{"id":325920,"date":"2024-03-11T01:48:11","date_gmt":"2024-03-11T00:48:11","guid":{"rendered":"https:\/\/liked.hu\/old\/?p=325920"},"modified":"2024-03-11T01:48:14","modified_gmt":"2024-03-11T00:48:14","slug":"kerekparadoxon-amikor-az-elmeletileg-lehetetlen-siman-megvalosul-a-valosagban","status":"publish","type":"post","link":"https:\/\/liked.hu\/old\/erdekes\/kerekparadoxon-amikor-az-elmeletileg-lehetetlen-siman-megvalosul-a-valosagban\/","title":{"rendered":"Ker\u00e9kparadoxon:\u00a0amikor az elm\u00e9letileg lehetetlen sim\u00e1n megval\u00f3sul a val\u00f3s\u00e1gban"},"content":{"rendered":"\n<p>Az \u00e9let tele van paradoxonokkal, amikre sokszor r\u00e1 se heder\u00edt\u00fcnk. N\u00e9ha az elm\u00e9let egyszer\u0171en nem egyezik a gyakorlattal. \u00cdme egy p\u00e9lda.<\/p>\n\n\n\n\n<div style=\"float:none;margin:0px 0 0px 0;text-align:center;\">\n<div class=\"mobileShowkakettes\"><div class=\"mobileShowka2\"><div style=\"padding-top:0px;padding-bottom:15px;min-height: 300px;\"><div class=\"hirdetes\">HIRDET\u00c9S<\/div>\n<!-- 300lista -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:250px\"\n     data-ad-client=\"ca-pub-9424088931673893\"\n     data-ad-slot=\"8471340766\"><\/ins>\n<script async>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><\/div><\/div><\/div>\n\n\n\n\n<p>K\u00e9pzelj el egy aut\u00f3gumit. Van a felni, amire a gumiabroncsot szerelt\u00e9k. A felni \u00e9s a gumiabroncs, most m\u00e1r egy egys\u00e9get alkotva &#8211; a ker\u00e9k &#8211; szinkronban g\u00f6rd\u00fcl, cs\u00fasz\u00e1s n\u00e9lk\u00fcl. A paradoxon az, hogy a felni \u00e9s a gumiabroncsnak m\u00e1s a sugara, \u00e9s emiatt m\u00e1s a ker\u00fclet\u00fck is, de m\u00e9gis ugyanazt a t\u00e1vot teszik meg. Hogy lehet ez?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"1200\" height=\"800\" src=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/03\/kerek.webp\" alt=\"kerek\" class=\"wp-image-325921\" srcset=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/03\/kerek.webp 1200w, https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/03\/kerek-768x512.webp 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Ezt a mechanikai-matematikai paradoxont m\u00e1r az \u00f3korban is \u00e9szrevett\u00e9k, de el\u0151sz\u00f6r Arisztotel\u00e9sz \u00edrta le \u00e9s tanulm\u00e1nyozta a &#8222;Mechanika&#8221; c\u00edm\u0171 m\u0171v\u00e9ben. Ez\u00e9rt a ker\u00e9k paradoxon\u00e1t Arisztotel\u00e9sz kerek\u00e9nek is nevezik. K\u00e9s\u0151bb Galileo Galilei is foglalkozott ezzel a paradoxonnal, de v\u00e9g\u00fcl a francia Jean Jacques de Meran magyar\u00e1zta meg 1715-ben.<\/p><\/blockquote>\n\n\n\n<style>.wp-block-quote {border-left: 3px solid black !important;text-align: left;font-size: 18px;}blockquote:before,blockquote:after{display:none;}<\/style>\n\n\n\n<p>Teljesen egy\u00e9rtelm\u0171, hogy ha fogunk egy felnit \u00e9s v\u00e9giggur\u00edtjuk a homokon, hogy teljes fordulatot tegyen, majd fogjuk a gumiabroncsot \u00e9s ugyan\u00edgy v\u00e9giggur\u00edtjuk mellette egy teljes fordulatot, akkor a gumiabroncs nyoma hosszabb lesz. De mi\u00e9rt tesznek meg ugyanazt a t\u00e1vot, ha a gumiabroncs a felnire van szerelve?<\/p>\n\n\n\n\n<div style=\"float:none;margin:0px 0 0px 0;text-align:center;\">\n<div class=\"mobileHideke5\"><div style=\"margin-top:25px;\"><div class=\"hirdeteshatter\"><div style=\"display: inline-block;width: 50%;min-width:305px;vertical-align: top;\"><div class=\"hirdetes\">HIRDET\u00c9S<\/div>\n<!-- LikedQ51 -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:250px\"\n     data-ad-client=\"ca-pub-9424088931673893\"\n     data-ad-slot=\"8284063326\"><\/ins>\n<script async>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><div style=\"display: inline-block;width: 50%;min-width:305px;vertical-align: top;\"><div class=\"hirdetes\">HIRDET\u00c9S<\/div>\n<!-- LikedQ52 -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:250px\"\n     data-ad-client=\"ca-pub-9424088931673893\"\n     data-ad-slot=\"2840164950\"><\/ins>\n<script async>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><\/div><\/div><\/div>\n<div style=\"display:flex;flex-direction:column;\"><div class=\"mobileShowka5\"><div style=\"padding-top:10px;padding-bottom:10px;min-height: 300px;\"><div class=\"hirdetes\">HIRDET\u00c9S<\/div>\n<!-- LikedQ5M -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:250px\"\n     data-ad-client=\"ca-pub-9424088931673893\"\n     data-ad-slot=\"9022429928\"><\/ins>\n<script async>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><\/div><\/div><\/div>\n\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"551\" height=\"173\" src=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/03\/orig.gif\" alt=\"orig\" class=\"wp-image-325922\"\/><\/figure>\n\n\n\n<p>A fenti anim\u00e1ci\u00f3 szeml\u00e9letesen mutatja, hogy az A \u00e9s B pontok \u00e1ltal megtett utak (k\u00e9k \u00e9s piros sz\u00ednnel jel\u00f6lve) egyenl\u0151ek. Azonban ez els\u0151re lehetetlennek t\u0171nik, hiszen a ker\u00fclet hossza 2r\u03c0, \u00e9s a felni sugara kisebb, mint a gumiabroncs k\u00fcls\u0151 sugara. A k\u00e9k \u00fatnak r\u00f6videbbnek kellene lennie! Ellenkez\u0151 esetben azt is \u00e1ll\u00edthatn\u00e1nk, hogy egy 5 cm ker\u00fclet\u0171 ker\u00e9k ugyanazt a t\u00e1vols\u00e1got tudja megtenni egy fordulat alatt, mint egy 5 m\u00e9ter ker\u00fclet\u0171 ker\u00e9k!<\/p>\n\n\n\n<p><strong>Ez azonban sem a gyakorlatban, sem az elm\u00e9letben nem lehets\u00e9ges. Teh\u00e1t mi a helyzet?<\/strong><\/p>\n\n\n\n<p>Ahhoz, hogy meg\u00e9rts\u00fck, mi t\u00f6rt\u00e9nik val\u00f3j\u00e1ban, meg kell vizsg\u00e1lnunk a k\u00e9t kiv\u00e1lasztott pont, a felni perem\u00e9n \u00e9s a gumiabroncs k\u00fcls\u0151 sugar\u00e1n l\u00e9v\u0151 pontok mozg\u00e1sp\u00e1ly\u00e1j\u00e1t.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"1200\" height=\"371\" src=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/03\/paraxodon.webp\" alt=\"paraxodon\" class=\"wp-image-325923\" srcset=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/03\/paraxodon.webp 1200w, https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/03\/paraxodon-768x237.webp 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/figure>\n\n\n\n<p>A p\u00e1ly\u00e1kat (k\u00e9k \u00e9s piros), amiket a pontok le\u00edrnak, cikloisnak nevezz\u00fck. K\u00f6nnyen \u00e9szrevehet\u0151, hogy ezeknek a p\u00e1ly\u00e1knak a hossza nem azonos. A k\u00e9k hosszabb, mint a piros.<\/p>\n\n\n\n<p>\u00c9s min\u00e9l kisebb a ker\u00e9k felnij\u00e9nek sugara, ann\u00e1l jobban kiegyenesedik a piros ciklois, a z\u00f6ld egyenes fel\u00e9 t\u00f6rekedve.<\/p>\n\n\n\n<p>Teh\u00e1t val\u00f3j\u00e1ban itt nincs paradoxon. Csak a &#8222;p\u00e1lya&#8221; \u00e9s az &#8222;elmozdul\u00e1s&#8221; fogalmai k\u00f6z\u00f6tt van egy kis kevered\u00e9s. A k\u00e9t pont elmozdul\u00e1sa val\u00f3ban azonos, de a megtett \u00fat nem.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>Elmozdul\u00e1s:<\/strong> a pont kiindul\u00f3 \u00e9s v\u00e9ghelyzet\u00e9t \u00f6sszek\u00f6t\u0151 ir\u00e1ny\u00edtott egyenes.<\/p><p><strong>P\u00e1lya:<\/strong> a pont \u00e1ltal megtett \u00fat hossza (az a vonal, amely ment\u00e9n a pont mozog).<\/p><\/blockquote>\n\n\n\n<p>K\u00e9pzeld el, hogy Budapestr\u0151l Debrecenbe utazol. Mehetsz Miskolc \u00e9s Ny\u00edregyh\u00e1za \u00e9rint\u00e9s\u00e9vel, de Szolnok, Kecskem\u00e9t \u00e9s Beretty\u00f3\u00fajfalu \u00e9rint\u00e9s\u00e9vel is. A t\u00e1vols\u00e1g (elmozdul\u00e1s) Budapest \u00e9s Debrecen k\u00f6z\u00f6tt azonos lesz, de a megtett \u00fat elt\u00e9r\u0151. A ker\u00e9k paradoxona pontosan ezen alapul.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Elvileg nem t\u00f6rt\u00e9nhetne meg, de m\u00e9gis.<\/p>\n","protected":false},"author":22,"featured_media":325924,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"buzzeditor_post_format":""},"categories":[23],"tags":[8700,5823,4394],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.6.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ker\u00e9kparadoxon:\u00a0amikor az elm\u00e9letileg lehetetlen sim\u00e1n megval\u00f3sul a val\u00f3s\u00e1gban<\/title>\n<meta name=\"description\" content=\"Elvileg nem t\u00f6rt\u00e9nhetne meg, de m\u00e9gis.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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