[{"@context":"https:\/\/schema.org\/","@type":"Article","@id":"https:\/\/www.zopz.sk\/matematicke-problemy-ktore-stale-cakaju-na-riesenie\/#Article","mainEntityOfPage":"https:\/\/www.zopz.sk\/matematicke-problemy-ktore-stale-cakaju-na-riesenie\/","headline":"Matematick\u00e9 probl\u00e9my, ktor\u00e9 st\u00e1le \u010dakaj\u00fa na rie\u0161enie","name":"Matematick\u00e9 probl\u00e9my, ktor\u00e9 st\u00e1le \u010dakaj\u00fa na rie\u0161enie","description":"V\u00e4\u010d\u0161ina \u0161tudentov vzdych\u00e1 u\u017e len pri spomenut\u00ed tejto vedy, n\u00e1jdu sa v\u0161ak samozrejme aj tak\u00ed, ktor\u00ed sa v nej vy\u017e\u00edvaj\u00fa.…","datePublished":"2020-01-09","dateModified":"2023-04-28","author":{"@type":"Person","@id":"https:\/\/www.zopz.sk\/author\/#Person","name":"","url":"https:\/\/www.zopz.sk\/author\/","identifier":1,"image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/92dd6dcbda4dc4d3f89fcc9fa0e3d3cb?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/92dd6dcbda4dc4d3f89fcc9fa0e3d3cb?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"zopz.sk","logo":{"@type":"ImageObject","@id":"\/logo.png","url":"\/logo.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/www.zopz.sk\/wp-content\/uploads\/img_a309734_w16884_t1580221120.jpg","url":"https:\/\/www.zopz.sk\/wp-content\/uploads\/img_a309734_w16884_t1580221120.jpg","height":0,"width":0},"url":"https:\/\/www.zopz.sk\/matematicke-problemy-ktore-stale-cakaju-na-riesenie\/","about":["Veda"],"wordCount":450,"articleBody":"V\u00e4\u010d\u0161ina \u0161tudentov vzdych\u00e1 u\u017e len pri spomenut\u00ed tejto vedy, n\u00e1jdu sa v\u0161ak samozrejme aj tak\u00ed, ktor\u00ed sa v nej vy\u017e\u00edvaj\u00fa. Ak si ale mysl\u00edte, \u017ee v nej u\u017e nemaj\u00fa \u010do nov\u00e9 n\u00e1js\u0165, ste na obrovskom omyle. Na matematick\u00fd d\u00f4kaz niektor\u00fdch komplikovane jednoduch\u00fdch (\u010di naopak, jednoducho komplikovan\u00fdch) \u00faloh, s\u00fa dokonca vyp\u00edsan\u00e9 mili\u00f3nov\u00e9 odmeny. Po dlh\u00e9 roky bola tou najstar\u0161ou nedok\u00e1zanou rovnicou Fermentova veta, ktor\u00e1 vyzer\u00e1 takto: xn + yn = zn, pri\u010dom dok\u00e1za\u0165 bolo treba, \u017ee pre v\u0161etky n v\u00e4\u010d\u0161ie ako 2 nem\u00f4\u017eu by\u0165 x, y a z cel\u00e9 \u010d\u00edsla. Je to ove\u013ea zlo\u017eitej\u0161ie ako to vyzer\u00e1, no nakoniec sa to v roku 1995 predsa len podarilo. Titul \u201eNajdlh\u0161ie nevyrie\u0161en\u00e1\u201c sa teda dostal k nov\u00e9mu majite\u013eovi, a t\u00fdm je Goldbachova domnienka. Rusko-nemeck\u00fd vedec tvrdil, \u017ee v\u0161etko v\u00e4\u010d\u0161ie ako 2 je v podstate s\u00fa\u010dtom dvoch prvo\u010d\u00edsel. Ke\u010f\u017ee sa v\u0161ak nesk\u00f4r zistilo, \u017ee 1 medzi ne nepatr\u00ed, muselo sa upravi\u0165. Dnes je teda tak\u00e9to: Ka\u017ed\u00e9 p\u00e1rne \u010d\u00edslo v\u00e4\u010d\u0161ie ako 4 sa d\u00e1 rozlo\u017ei\u0165 na s\u00fa\u010det dvoch prvo\u010d\u00edsel. V\u010faka modernej technol\u00f3gi\u00ed sme ho mohli do ur\u010ditej miery overi\u0165, st\u00e1le ale ch\u00fdba definit\u00edvne potvrdenie jeho pravdivosti. \u010eal\u0161ou z\u00e1le\u017eitos\u0165ou je ist\u00e1 postupnos\u0165 \u010d\u00edslic, ktor\u00fa pozn\u00e1me pod viacer\u00fdmi n\u00e1zvami, najpou\u017e\u00edvanej\u0161\u00edm z nich je Collatzov algoritmus. Predstavuje \u0161pecifick\u00fd syst\u00e9m upravovania \u010d\u00edsel. Zoberme si nezn\u00e1me n. Ak je p\u00e1rne, vydel\u00edme ho dvoma, ak je nep\u00e1rne vyn\u00e1sob\u00edme ho troma a pripo\u010d\u00edtame jeden. Toto opakujeme pok\u00fdm sa d\u00e1. Dosia\u013e sme sa zaka\u017ed\u00fdm dostali ku kone\u010dn\u00e9mu v\u00fdsledku 1. V\u0161eobecn\u00e9 pravidlo sme v\u0161ak zatia\u013e nesformulovali. Potom s\u00fa tu e\u0161te tak\u00e9 orie\u0161ky, v ktor\u00fdch ist\u00e9 rozl\u00fasknutie u\u017e niektor\u00ed logici ani neveria. Napr\u00edklad Prvo\u010d\u00edseln\u00e9 dvoji\u010dky, ktor\u00e9 h\u013eadaj\u00fa tak\u00e9to dvojice s rozdielom pr\u00e1ve 2. V tomto pr\u00edpade to matematici prosto pova\u017euj\u00fa za nie\u010do nemo\u017en\u00e9, alebo aspo\u0148 mimo n\u00e1\u0161ho ch\u00e1pania, ke\u010f\u017ee tieto p\u00e1ry m\u00f4\u017eu \u00eds\u0165 doslova donekone\u010dna. Alebo Probl\u00e9m P verzus NP, ktor\u00fd sa u\u017e trocha prel\u00edna s programovan\u00edm. Jeho ot\u00e1zka spo\u010d\u00edva v tom \u010di po\u010d\u00edta\u010d, ktor\u00fd dok\u00e1\u017ee r\u00fdchlo skontrolova\u0165 \u010di je rie\u0161enie pr\u00edkladu spr\u00e1vne, dok\u00e1\u017ee takisto r\u00fdchlo vyrie\u0161i\u0165 ten ist\u00fd pr\u00edklad samostatne. Odpove\u010f by mala znie\u0165 nie, no d\u00f4kaz, ako inak, ch\u00fdba. P vs. NP je dokonca zaraden\u00fd medzi probl\u00e9my tis\u00edcro\u010dia.                                                                                                                                                                                                                                                                                                                                                                                        4.5\/5 - (11 votes)        "},{"@context":"https:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Matematick\u00e9 probl\u00e9my, ktor\u00e9 st\u00e1le \u010dakaj\u00fa na rie\u0161enie","item":"https:\/\/www.zopz.sk\/matematicke-problemy-ktore-stale-cakaju-na-riesenie\/#breadcrumbitem"}]}]