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how to draw a 3d infinity sign

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Mathematical symbol, "∞"

∞ {\displaystyle \infty }

Infinity symbol
In Unicode U+221E ∞ INFINITY (HTML∞· ∞)
Different from
Different from U+267E ♾ PERMANENT Newspaper SIGN (HTML♾)

The infinity symbol ( ∞ {\displaystyle \infty } ) is a mathematical symbol representing the concept of infinity. This symbol is also chosen a lemniscate,[one] later on the lemniscate curves of a similar shape studied in algebraic geometry,[two] or "lazy eight", in the terminology of livestock branding.[three]

This symbol was commencement used mathematically by John Wallis in the 17th century, although it has a longer history of other uses. In mathematics, it oft refers to infinite processes (potential infinity) rather than infinite values (actual infinity). It has other related technical meanings, such as the employ of long-lasting paper in bookbinding, and has been used for its symbolic value of the space in modernistic mysticism and literature. It is a mutual chemical element of graphic design, for instance in corporate logos equally well as in older designs such equally the Métis flag.

Both the infinity symbol itself and several variations of the symbol are available in various character encodings.

History [edit]

Portrait of John Wallis, painted in 1701 by Sir Godfrey Kneller, from the National Portrait Gallery

John Wallis introduced the infinity symbol ∞ {\displaystyle \infty } to mathematical literature.

Eight variations of the infinity symbol

The ∞ {\displaystyle \infty } symbol in several typefaces

The lemniscate has been a common decorative motif since aboriginal times; for instance it is unremarkably seen on Viking Age combs.[4]

The English language mathematician John Wallis is credited with introducing the infinity symbol with its mathematical meaning in 1655, in his De sectionibus conicis.[five] [half-dozen] [7] Wallis did not explain his choice of this symbol. It has been conjectured to be a variant form of a Roman numeral, only which Roman numeral is unclear. One theory proposes that the infinity symbol was based on the numeral for 100 million, which resembled the same symbol enclosed within a rectangular frame.[8] Another proposes instead that it was based on the notation CIↃ used to represent i,000.[nine] Instead of a Roman numeral, information technology may alternatively be derived from a variant of ω, the lower-example form of omega, the concluding letter in the Greek alphabet.[ix]

Perhaps in some cases because of typographic limitations, other symbols resembling the infinity sign have been used for the same pregnant.[vii] Leonhard Euler used an open up letterform more closely resembling a reflected and sideways S than a lemniscate,[10] and even "O–O" has been used equally a stand-in for the infinity symbol itself.[7]

Usage [edit]

Mathematics [edit]

In mathematics, the infinity symbol is used more oft to represent a potential infinity,[eleven] rather than an actually infinite quantity as included in the extended real numbers, the cardinal numbers and the ordinal numbers (which apply other notations, such as ℵ 0 {\displaystyle \,\aleph _{0}\,} and ω, for infinite values). For instance, in mathematical expressions with summations and limits such as

∑ north = 0 ∞ 1 ii n = lim x → ∞ two 10 − 1 two x − i = two , {\displaystyle \sum _{n=0}^{\infty }{\frac {i}{2^{north}}}=\lim _{x\to \infty }{\frac {2^{x}-ane}{2^{ten-i}}}=two,}

the infinity sign is conventionally interpreted every bit meaning that the variable grows arbitrarily large towards infinity, rather than actually taking an infinite value, although other interpretations are possible.[12]

The infinity symbol may also be used to represent a betoken at infinity, especially when in that location is just one such signal under consideration. This usage includes, in particular, the infinite bespeak of a projective line,[13] and the point added to a topological space to form its 1-point compactification.[14]

Other technical uses [edit]

Minolta MD 4.5/300mm IF lens

Side view of a camera lens, showing infinity symbol on the focal length indicator

In areas other than mathematics, the infinity symbol may accept on other related meanings. For instance, it has been used in bookbinding to betoken that a book is printed on acid-free paper and will therefore be long-lasting.[xv] On cameras and their lenses, the infinity symbol indicates that the lens'southward focal length is prepare to an space distance, and is "probably one of the oldest symbols to be used on cameras".[16]

Symbolism and literary uses [edit]

Strength tarot card, depicting a woman crowned by an infinity symbol, holding shut a lion's mouth

In modern mysticism, the infinity symbol has become identified with a variation of the ouroboros, an ancient image of a serpent eating its ain tail that has also come to symbolize the infinite, and the ouroboros is sometimes drawn in figure-eight form to reflect this identification—rather than in its more than traditional circular form.[18]

In the works of Vladimir Nabokov, including The Gift and Pale Fire, the figure-eight shape is used symbolically to refer to the Möbius strip and the infinite, equally is the example in these books' descriptions of the shapes of wheel tire tracks and of the outlines of one-half-remembered people. Nabokov's verse form after which he entitled Pale Fire explicitly refers to "the miracle of the lemniscate".[xix] Other authors whose works use this shape with its symbolic meaning of the infinite include James Joyce, in Ulysses,[xx] and David Foster Wallace, in Space Jest.[21]

Graphic pattern [edit]

The well-known shape and pregnant of the infinity symbol have made it a mutual typographic element of graphic design. For instance, the Métis flag, used by the Canadian Métis people since the early on 19th century, is based effectually this symbol.[22] Dissimilar theories accept been put forward for the meaning of the symbol on this flag, including the hope for an space future for Métis culture and its mix of European and Commencement Nations traditions,[23] [24] but as well evoking the geometric shapes of Métic dances,[25], Celtic knots,[26] or Plains Starting time Nations Sign Language.[27]

A rainbow-coloured infinity symbol is also used by the neurodiversity movement, equally a style to symbolize the infinite variation of the people in the move and of man cognition.[28] The Bakelite company took up this symbol in its corporate logo to refer to the broad range of varied applications of the synthetic textile they produced.[29] Versions of this symbol accept been used in other trademarks, corporate logos, and emblems including those of Fujitsu,[30] Cell Press,[31] and the 2022 FIFA World Cup.[32]

Encoding [edit]

The symbol is encoded in Unicode at U+221E ∞ INFINITY [33] and in LaTeX as \infty: ∞ {\displaystyle \infty } .[34] An encircled version is encoded for use as a symbol for acrid-free paper.

Character information
Preview ∞ ♾
Unicode name INFINITY PERMANENT Paper SIGN
Encodings decimal hex dec hex
Unicode 8734 U+221E 9854 U+267E
UTF-eight 226 136 158 E2 88 9E 226 153 190 E2 99 BE
GB 18030 161 222 A1 DE 129 55 174 56 81 37 AE 38
Numeric character reference ∞ ∞ ♾ ♾
Named grapheme reference ∞
OEM-437 (Alt Code)[35] 236 EC
Mac OS Roman[36] 176 B0
Symbol Font encoding[37] 165 A5
Shift JIS[38] 129 135 81 87
EUC-JP[39] 161 231 A1 E7
EUC-KR[xl] / UHC[41] 161 196 A1 C4
EUC-KPS-9566[42] 162 172 A2 AC
Big5[43] 161 219 A1 DB
LaTeX[34] \infty \acidfree
CLDR text-to-speech name[44] infinity

The Unicode prepare of symbols also includes several variant forms of the infinity symbol that are less often available in fonts in the block Miscellaneous Mathematical Symbols-B.[45]

Character data
Preview ⧜ ⧝ ⧞
Unicode name INCOMPLETE INFINITY TIE OVER INFINITY INFINITY NEGATED WITH VERTICAL BAR
Encodings decimal hex dec hex december hex
Unicode 10716 U+29DC 10717 U+29DD 10718 U+29DE
UTF-viii 226 167 156 E2 A7 9C 226 167 157 E2 A7 9D 226 167 158 E2 A7 9E
Numeric grapheme reference ⧜ ⧜ ⧝ ⧝ ⧞ ⧞
Named grapheme reference ⧜ ⧝ ⧞
LaTeX[34] \iinfin \tieinfty \nvinfty

Encounter besides [edit]

  • Aleph number
  • History of mathematical notation
  • Lazy Eight (disambiguation)

References [edit]

  1. ^ Rucker, Rudy (1982). Infinity and the Mind: The science and philosophy of the space. Boston, Massachusetts: Birkhäuser. p. i. ISBN3-7643-3034-1. MR 0658492.
  2. ^ Erickson, Martin J. (2011). "1.1 Lemniscate". Cute Mathematics. MAA Spectrum. Mathematical Association of America. pp. 1–3. ISBN978-0-88385-576-8.
  3. ^ Humez, Alexander; Humez, Nicholas D.; Maguire, Joseph (1993). Zero to Lazy Eight: The Romance of Numbers. Simon and Schuster. p. 18. ISBN978-0-671-74281-2.
  4. ^ van Riel, Sjoerd (2017). "Viking Age Combs: Local Products or Objects of Trade?". Lund Archaeological Review. 23: 163–178. See p. 172: "Within this type the lemniscate (∞) is a unremarkably used motif."
  5. ^ Wallis, John (1655). "Pars Prima". De Sectionibus Conicis, Nova Methodo Expositis, Tractatus (in Latin). pp. 4.
  6. ^ Scott, Joseph Frederick (1981). The mathematical work of John Wallis, D.D., F.R.Southward., (1616-1703) (2nd ed.). American Mathematical Society. p. 24. ISBN0-8284-0314-7.
  7. ^ a b c Cajori, Florian (1929). "Signs for infinity and transfinite numbers". A History of Mathematical Notations, Volume II: Notations Mainly in Higher Mathematics. Open Court. pp. 44–48.
  8. ^ Maor, Eli (1991). To Infinity and Across: A Cultural History of the Infinite. Princeton, New Jersey: Princeton Academy Press. p. 7. ISBN0-691-02511-viii. MR 1129467.
  9. ^ a b Clegg, Brian (2003). "Affiliate half-dozen: Labelling the infinite". A Brief History of Infinity: The Quest to Recall the Unthinkable. Constable & Robinson Ltd. ISBN978-ane-84119-650-iii.
  10. ^ Cajori (1929) displays this symbol incorrectly, as a turned S without reflection. It can be seen equally Euler used it on page 174 of Euler, Leonhard (1744). "Variae observationes circa series infinitas" (PDF). Commentarii academiae scientiarum Petropolitanae (in Latin). 9: 160–188.
  11. ^ Barrow, John D. (2008). "Infinity: Where God Divides by Zero". Catholic Imagery: Key Images in the History of Scientific discipline. W. W. Norton & Company. pp. 339–340. ISBN978-0-393-06177-2.
  12. ^ Shipman, Barbara A. (April 2013). "Convergence and the Cauchy holding of sequences in the setting of actual infinity". PRIMUS. 23 (v): 441–458. doi:10.1080/10511970.2012.753963.
  13. ^ Perrin, Daniel (2007). Algebraic Geometry: An Introduction. Springer. p. 28. ISBN978-i-84800-056-8.
  14. ^ Aliprantis, Charalambos D.; Border, Kim C. (2006). Space Dimensional Assay: A Hitchhiker'due south Guide (3rd ed.). Springer. pp. 56–57. ISBN978-three-540-29587-7.
  15. ^ Zboray, Ronald J.; Zboray, Mary Saracino (2000). A Handbook for the Study of Volume History in the United states. Center for the Book, Library of Congress. p. 49. ISBN978-0-8444-1015-ix.
  16. ^ Crist, Brian; Aurello, David Due north. (October 1990). "Development of photographic camera symbols for consumers". Proceedings of the Human Factors Society Annual Meeting. 34 (5): 489–493. doi:10.1177/154193129003400512.
  17. ^ Armson, Morandir (June 2011). "The transitory tarot: an test of tarot cards, the 21st century New Age and theosophical thought". Literature & Aesthetics. 21 (ane): 196–212. See in particular p. 203: "Reincarnation is symbolised in a number of cards within the Waite-Smith tarot deck. The primary symbols of reincarnation used are the infinity symbol or lemniscate, the cycle and the circle."
  18. ^ O'Flaherty, Wendy Doniger (1986). Dreams, Illusion, and Other Realities. University of Chicago Press. p. 243. ISBN978-0-226-61855-v. The volume as well features this image on its embrace.
  19. ^ Toker, Leona (1989). Nabokov: The Mystery of Literary Structures . Cornell University Press. p. 159. ISBN978-0-8014-2211-ix.
  20. ^ Bahun, Sanja (2012). "'These heavy sands are linguistic communication tide and current of air have silted here': Tidal voicing and the poetics of dwelling house in James Joyce'due south Ulysses". In Kim, Rina; Westall, Claire (eds.). Cross-Gendered Literary Voices: Appropriating, Resisting, Embracing. Palgrave Macmillan. pp. 57–73. doi:10.1057/9781137020758_4.
  21. ^ Natalini, Roberto (2013). "David Foster Wallace and the mathematics of infinity". In Boswell, Marshall; Burn, Stephen J. (eds.). A Companion to David Foster Wallace Studies. American Literature Readings in the 21st Century. Palgrave Macmillan. pp. 43–57. doi:10.1057/9781137078346_3.
  22. ^ Healy, Donald T.; Orenski, Peter J. (2003). Native American Flags. University of Oklahoma Press. p. 284. ISBN978-0-8061-3556-4.
  23. ^ Gaudry, Adam (Spring 2018). "Communing with the Expressionless: The "New Métis," Métis Identity Cribbing, and the Displacement of Living Métis Civilisation". American Indian Quarterly. 42 (2): 162–190. doi:ten.5250/amerindiquar.42.2.0162. JSTOR 10.5250/amerindiquar.42.ii.0162. S2CID 165232342.
  24. ^ "The Métis flag". Gabriel Dumont Institute(Métis Civilization & Heritage Resource Center). Archived from the original on 2013-07-24.
  25. ^ Racette, Calvin (1987). Flags of the Métis (PDF). Gabriel Dumont Plant. ISBN0-920915-18-three.
  26. ^ Darren R., Préfontaine (2007). "Flight the Flag, Editor'due south note". New Brood Magazine (Winter 2007): half dozen. Retrieved 2020-08-26 .
  27. ^ Barkwell, Lawrence J. "The Metis Infinity Flag". Virtual Museum of Métis History and Culture. Gabriel Dumont Institute. Retrieved 2020-07-15 .
  28. ^ Gross, Liza (September 2016). "In search of autism's roots". PLOS Biology. 14 (9): e2000958. doi:10.1371/journal.pbio.2000958.
  29. ^ Crespy, Daniel; Bozonnet, Marianne; Meier, Martin (April 2008). "100 years of Bakelite, the fabric of a 1000 uses". Angewandte Chemie. 47 (xviii): 3322–3328. doi:ten.1002/anie.200704281.
  30. ^ Rivkin, Steve; Sutherland, Fraser (2005). The Making of a Name: The Inside Story of the Brands Nosotros Buy. Oxford University Press. p. 130. ISBN978-0-19-988340-0.
  31. ^ Willmes, Claudia Gisela (January 2021). "Scientific discipline that inspires". Trends in Molecular Medicine. 27 (ane): one. doi:10.1016/j.molmed.2020.11.001. PMID 33308981.
  32. ^ "Qatar 2022: Football game Earth Cup logo unveiled". Al Jazeera. September 3, 2019.
  33. ^ "Unicode Graphic symbol "∞" (U+221E)". Unicode. Compart AG. Retrieved 2019-eleven-15 .
  34. ^ a b c Pakin, Scott (May 5, 2021). "Table 294: stix Infinities". The Comprehensive LATEX Symbol List. CTAN. p. 118. Retrieved 2022-02-19 .
  35. ^ Steele, Shawn (April 24, 1996). "cp437_DOSLatinUS to Unicode tabular array". Unicode Consortium. Retrieved 2022-02-19 .
  36. ^ "Map (external version) from Mac OS Roman character set to Unicode 2.i and afterward". Apple Inc. April 5, 2005. Retrieved 2022-02-19 – via Unicode Consortium.
  37. ^ "Map (external version) from Mac OS Symbol character ready to Unicode 4.0 and after". Apple tree Inc. Apr 5, 2005. Retrieved 2022-02-nineteen – via Unicode Consortium.
  38. ^ "Shift-JIS to Unicode". Unicode Consortium. December two, 2015. Retrieved 2022-02-19 .
  39. ^ "EUC-JP-2007". International Components for Unicode. Unicode Consortium. Retrieved 2022-02-nineteen – via GitHub.
  40. ^ "IBM-970". International Components for Unicode. Unicode Consortium. May nine, 2007. Retrieved 2022-02-nineteen – via GitHub.
  41. ^ Steele, Shawn (January 7, 2000). "cp949 to Unicode table". Unicode Consortium. Retrieved 2022-02-19 .
  42. ^ "KPS 9566-2003 to Unicode". Unicode Consortium. Apr 27, 2011. Retrieved 2022-02-nineteen .
  43. ^ van Kesteren, Anne. "big5". Encoding Standard. WHATWG.
  44. ^ Unicode, Inc. "Annotations". Common Locale Data Repository – via GitHub.
  45. ^ "Miscellaneous Mathematical Symbols-B" (PDF). Unicode Consortium. Archived (PDF) from the original on 2018-eleven-12. Retrieved 2022-02-nineteen .

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Source: https://en.wikipedia.org/wiki/Infinity_symbol

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