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πολύγωνον (τό)

ΠΟΛΥΓΩΝΟΝ

LEXARITHMOS 1553

The polygon, a foundational concept in geometry, describes a plane figure with multiple straight sides and angles. The word, a compound of «πολύς» (many) and «γωνία» (angle), precisely captures this property. Its lexarithmos (1553) is numerically linked to the complexity and multiplicity of its constituent elements, characteristics that have made it a subject of intense study since antiquity.

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Definition

According to the Liddell-Scott-Jones Lexicon, πολύγωνον (to) is "a figure of many angles, a polygon." It is a technical term in geometry, referring to a plane figure bounded by three or more straight line segments (sides) connected sequentially at points (vertices), forming an equal number of angles. Its simplest form is the triangle, while other well-known forms include the square, pentagon, hexagon, and so forth.

The concept of the polygon was central to ancient Greek geometry, particularly in the works of Euclid, who in his "Elements" extensively deals with the properties of polygons, their construction, and the calculation of their areas. The study of regular polygons, i.e., those with equal sides and equal angles, was particularly significant for understanding the symmetry and harmony of shapes.

Beyond its purely geometric use, the word "πολύγωνον" could also imply something with many facets or aspects, although this metaphorical usage is less common in classical Greek literature compared to its strictly mathematical meaning. The precise and specific nature of the term makes it fundamental to scientific thought.

Etymology

πολύγωνον ← πολύς + γωνία
The word "πολύγωνον" is a compound, derived from two ancient Greek roots: the adjective «πολύς» (many, much, great number) and the noun «γωνία» (angle, corner, knee). This compound directly describes the characteristic feature of the shape: the existence of many angles (and by extension, many sides). The root of «πολύς» traces back to the Proto-Indo-European root *pelh₁- ("to fill, much"), while the root of «γωνία» is connected to «γόνυ» (knee), suggesting a bend or a point of meeting.

Cognate words derive either from «πολύς» (e.g., πολυάριθμος, πολύμορφος) or from «γωνία» (e.g., γωνιάζω, γωνιακός) or from their compound forms. This family highlights the Greek language's ability to create precise technical terms through the synthesis of simple concepts.

Main Meanings

  1. Plane geometric figure with many angles and sides — The primary and original meaning of the term in ancient Greek geometry, as defined by Euclid.
  2. Multilateral figure — Refers to any shape composed of straight line segments forming a closed perimeter.
  3. Regular polygon — A specific category of polygon with all sides and all angles equal.
  4. Object of geometric study — The use of the term to refer to the subject of studying properties, areas, and perimeters.
  5. Metaphorical use for something complex or multifaceted — Although rare in classical usage, the concept of a "polygon" can be extended to describe something with many aspects or dimensions.

Word Family

poly- (from πολύς, meaning 'many, much') and gon- (from γωνία, meaning 'angle, knee')

The family of "πολύγωνον" is built upon two strong Greek roots: «πολύς», denoting multitude, size, or intensity, and «γωνία», referring to a point of bending or meeting. The combination of these roots creates words that describe the multiplicity of angles or facets, whether in a literal geometric sense or in more abstract descriptions of complexity. Each member of the family develops a specific aspect of this fundamental connection.

πολύς adjective · lex. 780
Meaning "many, great in number or quantity." This is the primary root indicating the multitude of angles in a polygon. It is widely used throughout ancient Greek literature, from Homer to philosophers and scientists.
γωνία ἡ · noun · lex. 864
Meaning "angle, corner, edge." This is the second primary root that defines the shape. In geometry, an angle is the opening between two intersecting lines. It is frequently referenced by Euclid in his "Elements."
πολύγωνος adjective · lex. 1703
The adjective meaning "having many angles." Used to describe anything that has the form of a polygon or possesses many points of bending. It appears in geometric texts to characterize shapes.
πολυγωνικός adjective · lex. 1733
Meaning "pertaining to polygons, polygonal." A more specialized technical term, used to refer to properties or characteristics related to polygons.
πολυγωνισμός ὁ · noun · lex. 1953
The act of constructing or studying polygons. A term that denotes the action or process associated with polygons, often in the context of geometric problems.
πολυμερής adjective · lex. 933
Meaning "composed of many parts, multifaceted." While not strictly geometric, it highlights the concept of "πολύς" in a broader sense of complexity or composition from many elements.
γωνιάζω verb · lex. 1671
Meaning "to form an angle, to turn a corner." It describes the action of creating or having an angle, directly connecting to the noun «γωνία» and the form of the polygon.

Philosophical Journey

The concept of the polygon is as old as geometry itself, with its evolution inextricably linked to the development of mathematics in ancient Greece.

6th-5th C. BCE
Pythagoreans and early geometry
The Pythagoreans studied the properties of regular polygons, especially the triangle and square, and their relationship to numbers and harmony.
4th C. BCE
Plato and the Platonic solids
Plato, in his "Timaeus," connected regular polyhedra (whose faces are regular polygons) with the elements of nature, highlighting the philosophical significance of geometric shapes.
c. 300 BCE
Euclid, "Elements"
Euclid provided the first systematic and axiomatic foundation of geometry, defining polygons and proving their properties in Books I-VI and XII of the "Elements."
3rd C. BCE
Archimedes and the approximation of pi
Archimedes used inscribed and circumscribed polygons in a circle to approximate the value of pi, demonstrating the practical application of polygon theory.
1st C. BCE - 1st C. CE
Heron of Alexandria
Heron dealt with the calculation of polygon areas and other geometric problems, continuing the tradition of Greek mathematical thought.
Byzantine Period
Commentary and preservation
Byzantine scholars preserved and commented on the works of ancient Greek mathematicians, ensuring the transmission of knowledge about polygons to the West.

In Ancient Texts

We present key references that define the concept of the polygon in ancient Greek literature.

«Πολύγωνον δέ ἐστι σχῆμα περιεχόμενον ὑπὸ πλειόνων ἢ τριῶν εὐθειῶν.»
A polygon is a figure contained by more than three straight lines.
Euclid, "Elements", Definitions
«Πᾶν πολύγωνον σχῆμα δύναται διαγραφῆναι ἐν κύκλῳ καὶ περὶ κύκλον.»
Every polygonal figure can be inscribed in a circle and circumscribed about a circle.
Archimedes, "Measurement of a Circle", Proposition 1

Lexarithmic Analysis

The lexarithmos of the word ΠΟΛΥΓΩΝΟΝ is 1553, from the sum of its letter values:

Π = 80
Pi
Ο = 70
Omicron
Λ = 30
Lambda
Υ = 400
Upsilon
Γ = 3
Gamma
Ω = 800
Omega
Ν = 50
Nu
Ο = 70
Omicron
Ν = 50
Nu
= 1553
Total
80 + 70 + 30 + 400 + 3 + 800 + 50 + 70 + 50 = 1553

1553 is a prime number — indivisible, a quality the Pythagoreans considered the mark of pure essence.

The 18 Methods

Applying the 18 traditional lexarithmic methods to the word ΠΟΛΥΓΩΝΟΝ:

MethodResultMeaning
Isopsephy1553Prime number
Decade Numerology51+5+5+3 = 14 → 1+4 = 5. The Pentad, a number of harmony, balance, and man, signifies the completeness and proportion that characterize geometric shapes.
Letter Count99 letters (Π-Ο-Λ-Υ-Γ-Ω-Ν-Ο-Ν). The Ennead, a number of completion and perfection, reflects the fullness of the self-enclosed geometric figure.
Cumulative3/50/1500Units 3 · Tens 50 · Hundreds 1500
Odd/EvenOddMasculine force
Left/Right HandRightDivine (≥100)
QuotientComparative method
NotarikonΠ-Ο-Λ-Υ-Γ-Ω-Ν-Ο-ΝΠολλῶν Ὀρθῶν Λόγων Ὑποκείμενον Γεωμετρικῶν Ὠφελίμων Νόμων Ὁρισμός Νέος (Interpretive: "Subject of Many Right Geometric Arguments, Definition of Useful New Laws")
Grammatical Groups4Φ · 3Η · 2Α4 vowels (O, Y, Ω, O), 3 semivowels (Λ, Ν, Ν), 2 mutes (Π, Γ). This ratio suggests a balanced structure, much like the polygon itself.
PalindromesNo
OnomancyComparative
Sphere of DemocritusDivination with lunar day
Zodiacal IsopsephySaturn ♄ / Virgo ♍1553 mod 7 = 6 · 1553 mod 12 = 5

Isopsephic Words (1553)

Words from the Liddell-Scott-Jones Lexicon with the same lexarithmos (1553) but different roots, offering an interesting numerological correspondence:

γεωμετρικός
The adjective «γεωμετρικός» is directly connected to «πολύγωνον», as it describes anything belonging to or related to geometry, the science that studies polygons. Their numerical identity underscores their fundamental relationship.
ἐμβατεύω
The verb «ἐμβατεύω» means "to step in, to enter, to investigate deeply." Its numerical connection to «πολύγωνον» may suggest the need for thorough study and penetration into the properties of geometric shapes.
φυσιόλογος
The «φυσιόλογος» is one who studies nature, a natural philosopher. Its isopsephy with «πολύγωνον» may imply that understanding natural phenomena often requires the analysis of underlying geometric structures.
εὐλύτησις
The noun «εὐλύτησις» means "easy solution, ease of solving." Its numerical correspondence with «πολύγωνον» can be interpreted as the search for simple and elegant solutions to complex geometric problems.
δυσπενθέω
The verb «δυσπενθέω» means "to mourn greatly, to lament." The contrast of its meaning with the precision and order of the polygon highlights the diversity of concepts that can be linked by the same lexarithmos.

The LSJ lexicon contains a total of 36 words with lexarithmos 1553. 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.
  • EuclidThe Elements. Translated by Sir Thomas L. Heath. New York: Dover Publications, 1956.
  • ArchimedesThe Works of Archimedes. Edited and translated by T. L. Heath. Cambridge: Cambridge University Press, 1897.
  • Heath, T. L.A History of Greek Mathematics. Vol. 1 & 2. Oxford: Clarendon Press, 1921.
  • Pappus of AlexandriaCollection. Translated by P. Ver Eecke. Paris: Desclée de Brouwer, 1933.
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