ΣΥΜΜΕΤΡΙΚΟΝ (symmetriakos) — Lexarithmos 1235 · Etymology, Meanings

Definition

“Symmetrikon” (συμμετρικός, -ή, -όν) is an adjective describing something that possesses symmetry, i.e., the harmonious proportion of its parts to each other and to the whole. The word derives from “syn” (together, with) and “metron” (measure, proportion, rule), signifying a common measure or a shared ratio. In ancient Greek thought, symmetry was not merely a superficial beauty but a deeper expression of order, harmony, and perfection.

The concept of the symmetrical played a central role in numerous fields. In philosophy, particularly among the Pythagoreans and Plato, symmetry was linked to cosmic order, the harmony of the spheres, and the beauty of the universe, being regarded as a reflection of eternal Forms. In art and architecture, symmetry was the fundamental principle for creating works that embodied beauty and perfection, as exemplified in the sculptures of Polycleitus and the temples of the Classical era.

Beyond aesthetics, “symmetrikon” also held a mathematical significance, referring to magnitudes that are “commensurate,” meaning they share a common measure. This property was crucial in geometry and arithmetic, where ratio and proportionality were fundamental concepts. The idea of the symmetrical, therefore, permeated Greek thought, from the abstract to the concrete, from the cosmic to the human, as an expression of balance and harmony.

Etymology

symmetrikon ← symmetria ← syn + metron (root METR-)

The word “symmetrikon” is derived from the noun “symmetria,” which in turn is formed from the preposition “syn” (together, jointly) and the noun “metron” (measure, rule, proportion). The root METR- is an Ancient Greek root belonging to the oldest stratum of the language, denoting the concept of measurement, limit, and order. The compound “syn-metron” implies a common measure or the harmonious proportion of parts.

From the root METR- spring many words related to measurement, proportion, and order. The verb “metreō” (μετρέω) means “to measure,” while the noun “metron” (μέτρον) is the unit of measurement itself or the standard. The addition of the preposition “syn” creates “symmetros” (σύμμετρος, having a common measure) and “symmetria” (συμμετρία, the quality of being symmetrical). Conversely, the privative “a-” yields “asymmetros” (ἀσύμμετρος) and “ametria” (ἀμετρία), indicating a lack of measure or proportion. Other cognate words include “metrētēs” (μετρητής, a measurer) and “diametros” (διάμετρος, diameter, literally “through measure”).

Main Meanings

Proportional, harmonious, balanced — The primary meaning, describing something whose parts are in a harmonious relationship with each other and with the whole.
Having a common measure, commensurate — A mathematical concept, especially in geometry, for magnitudes that can be measured by the same unit.
Harmonized with a standard or rule — Refers to adherence to a rule (κανών) or an ideal measure, as in Polycleitus' "Canon."
Regular, orderly, well-arranged — A philosophical meaning, connected to cosmic order and the beauty of the universe, as found in Plato.
Appropriate, fitting — In a broader sense, something that is correctly measured for a specific use or occasion.
Compatible, matching — Describes the property of two or more things fitting together due to a common proportion.

Word Family

metr- (root of μέτρον, meaning “measure, proportion”)

The Ancient Greek root METR- forms the basis of an extensive family of words revolving around the concept of measurement, limit, proportion, and order. From this root, both concrete notions of measurement (e.g., units, tools) and abstract ideas of harmony and balance developed. The addition of prepositions like “syn-” or “dia-” and privatives like “a-” expanded the semantic field, allowing for the expression of agreement, division, or lack of measure, respectively. Each member of the family retains the core “measurable” quality, whether as an action, a result, or a characteristic.

μέτρον τό · noun · lex. 565

The fundamental noun from which all words of the family derive. It means “measure, unit of measurement, rule, limit.” In Homer, it often refers to “measure” for length or weight, while in philosophy it acquires the meaning of “right measure” or “proportion.”

μετρέω verb · lex. 1250

The verb meaning “to measure, to calculate, to distribute by measure.” It represents the action of applying a measure. In Herodotus, for example, it is used for measuring land areas, while in Plato for evaluating values.

σύμμετρος adjective · lex. 1355

The adjective from which “symmetrikon” derives. It means “having a common measure, proportional, harmonious.” It describes the property of parts being in correct proportion to each other and to the whole. It is often referred to in architectural and artistic works.

συμμετρία ἡ · noun · lex. 1096

The noun denoting the quality of being symmetrical, i.e., harmonious proportion, balance, and homogeneity of parts. It is a central concept in aesthetics, philosophy, and mathematics, as in Plato's “Timaeus.”

ἀσύμμετρος adjective · lex. 1356

The opposite of “symmetros,” meaning “having no common measure, disproportionate, disorderly.” It describes the lack of harmony and proportion, often with a negative connotation in ancient thought.

ἀμετρία ἡ · noun · lex. 457

The lack of measure, excess, a disproportionate state. In ethical philosophy, “ametria” is considered a fault, as it violates the principle of “nothing in excess.”

μετρητής ὁ · noun · lex. 961

One who measures, or a measuring instrument. Also, a specific unit of measure for liquids or dry goods. In daily life, the “metrētēs” was essential for trade and agriculture.

διάμετρος ἡ · noun · lex. 730

The line that passes through a circle or other geometric shape and divides it into equal parts. The word literally means “measure through.” A fundamental concept in Euclidean geometry.

γεωμετρία ἡ · noun · lex. 1264

The science of measuring the earth, which evolved into a branch of mathematics dealing with the properties of points, lines, surfaces, and solids. Fundamental to ancient Greek science and philosophy.

Philosophical Journey

The concept of the symmetrical, though seemingly simple, has a deep and complex history in ancient Greek thought, evolving from architecture and sculpture to cosmology and philosophy.

6th-5th C. BCE

Pythagorean Philosophers

The Pythagoreans were the first to connect symmetry with cosmic harmony and numbers. The idea that the universe is structured based on mathematical ratios laid the groundwork for the concept's further development.

5th C. BCE

Polycleitus of Argos

The renowned sculptor Polycleitus formulated his "Canon," a system of proportions for the human form, embodying ideal symmetry and beauty. His work "Doryphoros" epitomizes this principle.

4th C. BCE

Plato

In Plato, symmetry emerges as a fundamental principle of cosmic order and beauty. In the "Timaeus," the symmetry of geometric shapes is linked to the creation of the world and the harmony of its elements.

4th C. BCE

Aristotle

Aristotle, though approaching it differently from Plato, recognized the importance of symmetry in art and nature, connecting it with the perfection and harmony resulting from the proper arrangement of parts.

3rd C. BCE

Euclid

In Euclid's "Elements," the concept of "commensurate" (σύμμετρος) acquires a strictly mathematical meaning, referring to magnitudes that share a common measure, forming a fundamental principle of geometry.

1st C. BCE

Vitruvius

The Roman architect Vitruvius, deeply influenced by Greek thought, incorporated the principles of symmetry and proportion into his work "De Architectura," making them central to architectural theory.

In Ancient Texts

The significance of the symmetrical in ancient Greek thought is highlighted through texts spanning philosophy, aesthetics, and the sciences.

«πάντα γὰρ τὰ καλὰ σύμμετρα.»

“For all beautiful things are symmetrical.”

Plato, “Philebus” 64e

«τὸ γὰρ καλὸν ἐν μεγέθει καὶ τάξει ἐστίν, διὸ οὔτε πάμικρον ἂν τι γένοιτο καλὸν ζῷον (συγκεχυμένη γὰρ ἡ θεωρία ἐν ἀναισθήτῳ χρόνῳ), οὔτε παμμέγεθες (οὐ γὰρ ἅμα ἡ θεωρία ἀλλ' ἅμα μὲν ἡ ὄψις, οὐχ ἅμα δὲ ἡ ἕνωσις καὶ ἡ ὅλη θεωρία).»

“For beauty consists in magnitude and order; hence neither can a very small animal be beautiful (for the vision is confused in an imperceptible time), nor a very large one (for the vision is not simultaneous, but the sight is simultaneous, though not the unity and the whole vision).”

Aristotle, “Poetics” 1450b36-1451a4

«τὸ κάλλος ἐν τῇ συμμετρίᾳ τῶν μελῶν.»

“Beauty lies in the symmetry of the parts.”

Polycleitus, “Canon” (fragment preserved via Galen, “De Placitis Hippocratis et Platonis” V.3)

Lexarithmic Analysis

The lexarithmos of the word ΣΥΜΜΕΤΡΙΚΟΝ is 1235, from the sum of its letter values:

Σ = 200

Sigma

Υ = 400

Upsilon

Μ = 40

Mu

Μ = 40

Mu

Ε = 5

Epsilon

Τ = 300

Tau

Ρ = 100

Rho

Ι = 10

Iota

Κ = 20

Kappa

Ο = 70

Omicron

Ν = 50

Nu

= 1235

Total

200 + 400 + 40 + 40 + 5 + 300 + 100 + 10 + 20 + 70 + 50 = 1235

1235 decomposes into 1200 (hundreds) + 30 (tens) + 5 (units).

The 18 Methods

Applying the 18 traditional lexarithmic methods to the word ΣΥΜΜΕΤΡΙΚΟΝ:

Method	Result	Meaning
Isopsephy	1235	Base lexarithmos
Decade Numerology	2	1+2+3+5 = 11 → 1+1 = 2 — Dyad, the principle of balance, proportion, and the dual relationship between parts.
Letter Count	11	11 letters — Hendecad, the number often associated with transcendence and the pursuit of perfection beyond the simple decad.
Cumulative	5/30/1200	Units 5 · Tens 30 · Hundreds 1200
Odd/Even	Odd	Masculine force
Left/Right Hand	Right	Divine (≥100)
Quotient	—	Comparative method
Notarikon	Σ-Υ-Μ-Μ-Ε-Τ-Ρ-Ι-Κ-Ο-Ν	Synthesis of Underlying Measure and Form in Rhythmic Balance of Beautiful Similarities of Law.
Grammatical Groups	4V · 7C · 0A	4 vowels (upsilon, epsilon, iota, omicron), 7 consonants (sigma, mu, mu, tau, rho, kappa, nu), 0 atonic.
Palindromes	No
Onomancy	—	Comparative
Sphere of Democritus	—	Divination with lunar day
Zodiacal Isopsephy	Sun ☉ / Pisces ♓	1235 mod 7 = 3 · 1235 mod 12 = 11

Isopsephic Words (1235)

Words from the Liddell-Scott-Jones lexicon with the same lexarithmos (1235) as “symmetrikon,” but from different roots, offering interesting conceptual parallels or contrasts.

ἀνδριαντοπλαστική

The art of making statues or effigies. The connection is direct, as symmetry was a fundamental principle in ancient Greek sculpture, with Polycleitus establishing the “Canon” for the ideal proportion of the human body.

παραμετρητικός

Pertaining to measuring amiss or alongside, or to mismeasurement. This contrasts with “symmetrikon,” which implies precise and harmonious measurement.

ἐπιτελεστικός

Capable of accomplishing, completing, or bringing something to fruition. Symmetry was often considered essential for the perfection and completion of a work, whether artistic or philosophical.

ἀσύνθετος

Uncompounded, simple, indivisible. While symmetry relies on the harmony of parts, it presupposes the composition of these parts into a unified whole, in contrast to the simplicity of the uncompounded.

πρόχειρος

“At hand,” readily available, offhand. This can be contrasted with the precision and diligence required to achieve symmetry, suggesting a less rigorous or careful approach.

The LSJ lexicon contains a total of 76 words with lexarithmos 1235. For the full catalog and AI semantic filtering, see the interactive tool.

Sources & Bibliography

Liddell, H. G., Scott, R., Jones, H. S. — A Greek-English Lexicon. Oxford: Clarendon Press, 1940.
Plato — Philebus.
Plato — Timaeus.
Aristotle — Poetics.
Euclid — Elements.
Vitruvius Pollio, Marcus — De Architectura (translations and commentaries on Greek sources).
Galen — De Placitis Hippocratis et Platonis (for the Polycleitus fragment).
Pollitt, J. J. — The Art of Greece, 1400-31 B.C.: Sources and Documents. Cambridge University Press, 1990.