{"id":66,"date":"2022-01-20T14:39:00","date_gmt":"2022-01-20T13:39:00","guid":{"rendered":""},"modified":"2023-08-04T22:46:50","modified_gmt":"2023-08-04T20:46:50","slug":"o-cifernom-sucte","status":"publish","type":"post","link":"https:\/\/www.jankafialka.sk\/?p=66","title":{"rendered":"O cifernom s\u00fa\u010dte"},"content":{"rendered":"\n<p>Ned\u00e1vno sa ma m\u00f4j prvoroden\u00fd sp\u00fdtal, kedy za\u010dne jeho mal\u00fd bra\u010dek chodi\u0165. Hovor\u00edm, \u017ee ke\u010f bude ma\u0165 pribli\u017ene jeden rok. P\u00fdta sa: &#8222;A to bude kedy?&#8220;<\/p>\n\n\n\n<p>&#8222;Ke\u010f ty bude\u0161 ma\u0165 desa\u0165 rokov.&#8220;<\/p>\n\n\n\n<p>A nasledovala jeho \u00favaha: &#8222;To je super. Ve\u010f je to to ist\u00e9. Jedna a nula je jedna.&#8220;<\/p>\n\n\n\n<p>&#8222;A \u010fal\u0161\u00ed rok bude ma\u0165 dva a ty 11. A 1+1 je zasa dva.&#8220; A vlastne to tak bude po cel\u00fd \u017eivot, ak budeme cifern\u00fd s\u00fa\u010det po\u010d\u00edta\u0165 v\u017edy, a\u017e k\u00fdm nedostaneme jednocifern\u00e9 \u010d\u00edslo. \u010ci\u017ee 19 m\u00e1 cifern\u00fd s\u00fa\u010det 10 a z neho je cifern\u00fd s\u00fa\u010det jeden. Takto sme kedysi len tak zo srandy po\u010d\u00edtali \u0161\u0165astn\u00e9 \u010d\u00edslo. \u017de spo\u010d\u00edtame v\u0161etky \u010d\u00edsla v d\u00e1tume narodenia a v s\u00fa\u010dte zasa v\u0161etky \u010d\u00edslice a tak, a\u017e k\u00fdm nedostaneme jednocifern\u00e9 \u010d\u00edslo.<\/p>\n\n\n\n<p>Dnes nadr\u00e1nom som sa zamyslela nad t\u00fdm, \u017ee tak\u00e1to funkcia (cifern\u00fd s\u00fa\u010det z cifern\u00e9ho s\u00fa\u010dtu, a\u017e pokia\u013e nevyjde jednocifern\u00e9 \u010d\u00edslo) m\u00e1 celkom zauj\u00edmav\u00e9 vlastnosti. Napr\u00edklad deviatka na\u0148 nem\u00e1 vplyv. Pripo\u010d\u00edtajte 9 k ak\u00e9muko\u013evek \u010d\u00edslu, v\u00fdsledn\u00fd cifern\u00fd s\u00fa\u010det z cifern\u00e9ho s\u00fa\u010dtu bude st\u00e1le rovnak\u00fd.<\/p>\n\n\n\n<p>Pri po\u010d\u00edtan\u00ed \u0161\u0165astn\u00e9ho \u010d\u00edsla zasa \u013eahko objav\u00edme, \u017ee je jedno, v akom porad\u00ed budeme po\u010d\u00edta\u0165, \u010di sprav\u00edme najprv cifern\u00e9 s\u00fa\u010dty pre de\u0148, mesiac a rok a tie n\u00e1sledne s\u010d\u00edtame a ur\u010d\u00edme cifern\u00fd s\u00fa\u010det, alebo najprv v\u0161etko s\u010d\u00edtame a cifern\u00fd s\u00fa\u010det sprav\u00edme a\u017e z v\u00fdsledku. Matematicky by sme to zap\u00edsali, \u017ee f(<i>a+b<\/i>)=f(<i>a<\/i>)+f(<i>b<\/i>).<\/p>\n\n\n\n<p>Pre\u010do tak\u00e1to zauj\u00edmav\u00e1 funkcia nem\u00e1 svoj n\u00e1zov? \ud83e\udd14<\/p>\n\n\n\n<p>No, a vtedy mi to docvaklo. Ve\u010f m\u00e1! Je to predsa zvy\u0161ok po delen\u00ed deviatimi! Prekvapiv\u00e9, v\u0161ak? A teraz, ke\u010f tak nad t\u00fdm uva\u017eujem, je to vlastne \u00faplne prost\u00e9. D\u00e1vno viem, \u017ee cifern\u00fd s\u00fa\u010det m\u00e1 rovnak\u00fd zvy\u0161ok po delen\u00ed deviatkou ako p\u00f4vodn\u00e9 \u010d\u00edslo. Teda logicky aj cifern\u00fd s\u00fa\u010det z cifern\u00e9ho s\u00fa\u010dtu bude ma\u0165 ten ist\u00fd zvy\u0161ok. Jedin\u00fd rozdiel je v tom, \u017ee moje cifern\u00e9 s\u00fa\u010dty bud\u00fa obsahova\u0165 \u010d\u00edsla 1, 2, &#8230;, 9 a vo zvy\u0161koch je namiesto deviatky nula.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"768\" src=\"https:\/\/www.jankafialka.sk\/wp-content\/uploads\/2022\/01\/59869959.jpg\" alt=\"\" class=\"wp-image-1944\" srcset=\"https:\/\/www.jankafialka.sk\/wp-content\/uploads\/2022\/01\/59869959.jpg 768w, https:\/\/www.jankafialka.sk\/wp-content\/uploads\/2022\/01\/59869959-300x300.jpg 300w, https:\/\/www.jankafialka.sk\/wp-content\/uploads\/2022\/01\/59869959-150x150.jpg 150w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><figcaption class=\"wp-element-caption\">Nad\u0161enie z objavu<\/figcaption><\/figure>\n\n\n\n<p>Tie vlastnosti, ktor\u00e9 som len tak n\u00e1hodou objavila, vypl\u00fdvaj\u00fa z te\u00f3rie zvy\u0161kov\u00fdch tried.<\/p>\n\n\n\n<p>A takto si my matematici dv\u00edhame n\u00e1ladu. Kto neza\u017eil, nepochop\u00ed, ak\u00fd je to pocit, ke\u010f sa v mozgu zrazu prepoja neur\u00f3ny. Dve veci, ktor\u00e9 st\u00e1li oddelene, sa spoja a vytvoria kr\u00e1sne premostenie. Rozsvieten\u00e1 \u017eiarovka to celkom dobre vystihuje. To je to, \u010do matematika motivuje. To je to, \u010do by malo motivova\u0165 aj najmen\u0161\u00edch \u0161kol\u00e1kov. Nie zn\u00e1mky, vonkaj\u0161ie odmeny \u010di tresty. Ale dobr\u00fd pocit z toho, \u017ee na nie\u010do som s\u00e1m pri\u0161iel.<\/p>\n\n\n\n<p>Vr\u00e1tim sa e\u0161te na chv\u00ed\u013eu k t\u00fdm zvy\u0161kom. Nie ka\u017ed\u00e9mu je asi zrejm\u00e9, pre\u010do m\u00e1 cifern\u00fd s\u00fa\u010det rovnak\u00fd zvy\u0161ok ako p\u00f4vodn\u00e9 \u010d\u00edslo. Pointa je v desiatkovom z\u00e1pise \u010d\u00edsla. Ka\u017ed\u00e9 \u010d\u00edslo v desiatkovej s\u00fastave je vlastne s\u00fa\u010dtom cifier n\u00e1soben\u00fdch nejakou mocninou desiatky. Napr\u00edklad 123 = 1\u2022100+2\u202210+3. No, a tie mocniny desiatky vieme rozlo\u017ei\u0165 na s\u00fa\u010det nejak\u00e9ho dev\u00e4\u0165 n\u00e1sobku a jednotky. \u010ci\u017ee 123 = 1\u2022(99+1)+2\u2022(9+1)+3. A je jasn\u00e9, \u017ee n\u00e1sobok deviatky nijako nezmen\u00ed v\u00fdsledn\u00fd zvy\u0161ok, preto zvy\u0161ok po delen\u00ed deviatkou ovplyv\u0148uj\u00fa iba jednotliv\u00e9 cifry 1+2+3. Tak preto m\u00e1 cifern\u00fd s\u00fa\u010det rovnak\u00fd zvy\u0161ok ako cel\u00e9 \u010d\u00edslo. S cifern\u00fdm s\u00fa\u010dtom cifern\u00e9ho s\u00fa\u010dtu to nem\u00f4\u017ee by\u0165 inak.<\/p>\n\n\n\n<p>Ot\u00e1zka na z\u00e1ver: ak\u00fd bude cifern\u00fd s\u00fa\u010det z cifern\u00e9ho s\u00fa\u010dtu a\u017e po jednocifern\u00e9 \u010d\u00edslo z v\u00fdsledku tohto pr\u00edkladu: 1203627\u20229 + 1234567890.<\/p>\n\n\n\n<p>Komu vy\u0161lo dev\u00e4\u0165, m\u00f4\u017ee si pogratulova\u0165. \ud83d\ude01<\/p>\n\n\n\n<p>Komu sa toto spojilo s deviatkovou sk\u00fa\u0161kou, je \u0161\u0165astn\u00fdm matematikom. \ud83d\ude09<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ned\u00e1vno sa ma m\u00f4j prvoroden\u00fd sp\u00fdtal, kedy za\u010dne jeho mal\u00fd bra\u010dek chodi\u0165. Hovor\u00edm, \u017ee ke\u010f bude ma\u0165 pribli\u017ene jeden rok. P\u00fdta sa: &#8222;A to bude kedy?&#8220; &#8222;Ke\u010f ty bude\u0161 ma\u0165 desa\u0165 rokov.&#8220; A nasledovala jeho \u00favaha: &#8222;To je super. Ve\u010f je to to ist\u00e9. Jedna a nula je jedna.&#8220; &#8222;A \u010fal\u0161\u00ed rok bude ma\u0165 dva [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":1944,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[24,25,26],"class_list":["post-66","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nezaradene","tag-ciferny-sucet","tag-objav","tag-zvyskove-triedy"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>O cifernom s\u00fa\u010dte - jankafialka<\/title>\n<meta name=\"description\" content=\"O cifernom s\u00fa\u010dte cifern\u00e9ho s\u00fa\u010dtu, jeho vlastnostiach a objavenej s\u00favislosti so zvy\u0161kami po delen\u00ed deviatkou.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.jankafialka.sk\/?p=66\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"O cifernom s\u00fa\u010dte - 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