{"id":941,"date":"2024-08-29T11:38:01","date_gmt":"2024-08-29T08:38:01","guid":{"rendered":"https:\/\/teodordiamant.ro\/?page_id=941"},"modified":"2025-03-16T20:45:16","modified_gmt":"2025-03-16T17:45:16","slug":"blog-2","status":"publish","type":"page","link":"https:\/\/teodordiamant.ro\/?page_id=941","title":{"rendered":"BLOG"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"941\" class=\"elementor elementor-941\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-68e23b5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"68e23b5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-50fc9ea\" data-id=\"50fc9ea\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7d092f1 elementor-widget elementor-widget-text-editor\" data-id=\"7d092f1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.0 - 08-05-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p style=\"text-align: center;\"><strong>AN \u0218COLAR 2023-2024<\/strong><\/p><p style=\"text-align: center;\"><strong><a href=\"http:\/\/teodordiamant.ro\/wp-content\/uploads\/2025\/03\/IPT_Protectia-mediului-si-matematica.pdf\">IPT_Protectia mediului si matematica<\/a><\/strong><\/p><p style=\"text-align: center;\"><span style=\"text-decoration: underline;\"><strong><span style=\"color: #003300; text-decoration: underline;\">Implementarea instrumentelor digitale moderne \u00een activit\u0103\u0163i de predare \u2013 \u00eenv\u0103\u0163are-evaluare, cu aplicabilitate pentru matematic\u0103<\/span><\/strong><\/span><\/p><p style=\"text-align: right;\"><span style=\"color: #800000;\"><strong><em>Prof. Mara Iordache<\/em><\/strong><\/span><\/p><p><strong>Implementarea instrumentelor digitale moderne \u00een activit\u0103\u0163i de predare \u2013 \u00eenv\u0103\u0163are-evaluare, cu aplicabilitate pentru matematic\u0103<\/strong><\/p><p><em>Prof. Mara Iordache<\/em><\/p><p>Utilizarea instrumentelor TIC duce la \u00eenv\u0103\u0163are centrat\u0103 pe elev . Ea descrie modalit\u0103\u0163i de a g\u00e2ndi despre \u00eenv\u0103\u0163are \u015fi predare ce pun accentul pe responsabilitatea elevului pentru activit\u0103\u0163i de genul pl\u0103nuirii \u00eenv\u0103\u0163\u0103rii, interac\u0163iunii cu profesorii \u015fi al\u0163i elevi, cercet\u0103rii \u015fi evalu\u0103rii \u00eenv\u0103\u0163\u0103rii. Cannon, R. (2000) \u00cenv\u0103\u0163area centrat\u0103 pe elev le ofer\u0103 elevilor o autonomie \u015fi un control mai mare \u00een privin\u0163a alegerii subiectului, a metodelor de \u00eenv\u0103\u0163are \u015fi a ritmului de studiu. Gibbs, G. (1992)\u00a0 Se refer\u0103 la situa\u0163ia \u00een care elevii lucreaz\u0103 at\u00e2t \u00een grupuri c\u00e2t \u015fi individual pentru a explora probleme \u015fi a procesa activ cuno\u015ftin\u0163ele, mai degrab\u0103 dec\u00e2t a fi ni\u015fte receptori pasivi ai acestora. (Harmon, S.W. &amp; Hirumi, A., 1996) \u00cenv\u0103\u0163area centrat\u0103 pe elev este o abordare extins\u0103, ce presupune \u00eenlocuirea prelegerilor cu \u00eenv\u0103\u0163area activ\u0103, integrarea unor programe de \u00eenv\u0103\u0163are dup\u0103 un ritm propriu \u015fi\/sau a unor situa\u0163ii de cooperare \u00een grup, care \u00een ultim\u0103 instan\u0163 3. Platforme educa\u021bionale\/ Softuri educa\u021bionale &#8211; Tema: Implementarea instrumentelor digitale moderne \u00een activit\u0103\u0163i de predare \u2013 \u00eenv\u0103\u0163are-evaluare, cu aplicabilitate pentru toate ariile curriculare(\u0103 \u00eei confer\u0103 elevului responsabilitatea pentru propriile progrese \u00een educa\u0163ie . Astfel tehnologiile moderne ofer\u0103 c\u00e2teva oportunit\u0103\u0163i pentru evaluarea performan\u0163ei \u00een \u00eenv\u0103\u0163are. Exist\u0103 nenum\u0103rate proiecte care vizeaz\u0103 utilizarea noilor tehnologii \u00a0la clas\u0103, iar c\u00e2teva dintre acestea vizeaz\u0103 \u015fi \u00eembun\u0103t\u0103\u0163irea sau eficientizarea practicilor de evaluare a elevilor. \u00centotdeauna trebuie pus \u00een balan\u0163\u0103 ceea ce este posibil \u015fi este facilitat prin tehnologie, pe de o parte, \u015fi ceea ce este f\u0103cut mai dificil sau inhibat de c\u0103tre mediul nou folosit, pe de alt\u0103 parte. Punctul de plecare \u00eel constituie metodele tradi\u0163ionale de evaluare de performan\u0163e, care sunt preluate \u015fi validate (de cele mai multe ori, de practic\u0103) \u00een mediul tehnologic.<\/p><p>\u00a0Problemele care se pun constau \u00een aspectele privind eficien\u0163a evalu\u0103rilor cu ajutorul computerului, precum \u015fi cele privind rela\u0163ia dintre modalitatea de evaluare \u015fi comportamentul studen\u0163ilor evalua\u0163i.<\/p><p>Cel mai proeminent subiect abordat se refer\u0103 la efectele mediului de comunicare asupra modului \u00een care elevii g\u00e2ndesc \u015fi \u00een\u0163eleg sarcinile din test. Astfel, se pun \u00een balan\u0163\u0103 ceea ce este posibil \u015fi este facilitat prin tehnologie, pe de o parte, \u015fi ceea ce este f\u0103cut mai dificil sau \u201einhibat\u201d de c\u0103tre mediul nou folosit, pe de alt\u0103 parte. Punctul de plecare \u00eel constituie metodele tradi\u0163ionale de evaluare de performan\u0163e, care sunt preluate \u015fi validate (de cele mai multe ori, de practic\u0103) \u00een mediul tehnologic.<\/p><p>\u00cen ce prive\u015fte aspectele comparabile ale evalu\u0103rii cu ajutorul noilor tehnologii versus evaluarea tradi\u0163ional\u0103, etapele care sunt mai avantajate de utilizarea noilor tehnologii sunt administrarea testelor \u015fi analiza rezultatelor ob\u0163inute (Harvey, 1999, p.17).<\/p><p>Forme de evaluare cu ajutorul TIC:<\/p><p>Evaluarea cu ajutorul TIC poate \u00eembr\u0103ca diverse forme \u015fi se poate face \u00een diverse moduri. Enumer\u0103m \u00een cele ce urmeaz\u0103 principalele puncte de inciden\u0163\u0103 \u00eentre evaluarea studen\u0163ilor \u015fi utilizarea noile tehnologii:<\/p><p>Elevii sunt evalua\u0163i printr-un test scris, pe care \u00eel rezolv\u0103\/ completeaz\u0103 pe calculator;<\/p><p>-testul poate fi salvat local, pe calculatorul pe care lucreaz\u0103 elevul \u00a0(la ore \u00a0sau acas\u0103); reveniri succesive, pe m\u0103sur\u0103 ce elevul progreseaz\u0103 \u00een materialul de studiu, pot fi posibile<\/p><p>-testul poate fi dat pe Internet\/ Intranet; op\u0163iunile elevului sunt \u00eenscrise automat \u00eentr-o baz\u0103 de date \u015fi se poate calcula pe loc o not\u0103;<\/p><p>-variant\u0103 mixt\u0103, \u00een care un test din cadrul unui program de instruire trimite op\u0163iunile prin Internet, la un server care preia datele \u015fi le stocheaz\u0103; rezultatele pot fi consultate oric\u00e2nd de c\u0103tre profesor sau elevul respectiv;<\/p><p>-elevilor li se cere s\u0103 elaboreze o lucrare sau s\u0103 dezvolte un proiect pe care \u00eel vor prezenta utiliz\u00e2nd un calculator \u015fi un videoproiector\/ Whiteboard (alternativ, lucrarea sau proiectul pot fi trimise prin email cadrului didactic \u015fi colegilor);<\/p><p>-doar o etap\u0103 din evaluare \u2013 analiza rezultatelor \u2013 se face cu ajutorul calculatorului: evaluatorul \u00eenscrie datele ob\u0163inute din evalu\u0103ri \u00een baze de date, pentru stocare, prelucr\u0103ri statistice, compara\u0163ii, ameliorarea pred\u0103rii, interven\u0163ii precise pentru ameliorarea performan\u0163elor.<\/p><p>Exemple de site-uri educa\u0163ionale folosite cu scop didactic:<\/p><ul><li><a href=\"http:\/\/www.experior.ro\/\">www.experior.ro<\/a> \u00a0-faciliteaz\u0103 accesul la teste \u015fi gestionarea testelor \u00eencepute din punct de vedere al duratei (timpul total pentru efectuarea testului, timpul r\u0103mas), al dificult\u0103\u0163ii, al notei ob\u0163inute.<\/li><\/ul><p>&#8211;se poate utiliza Experior at\u00e2t ca suport de auto-evaluare, c\u00e2t \u015fi pentru evaluarea la clas\u0103.<\/p><p>-un elev care \u015fi-a creat cont poate consulta \u201eBiblioteca\u201d<\/p><ul><li><a href=\"https:\/\/freeonlinesurveys.com\/\">https:\/\/freeonlinesurveys.com\/<\/a>\u00a0 -se pot construi teste ce pot fi distribuite prin e-mail, iar rezultatele vor fi \u00eenregistrate \u015fi analizate.<\/li><li><a href=\"https:\/\/www.proprofs.com\/quiz-school\/create-a-quiz.php\">https:\/\/www.proprofs.com\/quiz-school\/create-a-quiz.php<\/a> -are posibilitatea de a crea o clasa virtual\u0103, iar testele se pot aplica \u00een sala de clas\u0103 sau atunci c\u00e2nd elevii sunt acas\u0103.<\/li><\/ul><p>-accesul la teste este posibil de pe laptop, tablet\u0103 sau telefon<\/p><ul><li><a href=\"https:\/\/www.nctm.org\/\">https:\/\/www.nctm.org\/<\/a><\/li><li><a href=\"http:\/\/www.e-scoala.ro\/\">http:\/\/www.e-scoala.ro\/<\/a> faciliteaz\u0103 accesul la materiale didactice , laboratoare virtuale<\/li><li><a href=\"http:\/\/www.mateinfo.ro\/\">http:\/\/www.mateinfo.ro<\/a>\u00a0 site-ul este dedicat elevilor c\u00e2t \u015fi pentru profesorilor<\/li><li><a href=\"http:\/\/www.geogebra.org\/cms\/en\/\">www.geogebra.org\/cms\/en\/<\/a>\u00a0 -descoperi\u021bi matematica pe geogebra.org calculatorului nostru grafic gratuit online, calculator de geometrie, calculator 3D, foaie de calcul, CAS, calculator de probabilitate<\/li><\/ul><p>\u00a0 <a href=\"http:\/\/www.tmmate.ro\/\">www.tmmate.ro<\/a>\u00a0<\/p><p>\u00a0<a href=\"http:\/\/www.artofproblemsolving.com\/\">www.artofproblemsolving.com<\/a>\u00a0<\/p><ul><li>\u00a0<a href=\"http:\/\/www.math-pdr.com\/\">www.math-pdr.com<\/a>\u00a0 lec\u0163ii online de matematic\u0103 care- \u015fi propune consolidarea no\u0163iunilor predate la clas\u0103<\/li><li><a href=\"http:\/\/www.ssmr.ro\/\">www.ssmr.ro<\/a><u>\u00a0 societatea are ca scop promovarea, indrumarea si sprijinirea cercet<\/u>\u0103<u>rilor, cultivarea interesului pentru matematic<\/u>\u0103<\/li><li><a href=\"http:\/\/www.gazetamatematica.ro\/\">www.gazetamatematica.ro<\/a><u>\u00a0 propune rezolvarea de probleme\u00a0 pentru pregatirea concursurilor , olimpiadelor<\/u><\/li><\/ul><p>Alte site-uri utile: <a href=\"http:\/\/www.mategl.com\/download.htm\">http:\/\/www.mategl.com\/download.htm<\/a> ,\u00a0 <a href=\"http:\/\/mate.info.ro\/acasa.html\">http:\/\/mate.info.ro\/acasa.html<\/a> ,<a href=\"http:\/\/www.didactic.ro\/discipline\">http:\/\/www.didactic.ro\/discipline<\/a> ,<\/p><p><a href=\"http:\/\/www.pro-didactica.ro\/\">http:\/\/www.pro-didactica.ro\/<\/a>\u00a0 ,<a href=\"http:\/\/www.slideshare.net\/\">http:\/\/www.slideshare.net\/<\/a>,<a href=\"http:\/\/www.teachertube.com\/\">http:\/\/www.teachertube.com\/<\/a> , <a href=\"http:\/\/iteach.ro\/\">http:\/\/iteach.ro\/<\/a>\u00a0<\/p><p style=\"text-align: center;\">\u00a0<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a81f4f0 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"a81f4f0\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.0 - 08-05-2023 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider .elementor-divider__element{margin:0 var(--divider-element-spacing);flex-shrink:0}.elementor-widget-divider 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.elementor-divider-separator,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:after,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:before,.elementor-widget-divider--separator-type-pattern:not([class*=elementor-widget-divider--view]) .elementor-divider-separator{width:100%;min-height:var(--divider-pattern-height);-webkit-mask-size:var(--divider-pattern-size) 100%;mask-size:var(--divider-pattern-size) 100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6da60ab elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6da60ab\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dce141b\" data-id=\"dce141b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9539c18 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"9539c18\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ee2df68 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ee2df68\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0b0f86c\" data-id=\"0b0f86c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e46df1d elementor-widget elementor-widget-text-editor\" data-id=\"e46df1d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p align=\"center\"><span style=\"color: #000000;\"><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: large;\"><b>TEORIA HAOSULUI <\/b><\/span><\/span><\/span><\/p><p align=\"right\"><span style=\"color: #000000;\"> <span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: large;\"><b>Prof. Stoica Viorica Ioana<\/b><\/span><\/span><\/span><\/p><p align=\"center\"><br \/><br \/><\/p><p align=\"center\"><span style=\"color: #474747;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">&#8222;<\/span><\/span><\/span><span style=\"color: #767676;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\"><b>Din chaos doamne-am ap\u0103rut<\/b><\/span><\/span><\/span><span style=\"color: #474747;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">, <\/span><\/span><\/span><\/p><p align=\"center\"><span style=\"color: #474747;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">\u0218i m-a\u0219 \u00eentoarce-n chaos <\/span><\/span><\/span><\/p><p align=\"center\"><span style=\"color: #474747;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">\u0218i din repaos m-am n\u0103scut, <\/span><\/span><\/span><\/p><p align=\"center\"><span style=\"color: #474747;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">Mi-e sete de repaos.&#8221;<\/span><\/span><\/span><\/p><p align=\"center\"><span style=\"color: #000000;\"> <span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">M. Eminescu<\/span><\/span><\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\"><i>Teoria Haosului <\/i><\/span><\/span><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">este o ramur\u0103 a matematicii \u0219i fizicii moderne care descrie comportamentul anumitor sisteme dinamice neliniare, a acelor sisteme care prezint\u0103 fenomenul de instabilitate numit sensibilitate fa\u021b\u0103 de condi\u021biile ini\u021biale, motiv pentru care comportamentul lor pe termen relativ lung (de\u0219i se conformeaz\u0103 legilor deterministe) este imprevizibil, adic\u0103 aparent haotic (de unde \u0219i denumirea teoriei).\u00a0<\/span><\/span><\/p><p>\u00a0<span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">un\u00a0fractal\u00a0este o figur\u0103 geometric\u0103 fragmentat\u0103 sau fr\u00e2nt\u0103 care poate fi divizat\u0103 \u00een p\u0103r\u021bi, astfel \u00eenc\u00e2t fiecare dintre acestea s\u0103 fie (cel pu\u021bin aproximativ) o copie miniatural\u0103 a \u00eentregului<\/span><\/span><\/p><p>\u00a0<\/p><p><span style=\"color: #000000;\"> <span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: xx-large;\">Teoria Haosului. Fractali <\/span><\/span><\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">In ciuda faptului c\u0103 evolu\u0163ia temporal\u0103 a sistemelor dinamice haotice este descris\u0103 de legi deterministe, comportamentul lor pe termen lung este imprevizibil datorit\u0103 impreciziei \u00een determinarea condi\u0163iilor ini\u0163iale. Apari\u0163ia teoriei, \u00een anii &#8217;60 ai secolului trecut, a fost favorizat\u0103 de cel pu\u0163in doi factori. In primul r\u00e2nd, dezvoltarea puterii de calcul a computerelor electronice a permis rezolvarea (numeric\u0103) a majorit\u0103\u0163ii ecua\u0163iilor care descriau comportamentul dinamic al unor sisteme fizice de interes, ecua\u0163ii care nu putuser\u0103 a fi solu\u0163ionate prin metodele analitice disponibile la acea dat\u0103. Al doilea factor este reprezentat de revolu\u0163ia produs\u0103 \u00een \u015ftiin\u0163\u0103 de mecanica cuantic\u0103 \u015fi de sf\u00e2r\u015fitul erei determinismului mecanicist al lui Laplace. Chiar dac\u0103 na\u015fterea teoriei haosului este legat\u0103 de numele lui Henri Poincare (1903), cel care a adus-o \u00een aten\u0163ia lumii \u015ftiin\u0163ifice a fost meteorologul american Edward Lorenz (1960)<\/span><\/span><\/p><p align=\"center\"><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: large;\">Efectul Fluture<\/span><\/span><\/p><p align=\"center\">\u00a0<\/p><p><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">\u00cen teoria haosului, efectul fluturelui este sensibilitatea dependen\u0163ei fa\u0163\u0103 de condi\u0163iile ini\u0163iale, \u00een care o mic\u0103 schimbare \u00eentr-un loc dintr-un sistem neliniar determinist poate duce la diferen\u0163e mari \u00eentr-o stare t\u00e2rzie. Numele efectului, inventat de Edward Lorenz, este derivat din exemplul teoretic de formare a unui uragan care este condi\u0163ionat de faptul dac\u0103 un fluture \u00eendep\u0103rtat a b\u0103tut sau nu din aripi \u00een urm\u0103 cu mai multe s\u0103pt\u0103m\u00e2ni. Cu alte cuvinte, &#8222;mi\u015fcarea aripilor unui fluture azi poate produce o mic\u0103 schimbare a atmosferei&#8221;. De\u015fi efectul fluturelui poate p\u0103rea a fi un comportament pu\u0163in probabil, acesta este expus prin sisteme foarte simple. De exemplu, o minge plasat\u0103 pe v\u00e2rful unui deal poate cobor\u00ee la vale \u00een orice direc\u0163ie \u00een func\u0163ie de, printre altele, mici diferen\u0163e ale pozi\u0163iei sale ini\u0163iale. Efectul fluturelui este o figur\u0103 de stil comun\u0103 \u00een fic\u0163iune, \u00een special \u00een scenariile care implic\u0103 c\u0103l\u0103toria \u00een timp. \u00cen plus, operele de fic\u0163iune care implic\u0103 puncte de la care povestea difer\u0103 \u00een timp datorit\u0103 unui eveniment aparent minor, duc\u00e2nd la un rezultat semnificativ diferit fa\u0163\u0103 de cazul \u00een care nu ar fi avut loc aceea divergen\u0163\u0103, sunt un exemplu de efect fluture.<br \/><\/span><\/span><\/p><p align=\"center\"><img decoding=\"async\" src=\"file:\/\/\/C:\/Users\/LENOVO\/AppData\/Local\/Temp\/lu123725foh38.tmp\/lu123725foh4m_tmp_b989f906039c784c.jpg\" name=\"Picture 1\" border=\"0\" \/><\/p><p><span style=\"color: #393939;\"> <span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\"> Profesorul Tim Palmer (Departamentul de fizic\u0103, Universitatea Oxford) ne invit\u0103 la o incitant\u0103 explorare a fundamentelor \u0219tiin\u021bifice aflate la baza conceptelor de incertitudine \u0219i haos, precum \u0219i a modului \u00een care diverse sisteme \u00ee\u0219i pot pierde brusc stabilitatea aparent\u0103, manifest\u00e2ndu-se dezordonat \u0219i imprevizibil.<\/span><\/span><\/span><\/p><p><span style=\"color: #393939;\"> <span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">Palmer argumenteaz\u0103 c\u0103 efectul fluturelui (<\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\"><i>apud<\/i><\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">\u00a0Edward Lorenz) este\u00a0<\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\"><i>profund intermitent<\/i><\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">\u00a0\u0219i, \u00een consecin\u021b\u0103,\u00a0<\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\"><i>ne putem l\u0103sa am\u0103gi\u021bi de un fals sentiment de siguran\u021b\u0103 cu privire la predictibilitatea unor sisteme precum vremea \u0219i economia<\/i><\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">, la care se mai ad\u0103ug\u0103 clima, pandemiile, ba chiar \u0219i mi\u0219carea planetelor, a c\u0103ror predictibilitate este epitomul \u201eceasornicului\u201d cosmic. Potrivit profesorului Palmer, exist\u0103 un \u201efir ro\u0219u\u201d, un element comun care leag\u0103 toate aceste sisteme:\u00a0<\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\"><i>geometria haosului<\/i><\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">, un tip de geometrie fractal\u0103 descoperit\u0103 de Ed Lorenz \u00een anii \u201960 \u0219i care ar avea aceea\u0219i importan\u021b\u0103 cu teoriile relativit\u0103\u021bii (Einstein) \u0219i teoria mecanicii cuantice (Schr\u00f6dinger \u0219i Heisenberg). Pe alt plan, geometria haosului, manifestat\u0103 \u00een structuri fractale complicate, ar de\u021bine cheia pentru \u00een\u021belegerea incertitudinii \u0219i influen\u021ba sa omniprezent\u0103 asupra lumii noastre<\/span><\/span><\/span><span style=\"color: #393939;\"><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: large;\">.<\/span><\/span><\/span><\/p><p align=\"center\"><span style=\"color: #393939;\"><span style=\"font-family: Arial, sans-serif;\">Geometrie fractal\u0103<\/span><\/span><\/p><p>\u00a0<\/p><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: small;\">Un <\/span><\/span><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: small;\"><i>fractal <\/i><\/span><\/span><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: small;\">este o figur\u0103 geometric\u0103 fragmentat\u0103 care poate fi divizat\u0103 \u00een p\u0103r\u021bi, astfel \u00eenc\u00e2t fiecare dintre acestea s\u0103 fie (cel pu\u021bin aproximativ) o copie miniatural\u0103 a \u00eentregului<\/span><\/span><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: small;\"><b>.<\/b><\/span><\/span><\/span><\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\">Elementele unui fractal sunt algoritmi care pot fi transfoma\u0163i \u00een forme \u015fi desene numai cu ajutorul calculatoarelor.<\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\">Termenul de fractal a fost introdus de Beno\u00eet Mandelbrot \u00een 1975 \u0219i este derivat din latinescul <\/span><span style=\"font-family: Arial, sans-serif;\"><i><b>fractus<\/b><\/i><\/span><span style=\"font-family: Arial, sans-serif;\">, \u00eensemn\u00e2nd <\/span><span style=\"font-family: Arial, sans-serif;\"><i><b>&#8222;fracturat&#8221;<\/b><\/i><\/span><span style=\"font-family: Arial, sans-serif;\">. Acesta observ\u0103 c\u0103 formele din natur\u0103 (mun\u021bi, nori, fulgere, fulgi de z\u0103pad\u0103, arbori etc.) nu sunt forme geometrice simple, ci forme complexe \u0219i unice.<\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\"><i>Geometria fractal\u0103 <\/i><\/span><span style=\"font-family: Arial, sans-serif;\">studiaz\u0103 formele complexe, cu aspect neregulat, care apar at\u00e2t \u00een natur\u0103, c\u00e2t \u0219i \u00een imagina\u021bia oamenilor. Ea este o ramur\u0103 a matematicii care studiaz\u0103 teoria haosului.<\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\">Geometria fractal\u0103 este arta matematicii \u0219i arat\u0103 c\u0103 ecua\u021biile matematice sunt mult mai mult dec\u00e2t o colec\u021bie de numere \u0219i de legi abstracte. \u00cen plus, fractalii sunt cele mai bune descrieri matematice a multor forme din natur\u0103.<\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\">Fractalii nu sunt numai rodul imagina\u021biei matematicienilor, ei pot fi observa\u021bi \u0219i \u00een natur\u0103 : norii, fulgii de z\u0103pad\u0103, diferite cristale din minereurile naturale, ramurile arborilor, frunzele unei ferigi, broccolii, arcele fulgerelor, lan\u021burile muntoase, re\u021beaua r\u00e2urilor, linia unui \u021b\u0103rm, dunele de nisip, sistemul vascular cu vase de s\u00e2nge, structura pl\u0103m\u00e2nilor, structura ADN-ului structura creierului <\/span><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">etc<\/span><\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\"><span style=\"font-size: medium;\">.<\/span><\/span><span style=\"font-size: medium;\">Fractalii \u00een corpul uman <\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\">Utiliz\u00e2nd grafica computerizat\u0103, formele naturale pot fi \u00een\u021belese \u00een toat\u0103 complexitatea lor. Cu instrumentele uzuale din geometria euclidian\u0103 (rigl\u0103, compas, raportor etc.) este imposibil de reprezentat astfel de figuri complexe.<\/span><\/p><p><span style=\"font-family: Arial, sans-serif;\"><i><b>Fractalul are urm\u0103toarele caracteristici:<\/b><\/i><\/span><\/p><ul><li><p><span style=\"font-family: Arial, sans-serif;\">Este <\/span><span style=\"font-family: Arial, sans-serif;\"><i><b>autosimilar <\/b><\/i><\/span><span style=\"font-family: Arial, sans-serif;\">(proprietate numit\u0103\u00a0 <\/span><span style=\"font-family: Arial, sans-serif;\"><i><b>utosimilaritate<\/b><\/i><\/span><span style=\"font-family: Arial, sans-serif;\">), fiind un ansamblu ale c\u0103rui p\u0103r\u021bi sunt \u00eentr- o bun\u0103 m\u0103sur\u0103 identice cu \u00eentregul. Chiar dac\u0103 este un obiect de o complexitate geometric\u0103, privit de la o anumit\u0103 distan\u021b\u0103, apoi f\u0103c\u00e2nd un zoom \u0219i privit din nou, imaginea care se vede este aceea\u0219i.<\/span><\/p><\/li><li><p><span style=\"font-family: Arial, sans-serif;\">Are o structur\u0103 fin\u0103, dat\u0103 de existen\u021ba detaliilor la toate sc\u0103rile.<\/span><\/p><\/li><li><p><span style=\"font-family: Arial, sans-serif;\">Este neregulat \u0219i nu poate fi descris cu limbajul geometric euclidian.<\/span><\/p><\/li><li><p><span style=\"font-family: Arial, sans-serif;\">Are dimensiunea Hausdorff mai mare dec\u00e2t dimensiunea topologic\u0103 (de\u0219i aceast\u0103 cerin\u021b\u0103 nu este \u00eendeplinit\u0103 de curbele Hilbert).<\/span><\/p><\/li><\/ul><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><i><b>Aplica\u021biile fractalilor:<\/b><\/i><\/span><\/span><\/p><ul><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">\u00cen <\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>economie<\/b><\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">, analiza pie\u021bei folose\u0219te graficele fractale. Pia\u021ba are memorie at\u00e2t pe termen scurt, c\u00e2t \u0219i pe lung \u0219i de aceea este definit\u0103 de trei atractori : cererea, oferta \u0219i structura fractal\u0103 ce va induce haosul \u00een sistem. Simularea tendin\u021bei pre\u021burilor produselor de consum prezice cu exactitate cantitatea de varia\u021bie din pre\u021bul produsului (lunar, anual etc.), dar nu poate indica pre\u021bul la o anumit\u0103 dat\u0103. Evolu\u021bia pre\u021bului ac\u021biunilor la burs\u0103, a cursului valutar \u00eentr-un anumit interval de timp este u\u0219or de modelat cu ajutorul fractalilor.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">\u00cen <\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>management<\/b><\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">, teoria haosului este folosit\u0103 pentru a realiza o serie de scenarii ale sistemului social studiat. Orice organiza\u021bie social\u0103 este privit\u0103 ca un sistem complex cu diferite nivele de stabilitate \u0219i haos. Un lider adev\u0103rat trebuie s\u0103 fie con\u0219tient c\u0103 evolu\u021bia rela\u021biilor \u00een orice comunitate este imposibil de prezis \u0219i c\u0103 singura solu\u021bie este s\u0103 ac\u021bioneze prompt atunci c\u00e2nd apar schimb\u0103ri provocatoare \u00een organiza\u021bia condus\u0103, pentru ca haosul local s\u0103 nu devin\u0103 un haos general, asemenea unei tornade.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>Grafica pe calculator <\/b><\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">este prima aplica\u0163ie major\u0103 a fractalilor, prin comprimarea unei imagini foarte mari \u00een coduri foarte mici, mai pu\u021bin de un sfert din dimensiunea ini\u021bial\u0103 a fi\u0219ierului. Comprimarea fractal\u0103 a imaginii este foarte util\u0103 \u00een multe domenii, ca de exemplu transmiterea \u00een timp real a imaginilor video prin liniile telefonice normale.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">\u00cen diferite <\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>domenii \u0219tiin\u021bifice<\/b><\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">, geometria fractal\u0103 de redare grafic\u0103 pe calculator este folosit\u0103 de oamenii de \u0219tiin\u021b\u0103 pentru a crea diferite structuri naturale. Fractali pot modela diferite forme din natur\u0103, cum ar fi nori, fulgii de z\u0103pad\u0103, cristalele, lan\u021burile montane, fulgerele, re\u021belele de r\u00e2uri etc. Cutremurele, debitele r\u00e2urilor sunt u\u0219or de modelat cu ajutorul curbelor fractale.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">\u00cen <\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>biologie \u0219i medicin\u0103<\/b><\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">, analiza fractal\u0103 este din ce \u00een ce mai folosit\u0103 la studierea sistemelor biologice, at\u00e2t la scar\u0103 macroscopic\u0103, c\u00e2t \u0219i la scar\u0103 microscopic\u0103. De exemplu, \u00een corpul uman pot fi modelate cu ajutorul fractalilor ramifica\u021biile vaselor de s\u00e2nge, structura rinichiului, structura scheletului, pl\u0103m\u00e2nii, inima, sistemul nervos, ADN-ul etc. Se pot analiza neregularit\u0103\u021bile care apar la grani\u021ba dintre un \u021besut s\u0103n\u0103tos \u0219i o tumoare.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">\u00cen <\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>meteorologie<\/b><\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">, geometria fractal\u0103 este folosit\u0103 pentru a explica de ce vremea nu poate fi anticipat\u0103 pe termen lung, ci numai pentru c\u00e2teva zile.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">\u00cen <\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>astronomie<\/b><\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">, pe termen scurt (zeci sau sute de ani) poate fi anticipat\u0103 traiectoria corpurilor cere\u0219ti, pe baza legii gravita\u021bionale a lui Newton. Pe termen foarte mare (milioane de ani) poate ap\u0103rea o comportare neliniar\u0103 \u00een dinamica orbitei corpului respectiv.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>Arta fractal\u0103 <\/b><\/span><\/span><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">este o form\u0103 de art\u0103 algoritmic\u0103 ce folose\u0219te fractalii \u0219i reprezent\u0103rile computerizate pentru a genera imagini, anima\u021bii, muzic\u0103, efecte speciale \u00een produc\u021biile cinematografice, diverse arhitecturi moderne etc.<\/span><\/span><\/p><\/li><\/ul><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\"><b>Exemple:<\/b><\/span><\/span><\/p><ul><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">Un fractal care modeleaz\u0103 structura unui profil muntos:<\/span><\/span><\/p><\/li><\/ul><p>\u00a0<\/p><ul><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">Degradarea unui bloc acrilic sub ac\u021biunea unui curent de \u00eenalt\u0103 tensiune produce un fractal figur\u0103 Lichtenberg.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">Un grup format prin agregare limitat\u0103 de difuzie, dezvoltat dintr-o solu\u021bie de sulfat de cupru \u00eentr-o celul\u0103 electrolitic\u0103.<\/span><\/span><\/p><\/li><li><p><span style=\"font-family: Times New Roman, serif;\"><span style=\"font-size: medium;\">Ob\u021binerea unor ace de amalgam de argint \u00een reac\u021bia dintre mercur \u0219i azotat de argint.<\/span><\/span><\/p><\/li><\/ul><p>\u00a0<\/p><p>Bibliografie:<\/p><ol><li>https:\/\/ro.wikipedia.org\/wiki\/Fractal<\/li><li>https:\/\/teoria-haosului-fractali0.webnode.ro\/<\/li><li>https:\/\/www.academia.edu\/33026293\/Teoria_fractalilor_si_teoria_haosului<\/li><\/ol>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>AN \u0218COLAR 2023-2024 IPT_Protectia mediului si matematica Implementarea instrumentelor digitale moderne \u00een activit\u0103\u0163i de predare \u2013 \u00eenv\u0103\u0163are-evaluare, cu aplicabilitate pentru &hellip; <\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.10 - 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