MedijaViki API rezultatas
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{
"compare": {
"fromid": 1,
"fromrevid": 1,
"fromns": 0,
"fromtitle": "Formulynas/Algebra",
"toid": 2,
"torevid": 2,
"tons": 0,
"totitle": "Matematika/Trikampiai",
"*": "<tr><td colspan=\"2\" class=\"diff-lineno\" id=\"mw-diff-left-l1\">1 eilut\u0117:</td>\n<td colspan=\"2\" class=\"diff-lineno\">1 eilut\u0117:</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\">== Trikampis ==</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\">Trikampiu vadiname fig\u016br\u0105, kuri\u0105 sudaro trys ta\u0161kai, nepriklausantys vienai tiesei, ir trys atkarpos, jungian\u010dios kiekvienus du i\u0161 t\u0173 ta\u0161k\u0173. Tuos tris ta\u0161kus vadiname trikampio vir\u0161\u016bn\u0117mis, o atkarpas jo kra\u0161tin\u0117mis. </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\">== Algebra ==</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Trikamp\u012f \u017eymime nurodydami jo vir\u0161\u016bnes:</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\">===Skai\u010diai===</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>[[<ins class=\"diffchange diffchange-inline\">Vaizdas</ins>:<ins class=\"diffchange diffchange-inline\">trikampiai_virsunes.png</ins>]]</div></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\">* <math> \\mathbb{N} </math> - </del>[[<del class=\"diffchange diffchange-inline\">w</del>:<del class=\"diffchange diffchange-inline\">Nat\u016briniai skai\u010diai | nat\u016brini\u0173]] [[w:Skai\u010dius | skai\u010di\u0173</del>]] <del class=\"diffchange diffchange-inline\">[[w:Aib\u0117 |aib\u0117]]: <math> {1, 2, 3, \\ldots} </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> \\mathbb{Z} </math> - sveik\u0173j\u0173 skai\u010di\u0173 aib\u0117: <math> {\\ldots, -2, -1, 0, 1, 2, \\ldots} </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> \\mathbb{Q} </math> - racionali\u0173j\u0173 skai\u010di\u0173 aib\u0117. J\u0105 sudaro visi skai\u010diai kurios \u012fmanoma u\u017era\u0161yti trupmeniniu pavidalu.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> \\mathbb{I} </math> - iracionali\u0173j\u0173 skai\u010di\u0173 aib\u0117. J\u0105 sudaro visi skai\u010diai, kuri\u0173 ne\u012fmanoma u\u017era\u0161yti trupmenomis. Toki\u0173 skai\u010di\u0173 i\u0161viso ne\u012fmanoma u\u017era\u0161yti, tod\u0117l juos paprastai \u017eymime raid\u0117mis <math>(\\pi, e, \\ldots)</math> arba tiesiog ra\u0161ome nesuskai\u010diuotus rei\u0161kinius <math>(\\sqrt{2}, \\cos{3}, \\ldots)</math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> \\mathbb{R} </math> - reali\u0173j\u0173 skai\u010di\u0173 aib\u0117. J\u0105 sudaro visi racionalieji ir iracionalieji skai\u010diai.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> \\mathbb{C} </math> - kompleksini\u0173 skai\u010di\u0173 aib\u0117. Aib\u0117 skai\u010di\u0173 pavidalo <math>a+ib</math>, \u010dia <math>a,b</math> - realieji skai\u010diai, <math>i=\\sqrt{-1}</math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> \\infty </math> - begalyb\u0117. Sutartinis \u017eym\u0117jimas, rei\u0161kiantis kiek norima didel\u012f skai\u010di\u0173.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Aibes galima i\u0161d\u0117styti taip: <math> \\mathbb{N} \\subset \\mathbb{Z} \\subset \\mathbb{Q} \\subset \\mathbb{R} </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Teisinga, jog <math> \\mathbb{Q} \\cup \\mathbb{I}=\\mathbb{R}</math> ir <math> \\mathbb{Q} \\cap \\mathbb{I}=\\emptyset</math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">===Skai\u010di\u0173 intervalai===</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''Trikampio ABC kampu prie vir\u0161\u016bn\u0117s A''' vadiname kamp\u0105</ins>, <ins class=\"diffchange diffchange-inline\">kur\u012f sudaro pusties\u0117s\u00a0 AB ir AC. Pana\u0161iai apibr\u0117\u017eiami to trikampio kampai prie vir\u0161\u016bni\u0173 B </ins>ir <ins class=\"diffchange diffchange-inline\">C</ins>.</div></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\">Tarkime, jog <math>a < b</math></del>, ir <del class=\"diffchange diffchange-inline\"><math>a, b \\in \\mathbb{R} </math></del>. <del class=\"diffchange diffchange-inline\">Tuomet</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">{| cellpadding=\"2\"</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|-</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|<math> [a,b] = \\left\\{x |\\, a \\leq x \\leq b \\right\\} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|u\u017edaras intervalas arba atkarpa</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|-</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|<math> (a,b) = \\left\\{x |\\, a < x < b \\right\\} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|atviras intervalas</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|-</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|<math> [a,b) = \\left\\{x |\\, a \\leq x < b \\right\\} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|pusiau atviras arba pusiau u\u017edaras intervalas</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|-</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|<math> (a,b] = \\left\\{x |\\, a < x \\leq b \\right\\} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|pusiau atviras arba pusiau u\u017edaras intervalas</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|-</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|<math> (a,\\infty) = \\left\\{x |\\, a < x < \\infty \\right\\} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|atviras intervalas arba atvirasis spindulys</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|-</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|<math> [a,\\infty) = \\left\\{x |\\, a \\leq x < \\infty \\right\\} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|pusiau atviras arba spindulys</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|-</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|<math> (-\\infty,\\infty) = \\mathbb{R} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|visa reali\u0173j\u0173 skai\u010di\u0173 ties\u0117''</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">|}</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">===Pagrindin\u0117s reali\u0173j\u0173 skai\u010di\u0173 savyb\u0117s (aksiomos)===</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''Trikampio auk\u0161tine''' vadiname statmen\u012f</ins>, <ins class=\"diffchange diffchange-inline\">i\u0161vest\u0105 i\u0161 trikampio vir\u0161\u016bn\u0117s \u012f ties\u0119</ins>, <ins class=\"diffchange diffchange-inline\">kurioje </ins>yra <ins class=\"diffchange diffchange-inline\">prie\u0161 vir\u0161\u016bn\u0119 esanti kra\u0161tin\u0117. BD yra trikampio auk\u0161tin\u0117:</ins></div></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\">Bet kuriems realies skaiciams <math>a</del>, <del class=\"diffchange diffchange-inline\">b</del>, <del class=\"diffchange diffchange-inline\">c</math> </del>yra <del class=\"diffchange diffchange-inline\">teisingos</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">Sud\u0117ti\u0117s aksiomos</del>:</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Vaizdas</ins>:<ins class=\"diffchange diffchange-inline\">Trikampis_aukstine</ins>.<ins class=\"diffchange diffchange-inline\">png]]</ins></div></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\"># <math>a+b=b+a</math> - komutatyvumas arba sud\u0117ties perstatymo d\u0117snis.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\"># <math>a+(b+c)=(a+b)+c</math> - asociatyvumas arba sud\u0117ties jungimo d\u0117snis.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\"># <math>a+0=a</math> - neutralaus skai\u010diaus arba nulio egzistavimas.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\"># <math>a+(-a)=0</math> - prie\u0161ingo skai\u010diaus egzistavimas</del>.</div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">Daugybos aksiomos</del>:</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''Trikampio pusiaukampine''' vadiname trikampio kampo pusiaukampin\u0117s atkarp\u0105, kuri dalija kamp\u0105 pusiau ir jungia trikampio vir\u0161\u016bn\u0119 su prie\u0161 j\u0105 esan\u010dios kra\u0161tin\u0117s ta\u0161ku</ins>:</div></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\"># <math>a \\cdot b=b \\cdot a</math> - komutatyvumas arba daugybos perstatymo d\u0117snis.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\"># <math>a \\cdot (b \\cdot c)=(a \\cdot b) \\cdot c</math> - asociatyvumas arba daugybos jungimo d\u0117snis.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\"># <math>a \\sdot 1=a</math> - neutralaus skai\u010diaus arba vieneto egzistavimas.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\"># <math>a \\cdot (b + c)=a \\cdot b + a \\cdot c</math> - distributyvumas arba skirstymo d\u0117snis.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">===Reali\u0173j\u0173 skai\u010di\u0173 nelygyb\u0117s===</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Vaizdas:Trikampis_pusiaukampine</ins>.<ins class=\"diffchange diffchange-inline\">png]]</ins></div></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\">Sakysime, jog <math> a,b,c \\in \\mathbb{R} </math>, tada teisingos \u0161ios nelygyb\u0117s</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Jei <math> a>b </math>, tai <math> b<a </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Jei <math> a>b </math> ir <math> b>c </math>, tai <math>a>c</math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Jei <math> a>b </math>, tai <math> a+c>b+c </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Jei <math> a>b </math> ir <math> c>0 </math>, tai <math> ac>bc </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Jei <math> a>b </math> ir <math> c<0 </math>, tai <math> ac<bc </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Jei <math> a>1 </math>, tai <math> a^n>a^m </math>, kai <math>n>m, m,n \\in \\mathbb{N}</math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Jei <math> 0<a<1 </math>, tai <math> a^n<a^m </math>, ki <math>n>m, n,n \\in \\mathbb{M}</math></del>.</div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">===Realiojo skai\u010diaus modulis===</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''Trikampio pusiaukra\u0161tine''' vadiname trikampio kampo pusiaukra\u0161tin\u0117s atkarp\u0105, kuri dalija kra\u0161tin\u0119 pusiau bei jungia trikampio vir\u0161\u016bn\u0119 su prie\u0161 j\u0105 esan\u010dios kra\u0161tin\u0117s viduriu</ins>:</div></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\">Modulio apibr\u0117\u017eimas</del>:</div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> |a|= \\begin{cases}\ta, \\mathrm{kai} \\, a \\geq 0, \\\\ -a, \\mathrm{kai} \\, a<0 \\, \\end{cases} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">Modulio savybes</del>:</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Vaizdas</ins>:<ins class=\"diffchange diffchange-inline\">Matematika_pusiaukrastine.png]]</ins></div></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\">* <math> |a| \\geq 0 </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> |a| = |-a| </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> |a|^2 = a^2 </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> \\left| \\frac{a}{b} \\right| = \\frac{|a|}{|b|}\u00a0 </math>, su s\u0105lyga, kad <math>b \\neq 0 </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> |a \\cdot b|=|a| \\cdot |b| </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> |a+b| \\leq |a| + |b|\u00a0 </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> |a-b| \\geq |a| - |b| </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* <math> a b = \\begin{cases}\t|a| \\cdot |b|, \\mathrm{kai} \\, (a>0 \\, \\mathrm{ir} \\, b>0) \\, \\mathrm{arba} \\, (a<0 \\, \\mathrm{ir} \\, b<0)\u00a0 \\\\ -|a| \\cdot |b|, \\mathrm{kai} \\, (a>0 \\, \\mathrm{ir} \\, b<0) \\, \\mathrm{arba} \\, (a<0 \\, \\mathrm{ir} \\, b>0)\u00a0 \\end{cases} </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">===Sveik\u0173j\u0173 skai\u010di\u0173 dalumo po\u017eymiai===</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''Trikampio vidurine linija''' vadiname atkarp\u0105</ins>, <ins class=\"diffchange diffchange-inline\">kuri jungia </ins>dviej\u0173 jo <ins class=\"diffchange diffchange-inline\">kra\u0161tini\u0173 vidurio ta\u0161kus</ins>.</div></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\">* Sumos dalumo teorema: jeigu <math>\\frac{a}{c} \\in \\mathbb{Z} </math> ir <math>\\frac{b}{c} \\in \\mathbb{Z} </math></del>, <del class=\"diffchange diffchange-inline\">tai ir <math>\\frac{a \\cdot b}{c} \\in \\mathbb{Z} </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Sandaugos dalumo teorema: jeigu <math>\\frac{a}{c} \\in \\mathbb{Z} </math> ir <math>\\frac{b}{d} \\in \\mathbb{Z} </math>, tai ir <math>\\frac{a \\cdot b}{c} \\in \\mathbb{Z} </math>, ir <math>\\frac{a \\cdot b}{d} \\in \\mathbb{Z} </math>.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Sveikasis skai\u010dius dalijasi i\u0161 2, kai jo paskutinis skaitmuo yra 0, 2, 4, 6, 8, t.y. lyginis.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Sveikasis skai\u010dius dalijasi i\u0161 3, kai jo vis\u0173 skaitmen\u0173 suma dalijasi i\u0161 3.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Sveikasis skai\u010dius dalijasi i\u0161 4, kai i\u0161 4 dalijasi dvi\u017eenklis skai\u010dius, sudarytas i\u0161 paskutini\u0173 </del>dviej\u0173 <del class=\"diffchange diffchange-inline\">skai\u010diaus skaitmen\u0173 arba paskutinai skaitmenys yra nuliai.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Sveikasis skai\u010dius dalijasi i\u0161 5, kai </del>jo <del class=\"diffchange diffchange-inline\">paskutinis skaitmuo yra 5 arba 0.</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">* Sveikasis skai\u010dius dalijasi i\u0161 11, kai lygin\u0117se ir nelygin\u0117se vietose esan\u010di\u0173 skaitmen\u0173 sumos sutampa arba skiriasi skai\u010diumi, kuris yra 11 kartotinis</del>.</div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">===Aritmetin\u0117 \u0161aknis ir jos savyb\u0117s===</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Vaizdas:Trikampis_vidurio_linija</ins>.<ins class=\"diffchange diffchange-inline\">PNG]]</ins></div></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\">..</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">===Logaritmai===</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">...</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">a\u0161 noriu su\u017einoti apie daugybos skirstymo d\u0117sn\u012f</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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 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\"><math>DE</math> \u2013 vidurin\u0117 linija.</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\"><math>DE=\\frac{1}{2}AC</math></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\">:'''Pagrindin\u0117s logaritm\u0173 savyb\u0117s'''. Su kiekvienu <math>a>0, \\;\\; a \\neq 1 \\;</math> teisingos lygyb\u0117s:</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>== <ins class=\"diffchange diffchange-inline\">Trikampio lygumas </ins>==</div></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\">:<math>\\log_a 1 </del>=<del class=\"diffchange diffchange-inline\">0;</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>\\log_a a </del>=<del class=\"diffchange diffchange-inline\">1;</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>\\log_a (xy) </del>=<del class=\"diffchange diffchange-inline\">\\log_a x + \\log_a y,</math> kai ''x''>0 ir ''y''>0;</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>\\log_a \\frac{x}{y} </del>=<del class=\"diffchange diffchange-inline\">\\log_a x - \\log_a y,</math> kai ''x''>0 ir ''y''>0;</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>\\log_a x^p = p \\log_a x,</math> kai ''x''>0, ''p'' - realusis skai\u010dius;</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>\\log_a x =\\frac{\\log_b x}{\\log_b a},</math> kai ''x''>0, ''b''>0, <math>b\\neq 1;</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>a^{\\log_a x} =x,</math> kai ''x''>0 (pagrindin\u0117 logaritm\u0173 tapatyb\u0117).</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>\\log_a b =\\frac{1}{\\log_b a}</del>.<del class=\"diffchange diffchange-inline\"></math></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Lygiomis atkarpomis vadiname atkarpas, kurios yra vienodo ilgio</ins>. <ins class=\"diffchange diffchange-inline\">Lygiais kampais vadiname kampus, kurie yra vienodo laipsninio mato</ins>.</div></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\">:<math>\\log_a b =\\log_{a^r} b^r</del>.<del class=\"diffchange diffchange-inline\"></math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">===Laipsnis===</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Yra trys trikampi\u0173 lygumo po\u017eymiai:</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\">:<math>a^2-b^2=(a-b)(a+b)</del>.<del class=\"diffchange diffchange-inline\"></math></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">#'''Trikampi\u0173 lygumo po\u017eymis pagal dvi kra\u0161tines ir kamp\u0105 tarp j\u0173</ins>.<ins class=\"diffchange diffchange-inline\">'''</ins></div></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\">:<math>a^3-b^3=(a-b)(a^2+ab+b^2)</del>.<del class=\"diffchange diffchange-inline\"></math></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">#'''Trikampi\u0173 lygumo po\u017eymis pagal kra\u0161tin\u0119 ir prie jos esan\u010dius kampus</ins>.<ins class=\"diffchange diffchange-inline\">'''</ins></div></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\">:<math>a^3+b^3=(a+b)(a^2-ab+b^2)</del>.<del class=\"diffchange diffchange-inline\"></math></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">#'''Trikampio lygumo po\u017eymis pagal tris kra\u0161tines</ins>.<ins class=\"diffchange diffchange-inline\">'''</ins></div></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\">:<math>(a+b)^2=a^2+2ab+b^2.</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>(a-b)^2=a^2-2ab+b^2.</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>(a^n)^m=a^{n \\cdot m}.</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>\\left( \\frac{a}{b} \\right) ^n = \\frac{a^n}{b^n}</math>, su s\u0105lyga, kad <math>b \\neq 0 </math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:Sakykime, <math>r</del>=<del class=\"diffchange diffchange-inline\">\\frac{m_1}{n_1}, \\; \\; s</del>=<del class=\"diffchange diffchange-inline\">\\frac{m_2}{n_2}.</math> \u010cia <math>m_1</math> ir <math>m_2</math> yra sveikieji skai\u010diai, o <math>n_1</math> ir <math>n_2</math> yra nat\u016briniai skai\u010diai. Tada</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>== <ins class=\"diffchange diffchange-inline\">Trikampio perimetras </ins>==</div></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\">:<math>a^r \\cdot a^s</del>=<del class=\"diffchange diffchange-inline\">a^{\\frac{m_1}{n_1}}\\cdot a^{\\frac{m_2}{n_2}}</del>=<del class=\"diffchange diffchange-inline\">a^{\\frac{m_1 n_2}{n_1 n_2}}\\cdot a^{\\frac{n_1 m_2}{n_1 n_2}}=a^{\\frac{m_1 n_2}{n_1 n_2} + \\frac{n_1 m_2}{n_1 n_2}}=a^{\\frac{m_1 n_2+ m_2 n_1}{n_1 n_2}}=a^{r+s}.</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:\u010cia ''a'' gali b\u016bti bet koks teigiamas (realusis) skai\u010dius. Jeigu sandauga <math>n_1\\cdot n_2</math> yra nelyginis (nat\u016brinis) skai\u010dius, tai tuomet ''a'' gali b\u016bti bet koks realusis skai\u010dius (tame tarpe ir neigiamas), i\u0161skyrus 0 (nes nulio negalima pakelti neigiamu laipsniu).</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\"><math>a^4-b^4=(a-b)(a^3+a^2 b+ab^2 +b^3)</del>.<del class=\"diffchange diffchange-inline\"></math></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Vaizdas</ins>:<ins class=\"diffchange diffchange-inline\">Trikampis_perimetras</ins>.<ins class=\"diffchange diffchange-inline\">PNG]]</ins></div></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\">:<math>a^5-b^5=(a-b)(a^4+a^3 b+a^2 b^2 +ab^3 +b^4).</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>a^4-b^4=(a+b)(a^3-a^2 b+ab^2 -b^3)</del>.<del class=\"diffchange diffchange-inline\"></math></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Trikampio perimetras yra vis\u0173 trikampio kra\u0161tini\u0173 ilgi\u0173 suma</ins>.</div></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\">:<math>a^5+b^5=(a+b)(a^4-a^3 b+a^2 b^2 -ab^3 +b^4).</math></del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:</del><math><del class=\"diffchange diffchange-inline\">x^n-y^n</del>=<del class=\"diffchange diffchange-inline\">(x-y)(x^{n-1}</del>+<del class=\"diffchange diffchange-inline\">x^{n-2}y</del>+<del class=\"diffchange diffchange-inline\">x^{n-3}y^2+...+xy^{n-2} +y^{n-1}).</math></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><math><ins class=\"diffchange diffchange-inline\">P</ins>=<ins class=\"diffchange diffchange-inline\">a</ins>+<ins class=\"diffchange diffchange-inline\">b</ins>+<ins class=\"diffchange diffchange-inline\">c</ins>\\,</math></div></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\">:<math>x^n+y^n=(x+y)(x^{n-1}-x^{n-2}y+x^{n-3}y^2-...-xy^{n-2} +y^{n-1}) </del>\\<del class=\"diffchange diffchange-inline\">;</math> (tik</del>, <del class=\"diffchange diffchange-inline\">kai ''n'' nelyginis!).</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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\">:<math>x^n-y^n=(x+y)(x^{n-1}-x^{n-2}y+x^{n-3}y^2-...+xy^{n-2} -y^{n-1}) \\;</del></math> <del class=\"diffchange diffchange-inline\">(tik, kai ''n'' lyginis!).</del></div></td><td colspan=\"2\" class=\"diff-side-added\"></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 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\">Trikampio pusperimetris lygus pusei perimetro.</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\">Stub</del>}} \u00a0</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math>p=\\frac</ins>{<ins class=\"diffchange diffchange-inline\">P}{2}=\\frac{a+b+c}{2}</math></ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>[[Category:<del class=\"diffchange diffchange-inline\">Formulynas</del>]]</div></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\">Trikampio kamp\u0173 suma lygi 180\u00b0</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\">==Trikampio pusiaukra\u0161tin\u0117s==</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\">I\u0161 trikampio kampo i\u0161\u0117jusi ties\u0117, kuri prie\u0161ais t\u0105 kamp\u0105 esan\u010di\u0105 kra\u0161tin\u0119 dalina pusiau, vadinama trikampio pusiaukra\u0161tin\u0117. Jei susikerta dvi trikampio pusiaukra\u0161tin\u0117s, tai jos vien\u0105 kita padalina santykiu 2:1. T. y. viena trikampio pusiaukra\u0161tin\u0117, kit\u0105 trikampio pusiaukra\u0161tin\u0119 dalina santykiu 2:1. Didesn\u0117 padalintos pusiaukra\u0161tin\u0117s dalis yra ar\u010diau kampo.</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\">==Trikampio ploto radimas \u017einant koordinates==</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\">[[File:Trikamplotas11pav.png|thumb|11 pav.]]</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\">'''Trikampio plotas'''. Bet kokiems ta\u0161kams <math>A(x_1; y_1)</math>, <math>B(x_2; y_2)</math> ir <math>C(x_3; y_3)</math> negulintiems ant vienos ties\u0117s, plotas ''S'' trikampio ''ABC'' i\u0161rei\u0161kiamas formule</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>S=\\frac{1}{2}|[(x_2-x_1)(y_3-y_1)-(x_3-x_1)(y_2-y_1)]|.</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\">:''\u012erodymas''. Plot\u0105 trikampio ''ABC'' pavaizduot\u0105 pav. 11, galima rasti taip:</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>S_{ABC}=S_{ADEC}+S_{BCEF}-S_{ABFD},\\;</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\">:kur <math>S_{ADEC}</math>, <math>S_{BCEF}</math>, <math>S_{ABFD}</math> - plotai atitinkam\u0173 trapecij\u0173.</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\">:Kadangi</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>S_{ADEC}=|DE|\\frac{|AD|+|CE|}{2}=\\frac{(x_3-x_1)(y_3+y_1)}{2},</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\">:<math>S_{BCEF}=|EF|\\frac{|EC|+|BF|}{2}=\\frac{(x_2-x_3)(y_2+y_3)}{2},</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\">:<math>S_{ABFD}=|DF|\\frac{|AD|+|BF|}{2}=\\frac{(x_2-x_1)(y_1+y_2)}{2},</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\">:\u012fstat\u0119\u00a0 i\u0161rai\u0161kas \u0161iems plotams \u012f lygyb\u0119 <math>S_{ABC}=S_</ins>{<ins class=\"diffchange diffchange-inline\">ADEC</ins>}<ins class=\"diffchange diffchange-inline\">+S_{BCEF</ins>}<ins class=\"diffchange diffchange-inline\">-S_{ABFD},</math> gausime formul\u0119</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>S_{ABC}=S_{ADEC}+S_{BCEF}-S_{ABFD}=\\frac{1}{2}|[(x_3-x_1)(y_3+y_1)+(x_2-x_3)(y_2+y_3)-(x_2-x_1)(y_1+y_2)]|=</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\">:<math>=\\frac{1}{2}|[(x_1-x_2)(y_1+y_2)+(x_2-x_3)(y_2+y_3)+(x_3-x_1)(y_3+y_1)]|=</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\">:<math>=\\frac{1}{2}|(x_1 y_1+x_1 y_2-x_2 y_1-x_2 y_2+x_2 y_2+ x_2 y_3-x_3 y_2- x_3 y_3+x_3 y_3+x_3 y_1-x_1 y_3-x_1 y_1)|=</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\">:<math>=\\frac{1}{2}|(x_1 y_2-x_2 y_1+ x_2 y_3-x_3 y_2+x_3 y_1-x_1 y_3)|=\\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=</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\">:<math>=\\frac{1}{2}|(x_2-x_1)(y_3-y_1)-(x_3-x_1)(y_2-y_1)|.</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>\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\">:'''Pavyzdis'''. Duoti ta\u0161kai ''A''(1; 1), ''B''(6; 4), ''C''(8; 2). Rasti trikampio ''ABC'' plot\u0105. Randame:</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>S_{ABC}=\\frac{1}{2}|[(x_2-x_1)(y_3-y_1)-(x_3-x_1)(y_2-y_1)]|=\\frac{1}{2}|(6-1)(2-1)-(8-1)(4-1)|=\\frac{1}{2}|5\\cdot 1-7\\cdot 3|=\\frac{1}{2}|5-21|=\\frac{1}{2}|-16|=\\frac{16}{2}=8;</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\">:<math>S_{ABC}=S_{ADEC}+S_{BCEF}-S_{ABFD}=\\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=\\frac{1}{2}|1(4-2)+6(2-1)+8(1-4)|=\\frac{1}{2}|2+6+8\\cdot (-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\">:<math>=\\frac{1}{2}|8-24|=\\frac{1}{2}|-16|=8.</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>\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>[[Category:<ins class=\"diffchange diffchange-inline\">Matematika</ins>]]</div></td></tr>\n"
}
}