{"id":331927,"date":"2024-04-12T08:18:01","date_gmt":"2024-04-12T07:18:01","guid":{"rendered":"https:\/\/liked.hu\/old\/?p=331927"},"modified":"2024-04-12T08:19:34","modified_gmt":"2024-04-12T07:19:34","slug":"a-hangya-paradoxona-egy-gumikotelen-ami-darabokra-tepi-a-logikat-es-ellentmond-a-jozan-esznek","status":"publish","type":"post","link":"https:\/\/liked.hu\/old\/erdekes\/a-hangya-paradoxona-egy-gumikotelen-ami-darabokra-tepi-a-logikat-es-ellentmond-a-jozan-esznek\/","title":{"rendered":"A hangya paradoxona egy gumik\u00f6t\u00e9len, ami darabokra t\u00e9pi a logik\u00e1t, \u00e9s ellentmond a j\u00f3zan \u00e9sznek"},"content":{"rendered":"\n<p>K\u00e9pzelj el egy hangy\u00e1t, ahogy egy 1 kilom\u00e9ter hossz\u00fa gumik\u00f6t\u00e9len m\u00e1szik, 1 centim\u00e9ter\/m\u00e1sodperc sebess\u00e9ggel. Tov\u00e1bb\u00e1 k\u00e9pzeld el, hogy a k\u00f6t\u00e9l minden m\u00e1sodpercben 1 kilom\u00e9tert ny\u00falik. Vajon a hangya el\u00e9ri valaha is a k\u00f6t\u00e9l v\u00e9g\u00e9t?<\/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>A legt\u00f6bben azt mondan\u00e1k, hogy nem. Ha a hangya m\u00e1sodpercenk\u00e9nt csak 1 centim\u00e9tert halad, mik\u00f6zben a k\u00f6t\u00e9l 1 kilom\u00e9terrel ny\u00falik, akkor az lehetetlen. A matematika azonban m\u00e1st mond: a hangya igen is el\u00e9ri a v\u00e9g\u00e9t.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"1200\" height=\"630\" src=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/04\/Hangya-paradoxon.jpg\" alt=\"Hangya paradoxon\" class=\"wp-image-331928\" srcset=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/04\/Hangya-paradoxon.jpg 1200w, https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/04\/Hangya-paradoxon-768x403.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/figure>\n\n\n\n<p>A szeml\u00e9ltet\u00e9s kedv\u00e9\u00e9rt tegy\u00fck a hangy\u00e1t a k\u00f6t\u00e9l k\u00f6zep\u00e9re. Hagyjuk, hogy ott \u00e1lljon, \u00e9s ne mozduljon. Amikor a k\u00f6t\u00e9l egy m\u00e1sodperc alatt 1 kilom\u00e9terrel megny\u00falik, a hangya tov\u00e1bbra is a k\u00f6t\u00e9l k\u00f6zep\u00e9n marad. \u00c9s egy m\u00e1sodperc m\u00falva is. V\u00e9g\u00fcl is a k\u00f6t\u00e9l mindk\u00e9t ir\u00e1nyba ny\u00falik, nem csak az egyik ir\u00e1nyba. Ha most elind\u00edtjuk a hangy\u00e1t, kider\u00fcl, hogy m\u00e1r t\u00faljutott a k\u00f6t\u00e9l fel\u00e9n, \u00e9s lassan (katasztrof\u00e1lisan lassan, ha pontosak akarunk lenni), de biztosan halad a c\u00e9l fel\u00e9.<\/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=\"1200\" height=\"675\" src=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/04\/doki.webp\" alt=\"doki\" class=\"wp-image-331929\" srcset=\"https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/04\/doki.webp 1200w, https:\/\/liked.hu\/old\/wp-content\/uploads\/2024\/04\/doki-768x432.webp 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/figure>\n\n\n\n<p>Val\u00f3j\u00e1ban a feladat meglehet\u0151sen bonyolult, \u00e9s nem iskol\u00e1s gyerekeknek val\u00f3, mivel sorozatokkal van dolgunk. Azonban vess\u00fcnk egy pillant\u00e1st a l\u00e9nyegre a bizony\u00edt\u00e1s elm\u00e9ly\u00edt\u00e9se n\u00e9lk\u00fcl.<\/p>\n\n\n\n<p>Teh\u00e1t a k\u00f6t\u00e9l kezdeti hossza 1 km = 1000 m = 100 000 cm.<\/p>\n\n\n\n<p>Az els\u0151 m\u00e1sodpercben a hangya 1 centim\u00e9tert m\u00e1szik meg, azaz a k\u00f6t\u00e9l 1\/100 000 r\u00e9sz\u00e9t. A m\u00e1sodik m\u00e1sodpercben, miut\u00e1n a k\u00f6t\u00e9l 1 kilom\u00e9terrel megny\u00falt, a k\u00f6t\u00e9l 1\/200 000 r\u00e9sz\u00e9t m\u00e1ssza meg, \u00e9s \u00edgy tov\u00e1bb.<\/p>\n\n\n\n<p>\u00d6sszegezz\u00fck \u00e9s megkapjuk: 1\/100 000 + 1\/200 000 + 1\/300 000 + &#8230; = 1\/100 000 \u2022 (1+1\/2+1\/3+1\/4+&#8230;)<\/p>\n\n\n\n<p>A figyelmes olvas\u00f3 \u00e9szreveheti, hogy a z\u00e1r\u00f3jelben egy v\u00e9gtelen, sz\u00e9tter\u00fcl\u0151 sorozatot kaptunk. Ennek \u00f6sszege folyamatosan n\u00f6vekszik a v\u00e9gtelen fel\u00e9, ami azt jelenti, hogy el\u0151bb-ut\u00f3bb a hangya m\u00e9giscsak t\u00e9nyleg el\u00e9ri a k\u00f6t\u00e9l v\u00e9g\u00e9t.<\/p>\n\n\n\n<p>Csakhogy ez a sorozat nagyon lassan n\u00f6vekszik, az els\u0151 sz\u00e1z tag \u00f6sszege alig haladja meg az 5-\u00f6t.<\/p>\n\n\n\n<p>Teh\u00e1t amikor azt mondjuk, hogy a hangya el\u00e9ri a k\u00f6t\u00e9l v\u00e9g\u00e9t, egy kis fenntart\u00e1ssal kell kezeln\u00fcnk: a hangy\u00e1nak halhatatlannak kell lennie. Ahogy az Univerzumunknak is, ami norm\u00e1l \u00e1llapotban v\u00e9ve val\u00f3sz\u00edn\u0171leg hamarabb hunyna ki, minthogy a hangya el\u00e9rje a k\u00f6t\u00e9l v\u00e9g\u00e9t.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Ha tetszett a feladat, akkor felteszek egy m\u00e1sik k\u00e9rd\u00e9st: pr\u00f3b\u00e1ld meg kisz\u00e1molni, hogy mennyi id\u0151be telik, am\u00edg a hangya el\u00e9ri a k\u00f6t\u00e9l v\u00e9g\u00e9t!<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A matematika n\u00e9ha szembe megy a j\u00f3zan \u00e9sszel.<\/p>\n","protected":false},"author":22,"featured_media":331928,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"buzzeditor_post_format":""},"categories":[23],"tags":[1657,9901,2719],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.6.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A hangya paradoxona egy gumik\u00f6t\u00e9len, ami 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