View source for Simplex

{{also|Simplex}}
==English==
{{was wotd|2025|April|18}}

===Etymology===
[[File:Simplex.jpg|thumb|A set of [[walkie-talkie]]s illustrates simplex ''(adjective {{senseno|en|telecoms}})'' [[wireless#Adjective|wireless]] [[communication]]. Only one user can talk at a time while the other user listens, as the [[radio signal]] can only carry [[information]] in one [[direction]].]]

{{root|en|ine-pro|*sem-|*meh₁-|*pleḱ-}}
The {{glossary|adjective}} is a {{lbor|en|la|simplex|t=plain, simple; single|nocap=1}},<ref name="OED">{{R:OED Online|pos=adj.'' and ''n|id=4406868537|date=September 2024}}</ref><ref>{{R:Lexico|pos=adj}}</ref> ultimately from {{der|en|ine-pro|*sem-|t=one; together}} + {{m|ine-pro|*meh₁-|t=to measure}} + {{m|ine-pro|*pleḱ-|t=to weave}}.

The {{glossary|noun}} is derived from the adjective.<ref name="OED"/><ref>{{R:Lexico|pos=n}}</ref> The {{glossary|plural}} forms {{m|en|simplices}} and {{m|en|simplicia}} are learned borrowings from {{lbor|en|la|simplicēs|notext=1}} ({{glossary|masculine}} or {{glossary|feminine}}) and {{m|la|simplicia}} ({{glossary|neuter}}), respectively plural forms of {{m|la|simplex}}.

Noun {{senseno|en|geometry}} (“generalization of a triangle or tetrahedron to an arbitrary dimension”) was apparently {{glossary|coined}} by the Dutch mathematician {{w|Pieter Hendrik Schoute}} (1846–1913) as a short version of ''Simplicissimum'' in ''Mehrdimensionale Geometrie'' (in German, 1902).<ref>{{cite-book|de|author=[[w:Pieter Hendrik Schoute|P[ieter] H[endrik] Schoute]]|chapter=Grundbegriffe|trans-chapter=Basic Concepts|title=Mehrdimensionale Geometrie|trans-title=Multidimensional Geometry|series=Sammlung Schubert|seriesvolume=XXXV|location=Leipzig, Saxony|publisher=[[w:Georg Joachim Göschen|G[eorg] J[oachim] Göschen]]’sche Verlagshandlung|year=1902|volume_plain=1st part (Die linearen Räume [The Linear Spaces])|section=paragraph 8|page=10|pageurl=https://books.google.com/books?id=31bvAAAAMAAJ&pg=PA12|oclc=1137467492|passage=Wir ziehen de namen ‚Simplicissimum‘ das viel kürzere ''Simplex'' vor und deuten das Simplex mit <math>d+1</math> Eckpunkten mittels des Symboles <math>S(d+1)</math> an.|translation=We prefer the name ‘simplicissimum’ to the much shorter ''simplex'' and indicate the simplex with <math>d+1</math> vertices using the symbol <math>S(d+1)</math>.}}</ref> (In his pioneering works on [[algebraic topology]], the French mathematician {{w|Henri Poincaré}} (1854–1912) had previously introduced the concept, but not the actual term ''simplex''.)<ref>{{cite-web|author=[[w:E. F. Robertson|Edmund [Frederick] Robertson]]; John O’Connor|entry=SIMPLEX|work={{w|MacTutor History of Mathematics Archive}}: Earliest Known Uses of Some of the Words of Mathematics|archiveurl=https://web.archive.org/web/20231225160442/https://mathshistory.st-andrews.ac.uk/Miller/mathword/s/|month=December|year=2023}}.</ref>

===Pronunciation===
* {{glossary|Adjective}} and {{glossary|noun}} ({{glossary|singular}} form):
** {{IPA|en|/ˈsɪmplɛks/|a=RP}}
** {{IPA|en|/ˈsɪmˌplɛks/|a=GA}}
** {{audio|en|LL-Q1860 (eng)-Vealhurl-simplex.wav|a=Southern England}}
** {{hyphenation|en|sim|plex}}
* Noun ({{glossary|plural}} form: {{m|en|simplices}}):
** {{IPA|en|/ˈsɪmplɪsiːz/|a=RP|nocount=1}}
** {{IPA|en|/ˈsɪmpləˌsiz/|a=GA|nocount=1}}
** {{hyphenation|en|sim|pli|ces}}
* Noun ({{glossary|plural}} form: {{m|en|simplicia}}):
** {{IPA|en|/sɪmˈplɪsiə/|a=RP,GA|nocount=1}}
** {{hyphenation|en|sim|pli|cia}}

===Adjective===
{{en-adj|-}}

# {{lb|en|dated}} Having a [[single#Adjective|single]] [[structure#Noun|structure]]; not [[composite#Adjective|composite]] or [[complex#Adjective|complex]]; [[undivided]], [[unitary]].
#: {{synonyms|en|monoplex|uniplex}}
#: {{antonyms|en|complex}}
# {{lb|en|anatomy|historical}} Of an [[eye#Noun|eye]]: ([[supposedly]]) having [[pigment#Noun|pigment]] on only the [[posterior#Adjective|posterior]] [[surface#Noun|surface]] of the [[iris#Noun|iris]] and not the [[anterior#Adjective|anterior]] surface, and thus [[appear]]ing [[blue#Adjective|blue]]; this was later [[find#Verb|found]] to be [[inaccurate]], as [[eye color|eye colour]] is due to the [[amount#Noun|amount]] of pigment in the anterior surface of the iris; also, of eye [[pigmentation]]: [[present#Adjective|present]] only on the posterior surface of the iris; and of a [[person#Noun|person]]: having eyes with this [[form#Noun|form]] of pigmentation.
#: {{antonyms|en|duplex}}
# {{senseid|en|telecoms}}{{lb|en|computing|telecommunications}} Of a [[circuit#Noun|circuit]] or [[device]]: [[involve|involving]] [[signal#Noun|signals]] which [[travel#Verb|travel]] in [[one#Numeral|one]] [[direction]] at a [[time#Noun|time]]; [[unidirectional#Adjective|unidirectional]].
#: {{antonyms|en|bidirectional|duplex}}
#: {{coordinate terms|en|full duplex|half-duplex|semiduplex}}
# {{lb|en|genetics}}
## Of a [[polyploid#Adjective|polyploid]] [[organism]]: having one [[dominant#Adjective|dominant]] [[allele]] at a [[given#Adjective|given]] [[locus]] on all [[homologous]] [[chromosome]]s.
##: {{coordinate terms|en|duplex|nulliplex|triplex}}
## {{lb|en|archaic|or|obsolete}} {{synonym of|en|heterozygous|t=of an organism: having [[two#Numeral|two]] [[different#Adjective|different]] alleles in a given [[gene]]}}
# {{lb|en|linguistics}} Of a [[word#Noun|word]]: having no ([[derivational]]) [[affix#Noun|affixes]]; [[simple#Adjective|simple]], [[monomorphemic]], [[uncompounded]].
#: {{antonyms|en|polymorphemic}}
# {{lb|en|originally|and|chiefly|US}} Of an [[apartment]] (or, sometimes, another [[type#Noun|type]] of [[property#Noun|property]]): having only one [[floor#Noun|floor]] or [[storey]]; single-storey.
#: {{coordinate terms|en|duplex|triplex}}

====Derived terms====
* {{l|en|simplexity}}

====Related terms====
* {{l|en|crux simplex}}
* {{l|en|herpes simplex}}

====Translations====
{{trans-see|having a single structure; not composite or complex|undivided|unitary}}

{{trans-top|of an eye: (supposedly) having pigment on only the posterior surface of the iris; of eye pigmentation: present only on the posterior surface of the iris; of a person: having eyes with this form of pigmentation}}
* Macedonian: {{t-needed|mk}}
{{trans-bottom}}

{{trans-top-also|of a circuit or device: involving signals which travel in one direction at a time|unidirectional}}
* Catalan: {{t|ca|símplex}}
* Finnish: {{t+|fi|yksisuuntainen}}
* Greek: {{t+|el|μονόδρομος}}
* Indonesian: {{t+|id|simpleks|alt=simplêks}}
* Macedonian: {{t-needed|mk}}
* Vietnamese: {{t|vi|đơn công}}
{{trans-bottom}}

{{trans-top|of a polyploid organism: having one dominant allele at a given locus on all homologous chromosomes}}
* Finnish: {{t|fi|simpleksinen}}
* Macedonian: {{t-needed|mk}}
{{trans-bottom}}

{{trans-see|''synonym of'' heterozygous|heterozygous}}

{{trans-top|of a word: having no affixes}}
* Finnish: {{t|fi|simpleksinen}}, {{t|fi|johtamaton}}
* Macedonian: {{t-needed|mk}}
{{trans-bottom}}

{{trans-top|of a property: having only one floor or storey}}
* Finnish: {{t|fi|yksikerroksinen}}
* Macedonian: {{t-needed|mk}}
{{trans-bottom}}

===Noun===
{{en-noun|+|pl2qual=algebraic topology, geometry, linguistics|simplices|simplicia}}
[[File:Simplexes.jpg|thumb|[[model#Noun|Models]] of 0-[[dimensional]] to 3-dimensional simplexes ''(noun {{senseno|en|geometry}})''.]]
{{examples|sense=algebraic topology, geometry|examples=
* A 0-dimensional simplex is a [[point#Noun|point]].
* A 1-dimensional simplex is a [[line segment]].
* A 2-dimensional simplex is a [[triangle]].
* A 3-dimensional simplex is a [[tetrahedron]].
* A 4-dimensional simplex is a [[5-cell]].
}}

# {{senseid|en|geometry}}{{lb|en|[[algebraic]]|_|topology|geometry}} A [[generalization]] of a [[triangle]] or [[tetrahedron]] to an [[arbitrary#Adjective|arbitrary]] [[dimension#Noun|dimension]], the generalization being the [[simple#Adjective|simplest]] [[possible#Adjective|possible]] [[convex#Adjective|convex]] [[polytope]] for a [[given#Adjective|given]] dimension; more [[accurately]], the [[convex hull]] of <math>n+1</math> [[linearly independent]] [[point#Noun|points]] in <math>n</math>-[[dimensional]] [[space#Noun|space]].
# {{lb|en|linguistics}}
## A [[word#Noun|word]] which is not [[compound#Adjective|compound]] and [[contain]]s no [[derivational]] [[affix#Noun|affixes]] ([[inflectional]] affixes are usually [[disregard#Verb|disregarded]]); a [[monomorphemic]] word.
##: {{ux|en|The word ''weak'' is a '''simplex'''. Its derivative ''weaken'' is not.}}
## {{lb|en|grammar|archaic}} ''In full'' '''simplex sentence''': in [[transformational grammar]]: a [[simple#Adjective|simple]] [[sentence#Noun|sentence]] which is the [[product#Noun|product]] of a few [[transformation]]s; a [[kernel#Noun|kernel]] sentence.
##* {{quote-book|en|year=1978|author=Helga Harries-Delisle|chapter=Contrastive Emphasis and Cleft Sentences|editor=[[w:Joseph Greenberg|Joseph H[arold] Greenberg]]|title=Universals of Human Language|location=Stanford, Calif.|publisher=w:Stanford University Press|volume=4 (Syntax)|page=460|pageurl=https://archive.org/details/universalsofhuma0004unse/page/460/mode/1up|isbn=978-0-8047-0969-9|passage=The question is: is 139. {{quote-gloss|“Priexal <u>Vanja</u>. ‘arrived Vanya’”}} a '''simplex''' or is it a cleft structure in which all 'superfluous' constituents were deleted. {{...}} The only indication that 139. is a '''simplex''' is the sentence intonation and the absence of a break between the verb and the subject.|footer={{small|A modified version of a paper published in ''Working Papers on Language Universals'' (November 1973), number 12, pages 85–144.}}}}
# {{lb|en|originally|and|chiefly|US}} An [[apartment]] (or, sometimes, another [[type#Noun|type]] of [[property#Noun|property]]) having only one [[floor#Noun|floor]] or [[storey]]; a single-storey property.
#: {{coordinate terms|en|duplex|triplex}}

====Synonyms====
* {{l|en|monoplex}}<!--Needs to be put under the correct sense(s)-->

====Derived terms====
* {{l|en|n-simplex}}
* {{l|en|simplex method}}

====Related terms====
* {{l|en|simplicial}}
* {{l|en|simplicial complex}}

====Translations====
{{trans-top|generalization of a triangle or tetrahedron to an arbitrary dimension, the generalization being the simplest possible convex polytope for a given dimension}}
* Albanian: {{t|sq|simpleks}}
* Arabic: {{t+|ar|مُبَسَّط|tr=mubassaṭ}}
* Armenian: {{t|hy|սիմպլեքս}}
* Basque: {{t|eu|simplex|?}}
* Bengali: {{t|bn|ক্রমবর্তী সিমপ্লেক্স}}
* Bulgarian: {{t|bg|симплекс}}
* Catalan: {{t|ca|símplex|m}}
* Chinese:
*: Mandarin: {{t|cmn|单纯形|tr=dānchún xíng}}
* Chuvash: {{t|cv|си́мплекс}}
* Dutch: {{t+|nl|simplex|?}}
* Finnish: {{t+|fi|simpleksi}}
* French: {{t+|fr|simplexe|m}}
* German: {{t+|de|Simplex|n}}
* Hebrew: {{t+|he|סימפלקס|m}}
* Hungarian: {{t+|hu|szimplex}}
* Icelandic: {{t+|is|hyrna|f}}
* Irish: {{t|ga|aonphléacs|m}}
* Italian: {{t+|it|simplesso|m}}
* Japanese: {{t+|ja|単体|tr=たんたい, tantai}}
* Kazakh: {{t|kk|симплекс}}
* Korean: {{t+|ko|단체(單體)}}
* Macedonian: {{t-needed|mk}}
* Norwegian:
*: Bokmål: {{t|nb|simpleks|?}}
*: Nynorsk: {{t-needed|nn}}
* Persian: {{t+|fa|سادک}}
* Polish: {{t|pl|sympleks|m-in}}
* Portuguese: {{t+|pt|simplex|?}}, {{t|pt|simplexo|?}}
* Romanian: {{t+|ro|simplex|n}}
* Russian: {{t+|ru|си́мплекс|m}}
* Slovak: {{t|sk|simplex|?}}
* Slovene: {{t|sl|simpleks|?}}
* Spanish: {{t|es|símplex|m}}
* Swedish: {{t|sv|simplex|?}}
* Thai: {{t|th|ซิมเพล็กซ์}}
* Ukrainian: {{t|uk|симплекс|m}}
* Uzbek: {{t|uz|simpleks}}
{{trans-bottom}}

{{trans-top|word which is not compound and contains no derivational affixes}}
* Finnish: {{t|fi|perussana}}
* German: {{t+|de|Simplex|n}}
* Macedonian: {{t-needed|mk}}
* Swedish: {{t|sv|simplex|n}}
{{trans-bottom}}

{{trans-top|in transformational grammar: a simple sentence which is the product of a few transformations}}
* Finnish: {{t|fi|[[simpleksinen]] [[virke]]}}
* Macedonian: {{t-needed|mk}}
{{trans-bottom}}

{{trans-top|property having only one floor or storey}}
* Finnish: {{t|fi|[[yksikerroksinen]] [[kiinteistö]]}}
* Macedonian: {{t-needed|mk}}
{{trans-bottom}}

===References===
<references/>

===Further reading===
* {{pedia}}
* {{pedia|simplex (disambiguation)}}

{{C|en|Higher-dimensional geometry|One}}

==Latin==
{{number box|la|1}}

===Etymology===
{{root|la|ine-pro|*sem-|*pleḱ-}}
From {{inh|la|itc-pro|*sempleks}}, from the same root as {{suffix|la|semel|-plex||-fold}}.

===Pronunciation===
* {{la-IPA}}

===Adjective===
{{la-adj|simplex|comp=simplicior|sup=simplicissimus|adv=simpliciter}}

# [[single]]
# [[simple]], [[plain]], [[uncompounded]]
# [[pure]], [[unmixed]]
# [[sincere]], [[naive]], [[frank]], [[open]], without [[guile]], [[guileless]], [[unsuspecting]], [[innocent]]
#* {{Q|la|Ovid|Fasti|2|225|thru=226|quote=male crēditis hostī: '''simplex''' nōbilitās, perfida tēla cave!|trans=You do wrong to trust the enemy: '''Guileless''' nobles, beware of treacherous weapons!}}

====Declension====
{{la-adecl|simplex}}

====Derived terms====
* {{l|la|simplicābilis}}
* {{l|la|simplicitās}}
* {{l|la|simpliciter}}

====Related terms====
* {{l|la|duplex}}
* {{l|la|simplus}}
* {{l|la|triplex}}
* {{l|la|quadruplex}}

====Descendants====
* {{desc|it|sempice|semprice|semplice}} {{i|latinized}}
* {{desc|fur|sempliç}} {{i|latinized}}
* {{desc|scn|sìmprici|sìmplici}} {{i|latinized}}
* {{desc|bor=1|ast|simple}}
* {{desc|bor=1|ca|simple}}
* {{desc|bor=1|nl|simpel}}
* {{desc|bor=1|en|simplex}}
* {{desc|bor=1|gl|simple}}
* {{desc|bor=1|de|simpel}}
** {{desc|bor=1|no|simpel}}
* {{desc|bor=1|gml|simpel}}
** {{desc|bor=1|gmq-osw|simpel}}
*** {{desctree|sv|simpel}}
* {{desctree|bor=1|fro|simple}}
* {{desc|roa-ole|-|bor=1}}
** {{desc|mwl|simples}}
* {{desc|roa-opt|simplez|bor=1}}
** {{desc|pt|simples|símplice}}
* {{desc|bor=1|rm|simpel|sempel}}
* {{desctree|bor=1|es|simple}}
* {{desc|cel-bry-pro|bor=1|*sɨml}}
** {{desc|wlm|symyl}}
*** {{desc|cy|syml}}

===References===
* {{R:L&S}}
* {{R:Elementary Lewis}}
* {{R:du Cange}}
* {{R:Gaffiot}}

{{C|la|Personality}}

==Romanian==

===Etymology===
{{bor+|ro|fr|simplex}}.

===Noun===
{{ro-noun|n|-}}

# {{l|en|simplex}}

====Declension====
{{ro-noun-n|n=sg}}