{"id":450,"date":"2024-12-22T23:13:34","date_gmt":"2024-12-22T20:13:34","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/caglart\/?p=450"},"modified":"2025-01-18T23:23:28","modified_gmt":"2025-01-18T20:23:28","slug":"pisagor-zeno-g-galileinin-babasi-ve-kuvantum-tunellemesi-quantum-tunelling","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/caglart\/2024\/12\/22\/pisagor-zeno-g-galileinin-babasi-ve-kuvantum-tunellemesi-quantum-tunelling\/","title":{"rendered":"Pisagor, Zeno, G. Galilei\u2019nin babas\u0131 ve Kuvantum T\u00fcnellemesi (\u2018Quantum Tunelling\u2019)"},"content":{"rendered":"

Fizik \u201312\u2013<\/p>\n

\u0130\u00e7erik: Her \u015feyde her \u015fey var m\u0131?<\/p>\n

\u00d6n not: Bu yaz\u0131da \u221e simgesi, \u2018bilinen Ger\u00e7ek Say\u0131lar\u0131n en b\u00fcy\u00fc\u011f\u00fc\u2019 anlam\u0131nda kullan\u0131lacakt\u0131r.
\nBak\u0131n\u0131z; 3\u2019\u00fcn karesi 9, 4\u2019\u00fcn karesi 16, 16\u2019ya 9\u2019u ekle 25 ve 25 de 5\u2019in karesi. Demek ki,
\nE\u015fitlik 1: 3\u00b2+4\u00b2=5\u00b2.
\nAyn\u0131 \u015fekilde; 6\u2019n\u0131n karesi 36, 8\u2019in karesi 64, 64\u2019e 36\u2019y\u0131 ekle 100 ve 100 de 10\u2019un karesi. Demek ki, E\u015fitlik 2: 6\u00b2+8\u00b2=10\u00b2.
\nBu son e\u015fitli\u011fin her iki taraf\u0131nda 4\u2019\u00fcn kat\u0131 olan Do\u011fal Say\u0131lar var.
\n4(3\u00b2+4\u00b2)=4(5\u00b2).
\nSon e\u015fitli\u011fin her iki taraf\u0131n\u0131 4\u2019e b\u00f6lersek
\n3\u00b2+4\u00b2=5\u00b2
\nelde edilir.
\nBuradan da \u015f\u00f6yle bir \u00f6neri \u00e7\u0131karsanabilir: A\u00b2+B\u00b2=C\u00b2 ise N herhangi bir s\u0131f\u0131rdan farkl\u0131 Do\u011fal Say\u0131 olmak ko\u015fuluyla
\n(NA)\u00b2+(NB)\u00b2=(NC)\u00b2
\noldu\u011fu, kolay bir T\u00fcmevar\u0131m Y\u00f6ntemi uygulamas\u0131yla g\u00f6sterilebilir. (*)
\nDemek ki, A\u00b2+B\u00b2=C\u00b2 e\u015fitli\u011fini sa\u011flayan \u221e kadar A, B ve C gibi Do\u011fal Say\u0131 \u00fc\u00e7l\u00fc\u011f\u00fc mevcuttur. Bu t\u00fcr say\u0131lara Pisagor \u00dc\u00e7l\u00fc(k)leri denir. (**)
\n\u015euna da dikkat etmeli;
\n3\u00b2+4\u00b2=4\u00b2+3\u00b2=5\u00b2 yani 4\u00b2+3\u00b2=5\u00b2.
\nSon e\u015fitli\u011fin iki taraf\u0131n\u0131 da 4 ile \u00e7arparsak e\u015fitlik bozulmaz;
\n(2×4)\u00b2+(2×3)\u00b2=(2×5)\u00b2 yani
\n8\u00b2+6\u00b2=10\u00b2
\nelde edilir. Ama \u015fu da bir Pisagor \u00dc\u00e7l\u00fc\u011f\u00fc\u2019d\u00fcr;
\n8\u00b2+15\u00b2=17\u00b2
\nve buradan da yeni bir \u221e kadar Pisagor \u00dc\u00e7l\u00fc\u011f\u00fc elde edilebilir.
\nDahas\u0131, herhangi bir Pisagor \u00dc\u00e7l\u00fc\u011f\u00fc herhangi bir (pozitif veya negatif) Ger\u00e7ek Say\u0131 ile \u00e7arp\u0131ld\u0131\u011f\u0131nda da yeni Pisagor \u00dc\u00e7l\u00fckler elde edilir.
\nPisagor\u2019dan \u00f6nceki binlerce y\u0131ld\u0131r bilinen bu ger\u00e7eklerin \u00fc\u00e7gen \u015fekiller ile ilgisini ilk fark eden(lerden biri ?) Pisagor idi yaz\u0131l\u0131 belgelere g\u00f6re.
\nDik A\u00e7\u0131\u2019l\u0131 \u00dc\u00e7genler (Dik \u00dc\u00e7genler) ba\u011flam\u0131nda, herhangi bir Pisagor \u00dc\u00e7l\u00fc\u011f\u00fc\u2019n\u00fc her hangi bir parametre ile \u00e7arpmak, ilgili \u00fc\u00e7genin kenar uzunluklar\u0131n\u0131 ayn\u0131 parametre ile \u00e7arpmak, yani o \u00fc\u00e7geni k\u00fc\u00e7\u00fcltmek ya da b\u00fcy\u00fcltmek anlam\u0131na gelmekteydi. Bu s\u0131rada, a\u00e7\u0131lar\u0131n ayn\u0131 kald\u0131\u011f\u0131n\u0131 ak\u0131lda tutmal\u0131.
\nDahas\u0131, en k\u00fc\u00e7\u00fck Tam Say\u0131\u2019s\u0131 tek, \u00e7ift veya asal olan Pisagor \u00dc\u00e7l\u00fckleri ile Dik \u00dc\u00e7genler aras\u0131nda Bire-Bir G\u00f6nderim (\u2018One to One Mapping\u2019) ili\u015fkisi yoktur. Bu ili\u015fki \u00d6rten G\u00f6nderim (\u2018Onto Mapping\u2019) olarak nitelenebilir.
\n\u00d6te yandan \u015fu soru da hayli ilgi \u00e7ekicidir: A, B ve C\u2019nin Ger\u00e7ek Say\u0131 olmas\u0131 halinde de yukar\u0131daki e\u015fitlikler sa\u011flan\u0131r m\u0131 acaba? Gayet tabii! L\u00e2kin bir \u015fartla; karek\u00f6k almay\u0131 biliyor olmak yetmez. Karek\u00f6k alarak bulunacak sonucun da sonlu bir Ger\u00e7ek Say\u0131 olmas\u0131 gerekir. Her Ger\u00e7ek Say\u0131 \u00e7iftini birbirine b\u00f6lerek \u00e7e\u015fitli sonlu veya sonsuz Ger\u00e7ek Say\u0131lar elde etmek m\u00fcmk\u00fcnd\u00fcr. \u00d6rne\u011fin 1\u2019i 3\u2019e b\u00f6lerseniz 0,333\u2026 elde edersiniz. 0,333\u2026 sonlu bir say\u0131 de\u011fil, sonu olmayan yani sonsuz bir say\u0131d\u0131r. Ba\u015fka \u00f6rnek \u015fudur; 0,999\u2026 sonsuz bir say\u0131d\u0131r ama 1 sonlu bir say\u0131d\u0131r. Ayr\u0131ca, E\u015fitlik 1 ve 2 sayesinde tan\u0131mlanan Pisagor \u00dc\u00e7l\u00fckleri dizisi de sonsuzdur; yani, orada son \u00fc\u00e7l\u00fcn\u00fcn ne oldu\u011fu bilinemez, saptanamaz.
\nEvet, tarihsel belgelere g\u00f6re ilk kez \u015fu bizim pek sevdi\u011fimiz Zeno\u2019nun kulland\u0131\u011f\u0131 anlamdaki sonsuz kavram\u0131n\u0131 tam olarak kar\u015f\u0131layabilecek kapasiteye sahip bir s\u00f6zc\u00fck ne g\u00fczel T\u00fcrk\u00e7e\u2019mizde var, ne \u0130ngilizce\u2019de, ne Latince\u2019de, ne de hatta Grek\u00e7e\u2019de. (***)
\nLatince\u2019deki \u2018finitum\u2019 s\u00f6zc\u00fc\u011f\u00fc g\u00fczel T\u00fcrk\u00e7e\u2019mizde \u2018bitmi\u015f\u2019 anlam\u0131na gelmektedir (****), \u0130ngilizce\u2019deki \u2018finite\u2019 s\u00f6zc\u00fc\u011f\u00fc de bitimli, sonlu, s\u0131n\u0131rl\u0131 anlam\u0131na gelmektedir. Latince\u2019deki \u2018infinitum\u2019 s\u00f6zc\u00fc\u011f\u00fcn\u00fcn Grek\u00e7e kar\u015f\u0131l\u0131\u011f\u0131 ise \u2018\u03ac\u03c0\u03b5\u03b9\u03c1\u03bf\u2019 (\u2018\u03acperio\u2019) olup sonsuz, yani sonu olmayan anlam\u0131ndad\u0131r. \u0130ngilizce\u2019deki \u2018endless\u2019 s\u00f6zc\u00fc\u011f\u00fc de sonsuz anlam\u0131ndad\u0131r. Demek ki, 1\/3, 2\/3, 2\u2019nin karek\u00f6k\u00fc, altm\u0131\u015f derecenin sin\u00fcs\u00fc gibi say\u0131lar sonsuzdur ve bir, \u00fc\u00e7 bu\u00e7uk ve virg\u00fclden sonra basama\u011f\u0131 olmayan Tam Say\u0131lar ile virg\u00fclden sonraki basamak say\u0131s\u0131 s\u0131n\u0131rl\u0131 olan Ger\u00e7ek Say\u0131lar sonlu say\u0131lard\u0131r.
\nA\u00e7\u0131kt\u0131r ki, Dik \u00dc\u00e7gen Geometri\u2019sinde kenar uzunluklar\u0131n\u0131n Tam Say\u0131 m\u0131, Ger\u00e7ek Say\u0131 m\u0131, sonlu say\u0131 m\u0131, sonsuz say\u0131 m\u0131 oldu\u011fu ile hemen hi\u00e7 ilgilenilmez. Demek ki, birbirinden farkl\u0131 Dik \u00dc\u00e7genlerin say\u0131s\u0131 birbirinden farkl\u0131 Pisagor \u00dc\u00e7l\u00fckleri\u2019nin say\u0131s\u0131ndan fazlad\u0131r.
\nPisagor da, ihtimalen b\u00fct\u00fcn bu ger\u00e7ekleri bilmekteydi. Hatta, yine ihtimaldir ki, Pisagor\u2019dan ba\u015fkalar\u0131 da Dik \u00dc\u00e7gen kenar uzunluklar\u0131 aras\u0131ndaki ili\u015fkiyi (Pisagor\u2019dan ba\u011f\u0131ms\u0131z olarak) bulgulam\u0131\u015ft\u0131. Ama, sadece Pisagor\u2019a ili\u015fkin yaz\u0131l\u0131 belge varl\u0131\u011f\u0131 nedeniyle ilgili bulu\u015f bilgisi onun ad\u0131yla kaydedilmi\u015ftir.
\nGelgelelim, ayn\u0131 kay\u0131tlara g\u00f6re, Pisagor\u2019un Fizik ile ilgisi genellikle g\u00f6z ard\u0131 edilir. Pisagor, telli \u00e7alg\u0131larda sesin olu\u015fumu ile yak\u0131ndan ilgilenmi\u015ftir ve bir telden yay\u0131lan sesin harmonik oldu\u011funu yani ayn\u0131 anda \u221e kadar farkl\u0131 dalga boyuna sahip ses \u00e7\u0131kt\u0131\u011f\u0131n\u0131 bulgulam\u0131\u015ft\u0131r. Dahas\u0131, bunlardan en bas olan\u0131n\u0131n yar\u0131 dalga boyu, tel uzunlu\u011fu kadar olmal\u0131; daha tiz (ince) olanlar\u0131n dalga boyu da bu en bas (kal\u0131n), temel sesin bir bu\u00e7ukda biri, ikide biri (yar\u0131s\u0131), iki bu\u00e7ukda biri, \u2026 olmal\u0131d\u0131r. \u00c7\u00fcnk\u00fc, teldeki titre\u015fimlerin bo\u011fum (\u2018node\u2019) denen k\u0131m\u0131lt\u0131s\u0131zl\u0131\u011fa denk gelen b\u00f6l\u00fcmler telin iki ucunda olu\u015fmal\u0131d\u0131r. (#) Bu nedenle de iki telden uzun olan\u0131 kal\u0131n sesleri yo\u011funlukla, k\u0131sa olan\u0131 da ilkine k\u0131yasla ince sesleri daha yo\u011fun olarak yayar.
\nPisagor\u2019dan yakla\u015f\u0131k 2000 y\u0131l sonra, G. Galilei\u2019nin babas\u0131 Vincenzo Galilei m\u00fczik\u00e7iydi, lavta \u00e7alard\u0131. (##) Bundan sebep olacak, tellerden \u00e7\u0131kan seslerle \u00e7ok yak\u0131ndan ilgilenmi\u015f ve telden \u00e7\u0131kan seslerin tel boyu ile ilintili oldu\u011funun yan\u0131 s\u0131ra teldeki gerilimle de de\u011fi\u015fti\u011fini bulgulam\u0131\u015ft\u0131. \u00c7alg\u0131c\u0131lar\u0131n, \u00f6rne\u011fin kemanc\u0131lar\u0131n ve gitarc\u0131lar\u0131n bir tak\u0131m d\u00fc\u011fmeleri \u00e7evirerek onlara ba\u011fl\u0131 telleri gererek ya da gev\u015feterek tellerden do\u011fru seslerin, \u00f6rne\u011fin la telinden la sesinin \u00e7\u0131kmas\u0131n\u0131 sa\u011flad\u0131klar\u0131 yani aletlerini acort ettikleri (\u2018tuning\u2019) an\u0131msanmal\u0131d\u0131r.
\nBak\u0131n\u0131z, \u015fimdi de, y\u00fckseklik de\u011feri \u221e olan bir Potansiyel Kuyusu i\u00e7inde hapsolmu\u015f bir nokta par\u00e7ac\u0131\u011f\u0131n kuvantum fizi\u011fini irdeleyelim (####) ve ayn\u0131 anda Pisagor\u2019u sessizce anal\u0131m.
\n\u0130lkin, bu kuyu tek boyutlu ve L geni\u015fli\u011fine sahip olsun. Demek ki, taneci\u011fimiz bu L geni\u015fli\u011findeki kuyunun d\u0131\u015f\u0131na \u00e7\u0131kamaz. Yani, demek ki, taneci\u011fimizin De Broglie dalgas\u0131n\u0131n dalga boyu (\u03bb) ancak 2L, L, 2L\/3, \u2026 ve \u00f6zetle N s\u0131f\u0131rdan farkl\u0131 bir Tam Say\u0131 ise, \u03bb=2L\/N olabilecektir. Yani, basamakl\u0131 (\u2018quantized\u2019) de\u011ferlere sahip olabilecektir.
\n\u0130kincileyin, Einstein-De Broglie e\u015fitli\u011fi olan p\u03bb=h e\u015fitli\u011fini\u00a0 do\u011frusal momentum (p) yani k\u00fctle (m) ve s\u00fcrat (v) niceliklerinin \u00e7arp\u0131m\u0131 (p=mv) olarak de\u011ferlendirdi\u011fimizde (mv)(2L\/N)=h e\u015fitli\u011fini elde edebiliriz. Buradan v\u2019yi e\u015fitlik solunda b\u0131rakarak di\u011fer terimleri e\u015fitlik sa\u011f\u0131na al\u0131rsak
\nv=Nh\/(2mL)
\ne\u015fitli\u011fini elde ederiz. Bu da bizi E enerji de\u011ferleri i\u00e7in
\nE=mv\u00b2\/2=N\u00b2(h\u00b2\/8mL\u00b2) ifadesine g\u00f6t\u00fcr\u00fcr.
\nSon e\u015fitlikte g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi, dalga boyunun basamakl\u0131 olu\u015fu nedeniyle enerji de basamakl\u0131d\u0131r.
\nKuyu i\u00e7indeki par\u00e7ac\u0131k v h\u0131z\u0131yla devinir ama L geni\u015fli\u011finin d\u0131\u015f\u0131na \u00e7\u0131kamaz g\u00f6r\u00fc\u015f\u00fc \u015f\u00f6yle yorumlanabilir (\u2018interpretation\u2019): Potansiyel duvarlar\u0131n\u0131n de\u011feri \u221e kadar oldu\u011fu i\u00e7in buraya \u00e7arpan par\u00e7ac\u0131\u011f\u0131n kinetik enerjisinde kay\u0131p olmaks\u0131z\u0131n, yani Tam Elastik \u00c7arp\u0131\u015fma yaparak geri d\u00f6ner. H\u0131z\u0131n y\u00f6n\u00fc de\u011fi\u015fir ama b\u00fcy\u00fckl\u00fc\u011f\u00fc yani s\u00fcrat de\u011fi\u015fmez.
\n\u2018Potansiyel duvarlar\u0131n\u0131n y\u00fckseklik de\u011feri \u221e kadar de\u011fil de s\u0131n\u0131rl\u0131 olsayd\u0131, par\u00e7ac\u0131k Kuvantum T\u00fcnellemesi (\u2018Quantum Tunelling\u2019) yoluyla kuyu d\u0131\u015f\u0131na s\u0131zabilirdi.\u2019 denir. Do\u011frudur. Birazdan, bu fiziksel ger\u00e7e\u011fin g\u00f6zle g\u00f6r\u00fcl\u00fcr daha do\u011frusu kulakla i\u015fitilir \u00f6rneklerini verece\u011fiz. \u2018Ama, bu t\u00fcnelleme olgusu sadece Kuvantum Fizi\u011fine \u00f6zg\u00fcd\u00fcr. Klasik Fizik\u2019te hi\u00e7bir \u00f6rne\u011fi mevcut de\u011fildir.\u2019 de denir. Oysa bu deyi\u015f yanl\u0131\u015ft\u0131r.
\nTelli \u00e7alg\u0131lar\u0131n kiri\u015fleri, yani iki u\u00e7ta telleri \u00e7alg\u0131 g\u00f6vdesinin yukar\u0131s\u0131nda tutan par\u00e7alar ve tellerin kendileri m\u00fckemmelen yal\u0131t\u0131lm\u0131\u015f olsalard\u0131, tellerdeki titre\u015fimler kiri\u015flerden s\u0131zarak veya ses halinde \u00e7alg\u0131 g\u00f6vdesine \u00e7arparak yeni t\u0131n\u0131lar olu\u015fturamazd\u0131. Bu da, \u221e kadar y\u00fcksek potansiyel kuyusuna iyi bir \u00f6rnek te\u015fkil ederdi. Ne ki, bu ek t\u0131n\u0131lar da kulaklarda ek tadlar, lezzetler yaratmaktad\u0131r. Bu nedenle \u00f6rne\u011fin Stradivarius kemanlar, Ovation gitarlar ba\u015f tac\u0131d\u0131r.
\nSonu\u00e7 olarak, Pisagor\u2019un telden \u00e7\u0131kan sesin form\u00fclasyonu ile Schr\u00f6dinger Denklemi\u2019nin tam (analitik) \u00e7\u00f6z\u00fcm verdi\u011fi d\u00f6rt olgudan biri olan \u2018Sonsuz Potansiyel Kuyusu\u2019 probleminin \u00e7\u00f6z\u00fcm\u00fc t\u0131pa t\u0131p ayn\u0131d\u0131r.
\nBelki, diyeceksiniz ki, \u201cAz gittik, uz gittik\u2026\u201d
\nBunda \u015fa\u015f\u0131racak ne var ki?
\nEvet, Pisagor ve \u00f6\u011frencilerinin, bug\u00fcn bize (en hafif deyimle) biraz tuhaf g\u00f6r\u00fcnen baz\u0131 fikirleri payla\u015ft\u0131klar\u0131n\u0131 biliyoruz. \u00d6rne\u011fin, Pisagor ve \u00f6\u011frencileri her \u015feyin matematikle ilgili oldu\u011funa, say\u0131lar\u0131n son ger\u00e7ek oldu\u011funa, matematik arac\u0131l\u0131\u011f\u0131yla her \u015feyin kestirilebilece\u011fine ve \u00f6l\u00e7\u00fclebilece\u011fine inanm\u0131\u015flard\u0131. \u0130ki say\u0131s\u0131 di\u015fili\u011fi ve do\u011fan\u0131n bu di\u015filikten geldi\u011fini ifade ediyordu, \u00f6rne\u011fin. \u00dc\u00e7 say\u0131s\u0131 uyum ve d\u00fczenle maddenin i\u00e7erdi\u011fi \u00fc\u00e7l\u00fc \u00f6\u011feyi temsil ediyordu. Bu say\u0131, ba\u015flang\u0131c\u0131, ortas\u0131 ve sonu olan ilk rakamd\u0131, yetkin bir say\u0131yd\u0131. D\u00f6rt tanr\u0131sal g\u00fcc\u00fc simgelerdi. \u0130lk \u00e7ift say\u0131 olan “iki”nin kendisi ile \u00e7arp\u0131m\u0131ndan elde edilen bu say\u0131 adaletin de simgesiydi. Be\u015f say\u0131s\u0131 evlili\u011fin simgesiydi. Alt\u0131 organik ve hayati varl\u0131klar\u0131n t\u00fcrl\u00fc \u015fekillerini g\u00f6sterirdi. Burada di\u015filik ilkesi olan (2), erkeklik ilkesi olan (3), mutlak (1) ile birle\u015fti\u011fi i\u00e7in soylar\u0131n devam\u0131n\u0131 da g\u00f6sterirdi. Yedi say\u0131s\u0131 kritik say\u0131lar\u0131 temsil ederdi; yedi g\u00fcnl\u00fck, yedi ayl\u0131k ya da yedi y\u0131ll\u0131k d\u00f6nemlerin varl\u0131klar\u0131n geli\u015fiminde bask\u0131n rolleri vard\u0131. Sekiz say\u0131s\u0131 ak\u0131l, ahlak ve erdemin temsilcisiydi. Dokuz say\u0131s\u0131 mutlak Bir ayr\u0131 tutulacak olursa ilk tek say\u0131 \u00dc\u00e7’\u00fcn karesiydi ve bu say\u0131 da adaleti temsil ederdi.
\nAma as\u0131l tuhafl\u0131k \u015furada de\u011fil midir?
\nDe\u011fil sadece Pisagor zaman\u0131nda, \u00e7ok daha \u00f6ncesinde bile kuru dal par\u00e7alar\u0131n\u0131 bir birine s\u00fcrterek ve kolay tutu\u015fan kuru ot, yaprak, liken vb. yard\u0131m\u0131yla ate\u015f yak\u0131lm\u0131yor muydu? G\u00fcn\u00fcm\u00fczde de, ucuna kolay tutu\u015fan kimyasal bile\u015fikler s\u00fcr\u00fclm\u00fc\u015f kibrit \u00e7\u00f6pleri kullanm\u0131yor muyuz ate\u015f yakmak i\u00e7in. Hadi olsun, bir metal \u00e7ark\u0131 k\u0131v\u0131lc\u0131m \u00e7\u0131kartmak amac\u0131yla \u00e7akmak ta\u015f\u0131na s\u00fcrtt\u00fcr\u00fcyor, o k\u0131v\u0131lc\u0131mlarla kolay yan\u0131c\u0131 bir gaz\u0131 tutu\u015fturarak \u00e7akmak yak\u0131yoruz. En geli\u015fmi\u015f ate\u015f yak\u0131c\u0131 aletlerimiz ise, son be\u015f on y\u0131llarda yayg\u0131nla\u015fan mutfak ocaklar\u0131nda gaz tutu\u015fturmak amac\u0131yla k\u0131v\u0131lc\u0131m yaratan elektrikli manyetolar. Dikkat etmeye de\u011fer; g\u00fcn\u00fcm\u00fcz n\u00fcfusunun b\u00fcy\u00fck \u00e7o\u011funlu\u011fu kibrit kullan\u0131rken ancak geli\u015fkin \u00fclke beldelerinde elektrikli \u00e7akmak kullan\u0131lmakta. Bu mudur on bin y\u0131ll\u0131k insan geli\u015fmi\u015fli\u011fi?
\nH\u00e2l bu iken, ni\u00e7in \u015fa\u015fmal\u0131 ki; Pisagor ile ayn\u0131 y\u00f6ntemi kullanarak ate\u015f yak\u0131yorken, onunkine benzer giysiler ve onunkine benzer pabu\u00e7lar giyiyorken matemati\u011fi de onun gibi evrenin asli unsuru san\u0131yor olu\u015fumuza?<\/p>\n

(*) https:\/\/www.google.com\/search?q=T%C3%BCme+Var%C4%B1m+Y%C3%B6ntemi<\/p>\n

(**) https:\/\/www.google.com\/search?q=pisagor+%C3%BC%C3%A7l%C3%BCleri
\nAyr\u0131ca; https:\/\/www.matematikdunyasi.org\/1991\/02\/pisagor-teoremi-ya-oncesi\/
\nAyr\u0131ca; https:\/\/www.matematikdunyasi.org\/pdf-arsiv\/#flipbook-df_3127\/23\/<\/p>\n

A\u00b2+B\u00b2+F\u00b2=G\u00b2 e\u015fitli\u011fini sa\u011flayan D\u00f6rtl\u00fckler de vard\u0131r ki, bunlar, kenar uzunluklar\u0131 A, B, F ve G olan Dik D\u00f6rtgenler Prizmalar\u0131\u2019n\u0131n g\u00f6vde k\u00f6\u015fegen uzunluklar\u0131d\u0131r. A\u00b2+B\u00b2+F\u00b2+H\u00b2=P\u00b2 ise, D\u00f6rt Boyutlu Dik D\u00f6rtgenler Prizmalar\u0131\u2019n\u0131n g\u00f6vde k\u00f6\u015fegen uzunluklar\u0131d\u0131r. Bkz., https:\/\/www.google.com\/search?q=4+boyutlu+k%C3%BCp<\/p>\n

(***) George Gamow\u2019un \u20181, 2, 3, \u2026 Sonsuz\u2019 adl\u0131 kitab\u0131nda (Bkz., https:\/\/www.google.com\/search?q=George+Gamow%E2%80%99un+1%2C+2%2C+3%2C+%E2%80%A6+Sonsuz+ )s\u00f6z\u00fcn\u00fc etti\u011fi Hotanto (Bkz., https:\/\/www.google.com\/search?q=Hotanto&sca_esv=fc5970edc32ae20c&sxsrf=ADLYWIKCkeKsSIDHYxsXGP657h3YgN0aUw%3A1734562442919&ei=ilJjZ8rkN92Jxc8PoMXd8Qo&ved=0ahUKEwjK0YDStLKKAxXdRPEDHaBiN64Q4dUDCBA&uact=5&oq=Hotanto&gs_lp=Egxnd3Mtd2l6LXNlcnAiB0hvdGFudG8yChAjGIAEGCcYigUyChAjGIAEGCcYigUyBBAjGCcyBRAAGIAEMgUQABiABDIEEAAYHjIGEAAYBRgeMgYQABgFGB4yBhAAGAUYHjIIEAAYgAQYogRI5khQ4BlYwCpwAngAkAEAmAF-oAGLBqoBAzEuNrgBA8gBAPgBAZgCB6ACrwbCAgsQABiABBixAxiDAcICERAuGIAEGLEDGNEDGIMBGMcBwgIOEC4YgAQYsQMY0QMYxwHCAggQABiABBixA8ICChAuGIAEGEMYigXCAg0QABiABBixAxiDARgKwgIFEC4YgATCAggQLhiABBixA5gDAIgGAZIHAzEuNqAHt1M&sclient=gws-wiz-serp ) dilinde \u20181, 2, 3, \u00e7ok\u2019 gibi sadece 4 tane nicelik yeterli olmu\u015f.<\/p>\n

(****) https:\/\/translate.yandex.com\/?utm_source=yandex&utm_medium=com&utm_campaign=morda&source_lang=la&target_lang=tr&text=finitum<\/p>\n

(#) https:\/\/tr.wikipedia.org\/wiki\/Dize_titre%C5%9Fimi
\nhttps:\/\/acikders.ankara.edu.tr\/pluginfile.php\/189894\/mod_resource\/content\/1\/SES%20DALGALARI%2C%20REZONANS%20OLAYI%2C%20B%C4%B0LE%C5%9E%C4%B0K%20SESLER.pdf
\nAyr\u0131ca; https:\/\/www.youtube.com\/watch?v=gsWRPpDlt9Y
\nAyr\u0131ca; https:\/\/muzikuniversitesi.com\/gam-nedir-gitarda-gamlar-nasil-ogrenilir\/<\/p>\n

(##) https:\/\/tr.wikipedia.org\/wiki\/Galileo_Galilei<\/p>\n

(###) Kat\u0131da ses h\u0131z\u0131: 1. Dkk. \u0130tibaren https:\/\/www.google.com\/search?q=maddei%C3%A7inde+ses+h%C4%B1z%C4%B1&sca_esv=189649982420d558&sxsrf=ADLYWIJRPaCopDTLLVj3pr9mX2U0QDVSIg%3A1734164456857&ei=6D9dZ7-ANLGIxc8P5MbRmAs&ved=0ahUKEwi_lLuD6qaKAxUxRPEDHWRjFLMQ4dUDCBA&uact=5&oq=maddei%C3%A7inde+ses+h%C4%B1z%C4%B1&gs_lp=Egxnd3Mtd2l6LXNlcnAiF21hZGRlacOnaW5kZSBzZXMgaMSxesSxMgcQIRigARgKMgcQIRigARgKMgcQIRigARgKMgcQIRigARgKSNuJAVDlEFjlgQFwAXgBkAEAmAGTAaABqB-qAQQxLjMzuAEDyAEA-AEBmAIUoAKoEsICChAAGLADGNYEGEfCAgcQIxiwAhgnwgIIEAAYogQYiQXCAggQABiABBiiBMICBRAAGO8FwgIKECEYoAEYwwQYCpgDAIgGAZAGCJIHBDEuMTmgB6WzAQ&sclient=gws-wiz-serp#fpstate=ive&vld=cid:75e94f95,vid:xMEKCLDVRIg,st:0
\nAyr\u0131ca bkz., https:\/\/en.wikipedia.org\/wiki\/Speed_of_sound<\/p>\n

\"\"<\/a><\/p>\n

(####) https:\/\/www.google.com\/search?q=sonsuz+potansiyel+kuyusu<\/p>\n","protected":false},"excerpt":{"rendered":"

Fizik \u201312\u2013 \u0130\u00e7erik: Her \u015feyde her \u015fey var m\u0131? \u00d6n not: Bu yaz\u0131da \u221e simgesi, \u2018bilinen Ger\u00e7ek Say\u0131lar\u0131n en b\u00fcy\u00fc\u011f\u00fc\u2019 anlam\u0131nda kullan\u0131lacakt\u0131r. Bak\u0131n\u0131z; 3\u2019\u00fcn karesi 9, 4\u2019\u00fcn karesi 16, 16\u2019ya 9\u2019u ekle 25 ve 25 de 5\u2019in karesi. Demek ki, E\u015fitlik 1: 3\u00b2+4\u00b2=5\u00b2. Ayn\u0131 \u015fekilde; 6\u2019n\u0131n karesi 36, 8\u2019in karesi 64, 64\u2019e 36\u2019y\u0131 ekle 100 […]<\/p>\n","protected":false},"author":1425,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1],"tags":[],"class_list":["post-450","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/450","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/users\/1425"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/comments?post=450"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/450\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=450"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=450"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}