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AdvancedSpecial charactersHelpHeadingLevel 2Level 3Level 4Level 5FormatInsertLatinLatin extendedIPASymbolsGreekGreek extendedCyrillicArabicArabic extendedHebrewBanglaTamilTeluguSinhalaDevanagariGujaratiThaiLaoKhmerCanadian AboriginalRunesÁáÀàÂâÄäÃãǍǎĀāĂ㥹ÅåĆćĈĉÇçČčĊċĐđĎďÉéÈèÊêËëĚěĒēĔĕĖėĘęĜĝĢģĞğĠġĤĥĦħÍíÌìÎîÏïĨĩǏǐĪīĬĭİıĮįĴĵĶķĹĺĻļĽľŁłŃńÑñŅņŇňÓóÒòÔôÖöÕõǑǒŌōŎŏǪǫŐőŔŕŖŗŘřŚśŜŝŞşŠšȘșȚțŤťÚúÙùÛûÜüŨũŮůǓǔŪūǖǘǚǜŬŭŲųŰűŴŵÝýŶŷŸÿȲȳŹźŽžŻżÆæǢǣØøŒœßÐðÞþƏəFormattingLinksHeadingsListsFilesDiscussionReferencesDescriptionWhat you typeWhat you getItalic''Italic text''Italic textBold'''Bold text'''Bold textBold & italic'''''Bold & italic text'''''Bold & italic textDescriptionWhat you typeWhat you getReferencePage text.<ref>[https://www.example.org/ Link text], additional text.</ref>Page text.[1]Named referencePage text.<ref name="test">[https://www.example.org/ Link text]</ref>Page text.[2]Additional use of the same referencePage text.<ref name="test" />Page text.[2]Display references<references />↑ Link text, additional text.↑ Link text== Cultural impact == {{Globalize|date=December 2022|1=section|2=West}} === Artistic expression === {{Main|Mathematics and art}} Notes that sound well together to a Western ear are sounds whose fundamental [[frequencies]] of vibration are in simple ratios. For example, an octave doubles the frequency and a [[perfect fifth]] multiplies it by <math>\frac{3}{2}</math>.<ref>{{cite journal | last = Cazden | first = Norman | date = October 1959 | doi = 10.1177/002242945900700205 | issue = 2 | journal = Journal of Research in Music Education | jstor = 3344215 | pages = 197–220 | title = Musical intervals and simple number ratios | volume = 7| s2cid = 220636812 }}</ref><ref>{{cite journal | last = Budden | first = F. J. | date = October 1967 | doi = 10.2307/3613237 | issue = 377 | journal = The Mathematical Gazette | jstor = 3613237 | pages = 204–215 | publisher = Cambridge University Press ({CUP}) | title = Modern mathematics and music | volume = 51| s2cid = 126119711 }}</ref> [[File:Julia set (highres 01).jpg|thumb|[[Fractal]] with a scaling symmetry and a central symmetry]] Humans, as well as some other animals, find symmetric patterns to be more beautiful.<ref>{{Cite journal |last1=Enquist |first1=Magnus |last2=Arak |first2=Anthony |date=November 1994 |title=Symmetry, beauty and evolution |url=https://www.nature.com/articles/372169a0 |journal=Nature |language=en |volume=372 |issue=6502 |pages=169–172 |doi=10.1038/372169a0 |pmid=7969448 |bibcode=1994Natur.372..169E |s2cid=4310147 |issn=1476-4687 |access-date=December 29, 2022 |archive-date=December 28, 2022 |archive-url=https://web.archive.org/web/20221228052049/https://www.nature.com/articles/372169a0 |url-status=live }}</ref> Mathematically, the symmetries of an object form a group known as the [[symmetry group]].<ref>{{Cite web |last=Hestenes |first=David |date=1999 |title=Symmetry Groups |url=http://geocalc.clas.asu.edu/pdf-preAdobe8/SymmetryGroups.pdf |access-date=December 29, 2022 |website=geocalc.clas.asu.edu |archive-date=January 1, 2023 |archive-url=https://web.archive.org/web/20230101210124/http://geocalc.clas.asu.edu/pdf-preAdobe8/SymmetryGroups.pdf |url-status=live }}</ref> For example, the group underlying mirror symmetry is the [[cyclic group]] of two elements, <math>\mathbb{Z}/2\mathbb{Z}</math>. A [[Rorschach test]] is a figure invariant by this symmetry,<ref>{{cite encyclopedia | last = Bender | first = Sara | editor1-last = Carducci | editor1-first = Bernardo J. | editor2-last = Nave | editor2-first = Christopher S. | editor3-last = Mio | editor3-first = Jeffrey S. | editor4-last = Riggio | editor4-first = Ronald E. | title = The Rorschach Test | date = September 2020 | doi = 10.1002/9781119547167.ch131 | pages = 367–376 | publisher = Wiley | encyclopedia = The Wiley Encyclopedia of Personality and Individual Differences: Measurement and Assessment| isbn = 978-1-119-05751-2 }}</ref> as are [[butterfly]] and animal bodies more generally (at least on the surface).<ref>{{cite book|title=Symmetry|volume=47|series=Princeton Science Library|first=Hermann|last=Weyl|author-link=Hermann Weyl|publisher=Princeton University Press|year=2015|isbn=978-1-4008-7434-7|page=[https://books.google.com/books?hl=en&lr=&id=GG1FCQAAQBAJ&pg=PA4 4]}}</ref> Waves on the sea surface possess translation symmetry: moving one's viewpoint by the distance between wave crests does not change one's view of the sea.{{Citation needed|date=December 2022}} [[Fractals]] possess [[self-similarity]].<ref>{{Cite web |last=Bradley |first=Larry |date=2010 |title=Fractals – Chaos & Fractals |url=https://www.stsci.edu/~lbradley/seminar/fractals.html |access-date=December 29, 2022 |website=www.stsci.edu |archive-date=March 7, 2023 |archive-url=https://web.archive.org/web/20230307054609/https://www.stsci.edu/~lbradley/seminar/fractals.html |url-status=live }}</ref><ref>{{Cite web |title=Self-similarity |url=https://math.bu.edu/DYSYS/chaos-game/node5.html |access-date=December 29, 2022 |website=math.bu.edu |archive-date=March 2, 2023 |archive-url=https://web.archive.org/web/20230302132911/http://math.bu.edu/DYSYS/chaos-game/node5.html |url-status=live }}</ref> === Popularization === {{Main|Popular mathematics}}Popular mathematics is the act of presenting mathematics without technical terms.<ref>{{Cite conference |last=Kissane |first=Barry |date=July 2009 |title=Popular mathematics |url=https://researchrepository.murdoch.edu.au/id/eprint/6242/ |conference=22nd Biennial Conference of The Australian Association of Mathematics Teachers |location=Fremantle, Western Australia |publisher=Australian Association of Mathematics Teachers |pages=125–126 |access-date=December 29, 2022 |archive-date=March 7, 2023 |archive-url=https://web.archive.org/web/20230307054610/https://researchrepository.murdoch.edu.au/id/eprint/6242/ |url-status=live }}</ref> Presenting mathematics may be hard since the general public suffers from [[mathematical anxiety]] and mathematical objects are highly abstract.<ref>{{Cite book |last=Steen |first=L. A. |url={{GBurl|id=-d3TBwAAQBAJ|dq="popular mathematics" analogies|p=2}} |title=Mathematics Today Twelve Informal Essays |date=2012|publisher=Springer Science & Business Media |isbn=978-1-4613-9435-8 |page=2 |language=en |access-date=January 3, 2023 }}</ref> However, popular mathematics writing can overcome this by using applications or cultural links.<ref>{{Cite book |last=Pitici |first=Mircea |url={{GBurl|id=9nGQDQAAQBAJ|dq="popular mathematics" analogies|p=331}} |title=The Best Writing on Mathematics 2016 |date=2017|publisher=Princeton University Press |isbn=978-1-4008-8560-2 |language=en |access-date=January 3, 2023 }}</ref> Despite this, mathematics is rarely the topic of popularization in printed or televised media. Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. 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