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Polygon

From Simple English Wikipedia, the free encyclopedia
Polygons: open (excluding its boundary), boundary only (excluding interior), closed (including both boundary and interior), and self-intersecting

Apolygon is a closedtwo-dimensionalshape. It is aplane figure that is made up of a number of sides. These are also called edges orline segments. Each side is connected to another one by a corner, orvertex. Each pair of connected sides makes anangle.

These sides and angles can be different from one another, or they can all be the same. Polygons made of only sides of the same length (equilateral) and angles the same width (equiangular) are calledregular polygons.

Asquare is a polygon because it has four sides. The smallest polygon inEuclidean geometry or "flat geometry" is thetriangle, which has three sides and three corners. On asphere, there can also be adigon and ahenagon.

If the edge lines of the polygon do not cross each other, the polygon is calledsimple; otherwise it iscomplex.

Incomputer graphics, polygons (especially triangles) are often used to make graphics.

Gallery

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  • A complex pentagon
    A complex pentagon
  • A simple concave hexagon
    A simpleconcave hexagon
  • A non-regular heptagon
    A non-regular heptagon
  • A non-regular octagon
    A non-regular octagon
  • A non-regular decagon
    A non-regular decagon
  • A enneacontakaienneagon (a polygon with 99 sides)
    A enneacontakaienneagon (a polygon with 99 sides)

List of polygons

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Polygon names and miscellaneous properties
NameSidesProperties
monogon1Not generally recognised as a polygon,[1] although some disciplines such as graph theory sometimes use the term.[2]
digon2Not generally recognised as a polygon in the Euclidean plane, although it can exist as aspherical polygon.[3]
triangle (or trigon)3The simplest polygon which can exist in the Euclidean plane. Cantile the plane.
quadrilateral (or tetragon)4The simplest polygon which can cross itself; the simplest polygon which can be concave; the simplest polygon which can be non-cyclic. Cantile the plane.
pentagon5[4] The simplest polygon which can exist as a regular star. A star pentagon is known as apentagram or pentacle.
hexagon6[4] Cantile the plane.
heptagon (or septagon)7[4] The simplest polygon such that the regular form is notconstructible withcompass and straightedge. However, it can be constructed using aNeusis construction.
octagon8[4]
enneagon (or nonagon)9[4] "Nonagon" mixes Latin [novem = 9] with Greek; "enneagon" is pure Greek.
decagon10[4]
hendecagon (or undecagon)11[4] The simplest polygon such that the regular form cannot be constructed with compass, straightedge, andangle trisector.
dodecagon (or duodecagon)12[4]
tridecagon (or trisdecagon)13[4]
tetradecagon14[4]
pentadecagon (or quindecagon)15[4]
hexadecagon (or hexakaidecagon)16[4]
heptadecagon (or septadecagon)17Constructible polygon
octadecagon18[4]
enneadecagon (or nonadecagon)19[4]
icosagon20[4]
icositetragon (or icosikaitetragon)24[4]
triacontagon30[4]
tetracontagon (or tessaracontagon)40[4][5]
pentacontagon (or pentecontagon)50[4][5]
hexacontagon (or hexecontagon)60[4][5]
heptacontagon (or hebdomecontagon)70[4][5]
octacontagon (or ogdoëcontagon)80[4][5]
enneacontagon (or enenecontagon)90[4][5]
hectogon (or hecatontagon)100[4]
hectotetracontagon140
257-gon257Constructible polygon
chiliagon1,000Philosophers includingRené Descartes,[6]Immanuel Kant,[7]David Hume,[8] have used the chiliagon as an example in discussions.
myriagon10,000Used as an example in some philosophical discussions, for example in Descartes'sMeditations on First Philosophy
65537-gon65,537Constructible polygon
megagon[9][10][11]1,000,000As with René Descartes's example of the chiliagon, the million-sided polygon has been used as an illustration of a well-defined concept that cannot be visualised.[12][13][14][15][16][17][18] The megagon is also used as an illustration of the convergence ofregular polygons to a circle.[19]
apeirogon∞A degenerate polygon of infinitely many sides.

References

[change |change source]
  1. ↑Grunbaum, B.; "Are your polyhedra the same as my polyhedra",Discrete and computational geometry: the Goodman-Pollack Festschrift, Ed. Aronov et al., Springer (2003), p. 464.
  2. ↑Hass, Joel; Morgan, Frank (1996), "Geodesic nets on the 2-sphere",Proceedings of the American Mathematical Society,124 (12):3843–3850,doi:10.1090/S0002-9939-96-03492-2,JSTOR 2161556,MR 1343696
  3. ↑Coxeter, H.S.M.;Regular polytopes, Dover Edition (1973), p. 4.
  4. ↑4.004.014.024.034.044.054.064.074.084.094.104.114.124.134.144.154.164.174.184.194.204.214.224.23Salomon, David (2011).The Computer Graphics Manual. Springer Science & Business Media. pp. 88–90.ISBN 978-0-85729-886-7.
  5. ↑5.05.15.25.35.45.5Peirce, Charles Sanders (1976).The New Elements of Mathematics: Algebra and geometry. Mouton Publishers. p. 298.ISBN 978-0-391-00612-6.
  6. ↑Sepkoski, David (2005)."Nominalism and constructivism in seventeenth-century mathematical philosophy"(PDF).Historia Mathematica.32:33–59.doi:10.1016/j.hm.2003.09.002.S2CID 120467581. Archived fromthe original(PDF) on 12 May 2012. Retrieved18 April 2012.
  7. ↑Martin, Gottfried (1955).Kant's Metaphysics and Theory of Science. Manchester University Press. p. 22.
  8. ↑Hume, David (1826).The Philosophical Works: Including All the Essays, and Exhibiting the More Important Alterations and Corrections in the Successive Ed. Publ. Black and Tait. p. 101.
  9. ↑Gibilisco, Stan (2003).Geometry demystified (Online-Ausg. ed.). New York: McGraw-Hill.ISBN 978-0-07-141650-4.
  10. ↑Darling, David (2004).The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes. Wiley. p. 249.ISBN 978-0-471-66700-1.
  11. ↑Dugopolski, Mark (1999).College Algebra and Trigonometry. Addison-Wesley. p. 505.ISBN 978-0-201-34712-8.
  12. ↑McCormick, John Francis (1928).Being, its division and causes. Loyola University Press. p. 18.
  13. ↑Merrill, John Calhoun; Odell, S. Jack (1983).Philosophy and Journalism. Longman. p. 47.ISBN 978-0-582-28157-8.
  14. ↑Hospers, John (1997).An Introduction to Philosophical Analysis. Psychology Press. p. 56.ISBN 978-0-415-15792-6.
  15. ↑Mandik, Pete (2010).Key Terms in Philosophy of Mind. A&C Black. p. 2010.ISBN 978-1-84706-349-6.
  16. ↑Kenny, Anthony (2006).The Rise of Modern Philosophy: A New History of Western Philosophy. Oxford University Press. p. 124.ISBN 978-0-19-875277-6.
  17. ↑BALMES, REV JAMES (1856).FUNDAMENTAL PHILOSOPHY. p. 27.
  18. ↑Potter, Vincent G. (1993).On Understanding Understanding: A Philosophy of Knowledge. Fordham University Press. p. 86.ISBN 978-0-8232-1486-0.
  19. ↑Russell, Bertrand (2004).History of Western Philosophy. Psychology Press. p. 202.ISBN 978-0-415-32505-9.
Special cases, includingregular polygons with their own names, in parentheses
List of polygons by number of sides
1–10 sides
11–20 sides
21–30 sides
31–50 sides
51–100 sides
(selected)
>100 sides
Star polygons
(5–12 sides)
Triangles
Quadrilaterals
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