MediaWiki API result
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{
"compare": {
"fromid": 1,
"fromrevid": 1,
"fromns": 0,
"fromtitle": "Pr\u00edomhleathanach",
"toid": 2,
"torevid": 2,
"tons": 0,
"totitle": "Matamaitic",
"*": "<tr><td colspan=\"2\" class=\"diff-lineno\" id=\"mw-diff-left-l1\">L\u00edne 1:</td>\n<td colspan=\"2\" class=\"diff-lineno\">L\u00edne 1:</td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">'''D'\u00e9irigh le suite\u00e1il MediaWiki.'''</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{{glanadh}}</ins></div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">F\u00e9ach </del>ar [https://www.<del class=\"diffchange diffchange-inline\">mediawiki</del>.org/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Localisation#Translation_resources doicim\u00e9id um conas </del>an <del class=\"diffchange diffchange-inline\">chomh\u00e9ad\u00e1n </del>a <del class=\"diffchange diffchange-inline\">athr\u00fa</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[\u00cdomh\u00e1:Euclid.jpg|thumb|[[Eoicl\u00edd\u00e9as]], matamaiticeoir Gr\u00e9agach \u00f3n 3\u00fa haois [[Roimh Chr\u00edost|RCh]]]]</ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>agus an [https://<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.org/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Help</del>:<del class=\"diffchange diffchange-inline\">Contents L\u00e1mhleabhar \u00fas\u00e1ideora</del>] chun <del class=\"diffchange diffchange-inline\">cabhair \u00fas\u00e1ide </del>agus <del class=\"diffchange diffchange-inline\">f\u00edora\u00edochta </del>a <del class=\"diffchange diffchange-inline\">fh\u00e1il</del>.</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[File:Leonhard Euler identitatea.png|thumb|C\u00e9annacht Euler, </ins>ar <ins class=\"diffchange diffchange-inline\">a dtugtar uaireanta an teoirim is \u00e1ille sa mhatamaitic<ref>{{cite journal |\u00a0 last1 = Wells | first1 = David | year = 1990 | title = Are these the most beautiful? |\u00a0 url = https://archive.org/details/sim_mathematical-intelligencer_summer-1990_12_3/page/37 | journal = [[The Mathematical Intelligencer]] | volume = 12 | issue = 3| pages = 37\u201341 | doi = 10.1007/BF03024015 | s2cid = 121503263 }}</ref>]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Is \u00e9ard is '''matamaitic''' ann (\u00f3n t[[An tSean-Ghr\u00e9igis|Sean-Ghr\u00e9igis]] \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1; ''m\u00e1th\u0113ma'': 'eolas, staid\u00e9ar, foghlaim ') n\u00e1 r\u00e9imse eolais a chuims\u00edonn topaic\u00ed amhail; uimhreacha (Teoiric na [[Uimhr\u00edocht|matamaitice]] agus na [[Uimhirtheoiric|huimhirtheoirice]]), foirml\u00ed agus strucht\u00fair ghaolmhara ([[ailg\u00e9abar]]), cruthanna agus na sp\u00e1sanna ina bhfuil siad ([[geoim\u00e9adracht]]), agus cainn\u00edochta\u00ed agus a n-athruithe ([[calcalas]] agus [[Anail\u00eds mhatamaitici\u00fail|anail\u00eds]]). Baineann an chuid is m\u00f3 den ghn\u00edomha\u00edocht mhatamaitici\u00fail le h\u00fas\u00e1id a bhaint as glanr\u00e9as\u00fana\u00edocht theib\u00ed chun air\u00edonna r\u00e9ad teib\u00ed a fh\u00e1il amach n\u00f3 a chruth\u00fa, arb \u00e9ard at\u00e1 i gceist leo n\u00e1 teibithe \u00f3 n\u00e1d\u00far, n\u00f3 sa mhatamaitic nua-aimseartha, aon\u00e1in a bhfuil air\u00edonna \u00e1irithe acu, ar a dtugtar aics\u00edm\u00ed. Is \u00e9ard at\u00e1 i gcruth\u00fanas matamaitici\u00fail n\u00e1 sraith d'fheidhmeanna ar roinnt rialacha d\u00e9aduchtacha do thortha\u00ed at\u00e1 ar eolas cheana f\u00e9in, lena n-\u00e1ir\u00edtear [[Teoirim|teoirim\u00ed]] cruthaithe roimhe seo, [[Aics\u00edm|aics\u00edm\u00ed]] a bh\u00ed cruthaithe roimhe seo agus (i gc\u00e1s [[Teibi\u00fa|teibithe]] \u00f3n n\u00e1d\u00far) roinnt air\u00edonna bun\u00fasacha a mheastar mar fh\u00edorphoint\u00ed tosaigh na teoirice at\u00e1 \u00e1 meas.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00das\u00e1idtear an mhatamaitic san eola\u00edocht chun feinim\u00e9in a [[Mionsamhl\u00fa matamaitici\u00fail|shamhalt\u00fa]], rud a cheada\u00edonn tuar a dh\u00e9anamh ansin \u00f3 dhl\u00edthe turgnamhacha. Tugann neamhsple\u00e1chas na f\u00edrinne matamaitici\u00fala \u00f3 aon turgnamh le tuiscint go mbraitheann cruinneas na dtuartha sin ach amh\u00e1in ar leordh\u00f3thanacht na samhla. Tuartha m\u00edchruinn, seachas a bheith de bharr na matamaitice m\u00edchirte, le tuiscint go bhfuil g\u00e1 leis tsamhail mhatamaitici\u00fail a \u00fas\u00e1idtear a athr\u00fa. an g\u00e1 leis an tsamhail matamaitice a \u00fas\u00e1idtear a athr\u00fa. Mar shampla, n\u00ed fh\u00e9adfa\u00ed luain\u00edocht pheirih\u00e9ileach [[Mearcair (pl\u00e1in\u00e9ad)|Mhearcair]] a mh\u00edni\u00fa ach amh\u00e1in tar \u00e9is coibhneasacht ghinear\u00e1lta [[Albert Einstein|Einstein]] a bheith tagtha chun cinn, a th\u00e1inig in ionad [[Dl\u00ed na himtharraingthe|dhl\u00ed imtharraingthe]] [[Isaac Newton|Newton]] mar mh\u00fanla matamaitici\u00fail n\u00edos fearr.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">T\u00e1 an mhatamaitic riachtanach sna heola\u00edochta\u00ed, san [[Innealt\u00f3ireacht|innealt\u00f3ireach]]<nowiki/>t, sa [[leigheas]], san [[airgeadas]], san [[r\u00edomheola\u00edocht]] agus sna h[[Eola\u00edocht sh\u00f3isialta|eola\u00edochta\u00ed s\u00f3isialta]]. Forbra\u00edtear roinnt r\u00e9ims\u00ed matamaitice, ar n\u00f3s [[Staitistic|staitistic\u00ed]] agus [[teoiric na gcluich\u00ed]], i ndl\u00fathghaol lena n-\u00fas\u00e1id\u00ed agus is minic a ghr\u00fap\u00e1iltear iad faoin [[Matamaitic fheidhmeach|mhatamaitic fheidhmeach]]. Forbra\u00edtear r\u00e9ims\u00ed matamaitici\u00fala eile go neamhsple\u00e1ch ar aon fheidhm (agus mar sin tugtar glanmhatamaitic orthu), ach is minic a aims\u00edtear feidhmeanna praitici\u00fala n\u00edos d\u00e9ana\u00ed. Is sampla oiri\u00fanach \u00e9 an fhadhb a bhaineann le facht\u00f3iri\u00fa sl\u00e1nuimhir, a th\u00e9ann ar ais go dt\u00ed [[Eoicl\u00edd\u00e9as]], ach nach raibh aon fheidhm phraitici\u00fail aige sular \u00fas\u00e1ideadh \u00e9 i gcripteach\u00f3ras le heochair phoibl\u00ed RSA (le haghaidh sl\u00e1nd\u00e1il [[L\u00edonra r\u00edomhaireachta|l\u00edonra\u00ed r\u00edomhaireachta]]).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Go stairi\u00fail, ba sa mhatamaitic Ghr\u00e9agach a th\u00e1inig coincheap an chruth\u00fanais agus na cr\u00edochn\u00falachta matamaitici\u00fala a bhaineann leis chun cinn ar dt\u00fas, go h\u00e1irithe sna\u00a0 [[Uraiceachta\u00ed (leabhar)|hUraiceachta\u00ed]]. \u00d3 th\u00fas, roinneadh an mhatamaitic go bun\u00fasach i g[[Geoim\u00e9adracht]], agus [[Uimhr\u00edocht|uimhr\u00edocht]] (ionramh\u00e1il [[Uimhir aiceanta|uimhreacha aiceanta]] agus cod\u00e1in), go dt\u00ed an 16\u00fa agus an 17\u00fa haois, nuair a tugadh [[Ailg\u00e9abar|ailg\u00e9abar]] agus [[Calcalas|calcalas]] an-bh\u00eddeach isteach mar r\u00e9ims\u00ed nua den \u00e1bhar. \u00d3 shin i leith, t\u00e1 an t-idirghn\u00edomh\u00fa idir nu\u00e1la\u00edochta\u00ed matamaitici\u00fala agus fionnachtana eola\u00edocha mar thoradh ar mh\u00e9ad\u00fa tapa i bhforbairt na matamaitice. Ag deireadh an 19\u00fa haois, d'eascair an gh\u00e9arch\u00e9im bhun\u00fasach sa mhatamaitic ([[An Ghearm\u00e1inis|Gearm\u00e1inis]]; ''Grundlagenkrise der Mathematik'') as an modh\u00a0 aics\u00edmeach a ch\u00f3ras\u00fa. Mar thoradh air seo th\u00e1inig m\u00e9ad\u00fa m\u00f3r ar l\u00edon na r\u00e9ims\u00ed matamaitice agus ar a r\u00e9ims\u00ed feidhmeanna. Sampla de seo is ea Rang\u00fa \u00c1bhair na Matamaitice, a liosta\u00edonn n\u00edos m\u00f3 n\u00e1 60 r\u00e9imse matamaitice den ch\u00e9ad leibh\u00e9al.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==Sanasa\u00edocht ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Tagann an focal matamaitic \u00f3n tSean-Ghr\u00e9igis m\u00e1th\u0113ma (\u03bc\u03ac\u03b8\u03b7\u03bc\u03b1), a chialla\u00edonn \"an rud a fhoghlaim\u00edtear,\"<ref>{{cite encyclopedia |title=mathematic (n.)|dictionary=[[Online Etymology Dictionary]]|url=http://www.etymonline.com/index.php?term=mathematic&allowed_in_frame=0|url-status=live|archive-url=https://web.archive.org/web/20130307093926/http://etymonline.com/index.php?term=mathematic&allowed_in_frame=0|archive-date=March 7, 2013}}</ref> \"an t-eolas a fhaigheann duine,\" mar sin freisin \"staid\u00e9ar\" agus \"eola\u00edocht\". Th\u00e1inig an bhr\u00ed n\u00edos c\u00fainge agus n\u00edos teicni\u00fala chun cinn; \"staid\u00e9ar matamaitice\" ar an bhfocal \"matamatice\" fi\u00fa sa tr\u00e9imhse Chlasaiceach.<ref>Both meanings can be found in Plato, the narrower in [[Republic (Plato)|''Republic'']] </ins>[https://www.<ins class=\"diffchange diffchange-inline\">perseus.tufts.edu/hopper/text?doc=Plat.+Rep.+6.510c&fromdoc=Perseus%3Atext%3A1999.01.0168 510c] {{Webarchive|url=https://web.archive.org/web/20210224152747/http://www.perseus.tufts.edu/hopper/text?doc=Plat.+Rep.+6.510c&fromdoc=Perseus%3Atext%3A1999.01.0168 |date=February 24, 2021 }}, but Plato did not use a ''math-'' word; Aristotle did, commenting on it. {{LSJ|maqhmatiko/s|\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae|ref}}. ''OED Online'', \"Mathematics\".</ref> Is \u00ed a aidiacht n\u00e1 math\u0113matik\u00f3s (\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2), a chialla\u00edonn \"bainteach le foghlaim\" n\u00f3 \"staid\u00e9arach,\" rud a chiallaigh freisin \"matamaitici\u00fail.\" Go h\u00e1irithe, chiallaigh math\u0113matik\u1e17 t\u00e9khn\u0113 (\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u1f74 \u03c4\u03ad\u03c7\u03bd\u03b7; Laidin: ars mathematica) \"an eala\u00edn mhatamaitici\u00fail.\"</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Ar an dul c\u00e9anna, tugadh an math\u0113matikoi (\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03af) ar cheann den d\u00e1 phr\u00edomhscoil smaointeoireachta sa [[P\u00edot\u00e1gar\u00e1s|Ph\u00edotagar\u00e1iteachas]]\u2014rud a chiallaigh \"foghlaimeoir\u00ed\" seachas \"matamaiticeoir\u00ed\" sa chiall nua-aimseartha.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Sa Laidin, agus sa Bh\u00e9arla go timpeall na bliana 1700, is \u00e9 a bh\u00ed i gceist leis an t\u00e9arma matamaitic n\u00e1\u00a0 \"astrala\u00edocht \" (n\u00f3 uaireanta \"r\u00e9alteola\u00edocht \") seachas \"matamaitic\"; d'athraigh an bhr\u00ed de r\u00e9ir a ch\u00e9ile go dt\u00ed an ceann at\u00e1 ann faoi l\u00e1thair \u00f3 thart ar 1500 go 1800. Mar thoradh air sin, bh\u00ed roinnt m\u00ed-aistri\u00fach\u00e1n ann. Mar shampla, uaireanta d\u00e9antar\u00a0 m\u00ed-aistri\u00fach\u00e1n ar rabhadh San Agaist\u00edn, gur ch\u00f3ir do Chr\u00edostaithe a bheith a bheith airdeallach ar ''mathematici'', rud a chialla\u00edonn '' astralaithe '',\u00a0 mar c\u00e1ineadh ar na matamaiticeoir\u00ed.<ref name=\"Boas\">{{cite book | title=Lion Hunting and Other Mathematical Pursuits: A Collection of Mathematics, Verse, and Stories by the Late Ralph P. Boas, Jr | publisher=Cambridge University Press | author=Boas, Ralph | author-link=Ralph P. Boas Jr. | year=1995 | orig-year=1991 | page=257 | chapter-url=https://books.google.com/books?id=f-EWj5WtQHgC&pg=PA257 | chapter=What Augustine Didn't Say About Mathematicians | isbn=978-0-88385-323-8 | access-date=January 17, 2018 | archive-date=May 20, 2020 | archive-url=https://web.archive</ins>.org/<ins class=\"diffchange diffchange-inline\">web/20200520183837</ins>/<ins class=\"diffchange diffchange-inline\">https</ins>:/<ins class=\"diffchange diffchange-inline\">/books.google.com/books?id=f-EWj5WtQHgC&pg=PA257 | url-status=live }}</ref></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">T\u00e9ann an fhoirm iolra dealraitheach sa Bh\u00e9arla siar go dt\u00ed neodar iolra na Laidine ''mathematica'' ([[Cicear\u00f3|Cicero]]), bunaithe ar </ins>an <ins class=\"diffchange diffchange-inline\">iolra Gr\u00e9agach ta math\u0113matik\u00e1 (\u03c4\u1f70 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac), </ins>a <ins class=\"diffchange diffchange-inline\">d\u2019\u00fas\u00e1id [[Arastatal]</ins>] <ins class=\"diffchange diffchange-inline\">(384 -322 RC), agus a chialla\u00edonn go garbh \"gach rud matamaitici\u00fail \", c\u00e9 go bhfuil s\u00e9 sochreidte nach bhfuair an B\u00e9arla ach an aidiacht ''mathematic(al)''\u00a0 ar iasacht </ins>agus <ins class=\"diffchange diffchange-inline\">gur bhunaigh s\u00ed an t-ainmfhocal ''mathematics''\u00a0 as </ins>an <ins class=\"diffchange diffchange-inline\">\u00faire, i ndiaidh phatr\u00fan ''physics'' agus ''metaphysics'', a fuarthas le hoidhreacht \u00f3n nGr\u00e9igis.<ref>''[</ins>[<ins class=\"diffchange diffchange-inline\">The Oxford Dictionary of English Etymology]]'', ''[[Oxford English Dictionary]]'', ''sub'' \"mathematics\", \"mathematic\", \"mathematics\"</ref>\u00a0 Sa Bh\u00e9arla, glacann an t-ainmfhocal ''mathematics'' briathar uatha. Is minic a ghiorra\u00edtear \u00e9 go dt\u00ed ''maths'' n\u00f3, i Meirice\u00e1 Thuaidh, ''math''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><ref name=maths>[http://oed.com/view/Entry/114982 \"maths, ''n.''\"] and [http://oed.com/view/Entry/114962 \"math, ''n.3''\"] {{Webarchive|url=</ins>https://<ins class=\"diffchange diffchange-inline\">web</ins>.<ins class=\"diffchange diffchange-inline\">archive</ins>.org/<ins class=\"diffchange diffchange-inline\">web</ins>/<ins class=\"diffchange diffchange-inline\">20200404201407/http</ins>:/<ins class=\"diffchange diffchange-inline\">/oed.com/view/Entry/114982 |date=April 4, 2020 }}. ''Oxford English Dictionary,'' on-line version (2012).</ref></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==R\u00e9ims\u00ed na matamaitice==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Roimh an [[An Renaissance|Renaissance]], roinneadh an mhatamaitic ina dh\u00e1 phr\u00edomhr\u00e9imse</ins>: <ins class=\"diffchange diffchange-inline\">[[Uimhr\u00edocht|uimhr\u00edocht]] \u2014 maidir le hionramh\u00e1il uimhreacha, agus [[Geoim\u00e9adracht|geoim\u00e9adracht]] (n\u00f3 c\u00e9imseata) - maidir le staid\u00e9ar a dh\u00e9anamh ar chruthanna. N\u00ed raibh idirdheal\u00fa soil\u00e9ir ansin ag cine\u00e1lacha \u00e1irithe br\u00e9ageola\u00edochta, amhail uimhireola\u00edocht agus astrala\u00edocht, \u00f3n matamaitic.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Le linn an Renaissance, bh\u00ed dh\u00e1 r\u00e9imse eile le feice\u00e1il. Nodaireacht mhatamaitici\u00fail ba ch\u00fais le hailg\u00e9abar, arb \u00e9ard at\u00e1 ann, go garbh,\u00a0 staid\u00e9ar agus ionramh\u00e1il foirml\u00ed. Is \u00e9ard is calcalas ann, ina bhfuil an d\u00e1 fho-r\u00e9imse, mionchalcalas agus calcalas suime\u00e1lach, n\u00e1 staid\u00e9ar ar fheidhmeanna lean\u00fanacha, a mh\u00fanla\u00edonn na caidrimh neamhl\u00edneacha idir cainn\u00edochta\u00ed \u00e9ags\u00fala ([[Athr\u00f3g (anail\u00eds uimhri\u00fail)|athr\u00f3ga]]) de ghn\u00e1th. Mhair an roinnt seo ina cheithre phr\u00edomhr\u00e9imse - uimhr\u00edocht, geoim\u00e9adracht, ailg\u00e9abar, calcalas [f\u00edor\u00fa de dh\u00edth] - go dt\u00ed deireadh an 19\u00fa haois. Is minic a measadh r\u00e9ims\u00ed mar mheicnic neamha\u00ed agus meicnic sholadach mar chuid den mhatamaitic, ach anois meastar go mbaineann siad leis an bhfisic. Bh\u00ed roinnt \u00e1bhar a forbra\u00edodh le linn na tr\u00e9imhse seo ann roimh th\u00fas na na matamaitic, agus t\u00e1 siad roinnte ina r\u00e9ims\u00ed cos\u00fail le [[Teoiric na d\u00f3ch\u00falachta|teoiric na d\u00f3ch\u00falachta</ins>]<ins class=\"diffchange diffchange-inline\">] agus an mhatamaitic theaglamach, a measadh n\u00edos d\u00e9ana\u00ed mar r\u00e9imse uathrialaitheach. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Ag deireadh an 19\u00fa haois, mar thoradh ar an ng\u00e9arch\u00e9im bhunaitheach sa mhatamaitic agus mar thoradh ar an modh aics\u00edmeach, th\u00e1inig borradh m\u00f3r ar r\u00e9ims\u00ed nua na matamaitice. Sa l\u00e1 at\u00e1 inniu ann, n\u00edl n\u00edos l\u00fa n\u00e1 64 r\u00e9imse den ch\u00e9ad leibh\u00e9al i Rang\u00fa \u00c1bhar na Matamaitice. Freagra\u00edonn cuid de na r\u00e9ims\u00ed seo don rann\u00e1n n\u00edos sine, mar at\u00e1 f\u00edor maidir le huimhirtheoiric\u00a0 (an t-ainm nua-aimseartha don arduimhr\u00edocht) agus geoim\u00e9adracht. (Mar sin f\u00e9in, t\u00e1 \"geoim\u00e9adracht\" ina n-ainmneacha ag go leor r\u00e9ims\u00ed c\u00e9adleibh\u00e9il eile n\u00f3 meastar go coitianta iad ar shl\u00ed eile mar chuid den gheoim\u00e9adracht.) N\u00ed fheictear an t-ailg\u00e9abar agus an calcalas mar limist\u00e9ir ch\u00e9ad leibh\u00e9al, ach roinntear iad i roinnt r\u00e9ims\u00ed c\u00e9adleibh\u00e9il faoi seach. Th\u00e1inig r\u00e9ims\u00ed eile den ch\u00e9ad leibh\u00e9al chun cinn le linn an 20\u00fa haois (mar shampla teoiric na gcatag\u00f3ir\u00ed; ailg\u00e9abar hoimeola\u00edoch, agus r\u00edomheola\u00edocht) n\u00f3 n\u00e1r breathna\u00edodh orthu roimhe seo mar mhatamaitic, amhail; [[Loighic mhatamaitici\u00fail|loighic]] agus bun\u00fais na matamaitice (lena n-\u00e1ir\u00edtear teoiric na mionsamhla, r\u00edomhtheoiric, tacartheoiric, teoiric an chruth\u00fanais, agus loighic ailg\u00e9abrach).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">===Uimhirtheoiric===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">===Geoim\u00e9adracht===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">===Ailg\u00e9abar===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">===Calcalas agus anail\u00eds ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">===Matamaitic scoite===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">===Matamaitic r\u00edomhaireacht\u00fail===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==== Cainn\u00edocht ====</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Tosa\u00edonn staid\u00e9ar an cainn\u00edocht le uimhreacha, ar dt\u00fas le na [[uimhreacha aiceanta]] agus [[sl\u00e1nuimhir]] agus uimhr\u00edocht orthu. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Agus a tagann forbairt ar an ch\u00f3ras uimhir, aithn\u00edtear na sl\u00e1nuimhir mar fo-thacar do na uimhir ch\u00f3imheasta. Ach t\u00e1 na uimhreacha ch\u00f3imheasta fo-thacar freisin do na [[r\u00e9aduimhir]]. T\u00e1 an [[uimhir choimpl\u00e9ascach]] tacar ginear\u00e1laithe do na [[r\u00e9aduimhir]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">:{| style=\"border:1px solid #ddd; text-align:center; margin:auto\" cellspacing=\"20\"</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>1, 2, 3\\,...\\!</math> || <math>...-2, -1, 0, 1, 2\\,...\\!</math> || <math> -2, \\frac{2}{3}, 1.21\\,\\!</math> || <math>-e, \\sqrt{2}, 3, \\pi\\,\\!</math> || <math>2, i, -2+3i, 2e^{i\\frac{4\\pi}{3}}\\,\\!</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| [[uimhreacha aiceanta]] || [[sl\u00e1nuimhir]] || [[uimhir ch\u00f3imheasta]] || [[r\u00e9aduimhir]] || [[uimhir choimpl\u00e9ascach]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==== Matamaitic Fheidhmeach ====</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Is brainse den mhatamaitic \u00ed an [[Matamaitic fheidhmeach|mhatamaitic fheidhmeach]] a bhaineann \u00fas\u00e1id as uirlis\u00ed teib\u00ed matamaitice </ins>chun <ins class=\"diffchange diffchange-inline\">fadhbanna a r\u00e9iteach sna heola\u00edochta\u00ed, i ngn\u00f3 </ins>agus <ins class=\"diffchange diffchange-inline\">i r\u00e9ims\u00ed eile nach iad. Is r\u00e9imse t\u00e1bhachtach matamaitice feidhm\u00ed \u00e9 an staidreamh </ins>a <ins class=\"diffchange diffchange-inline\">bhaineann leas as teoiric na d\u00f3ch\u00falachta mar uirlis agus a cheada\u00edonn tuairisci\u00fa, anail\u00edsi\u00fa agus r\u00e9amhaisn\u00e9is na bhfeinim\u00e9an ina bhfuil r\u00f3l ag seans.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">:{|style=\"border:1px solid #ddd; text-align:center; margin:auto\" cellspacing=\"20\"</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|[[\u00cdomh\u00e1:Gravitation_space_source.png|100px]] || [[\u00cdomh\u00e1:Two red dice 01.svg|100px]] || [[\u00cdomh\u00e1:Oldfaithful</ins>.<ins class=\"diffchange diffchange-inline\">png|100px]] ||</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|[[Fisic Mhatamaitici\u00fail]] || [[D\u00f3ch\u00falacht]] || [[Staidreamh]] ||</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Tagairt\u00ed ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{{reflist}}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{{s\u00edol-mata}}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Catag\u00f3ir:Matamaitic| ]]</ins></div></td></tr>\n"
}
}