 7000 units (100 x 70 = 7000). That 7000 unit measurement is revealed as the diagonal of a 5000 x 5000 square module. Smaller relationships of the measurement are revealed in the overall Triglyph Pattern (image 14) of the four exterior facades, the Inner Temple’s plan and its exterior facade length (bottom step to bottom step), and the length of the floor plan of the Naos. (images 13,15)
