{"id":71,"date":"2022-01-08T09:57:00","date_gmt":"2022-01-08T08:57:00","guid":{"rendered":""},"modified":"2023-08-04T22:48:15","modified_gmt":"2023-08-04T20:48:15","slug":"geometricke-pocitanie","status":"publish","type":"post","link":"https:\/\/www.jankafialka.sk\/?p=71","title":{"rendered":"Geometrick\u00e9 po\u010d\u00edtanie"},"content":{"rendered":"\n

Kdesi som kedysi po\u010dula alebo \u010d\u00edtala, \u017ee matematik je \u010dlovek, ktor\u00fd h\u013ead\u00e1 odpovede na ot\u00e1zky, ktor\u00e9 nikto nepolo\u017eil. Mne nikto nepolo\u017eil ot\u00e1zku, ktor\u00fa oblas\u0165 matematiky m\u00e1m najrad\u0161ej. A ke\u010f\u017ee som tak trochu matematik, idem ju sk\u00fasi\u0165 zodpoveda\u0165.<\/p>\n\n\n\n

V \u0161kole sa matematika oby\u010dajne del\u00ed na dve ve\u013ek\u00e9 oblasti – geometria a t\u00e1 druh\u00e1, ktor\u00e1 sa ozna\u010duje ako matematika. Obsahuje aritmetiku, te\u00f3riu \u010d\u00edsel, algebru, pravdepodobnos\u0165, kombinatoriku, \u0161tatistiku, ale to sa de\u0165om ve\u013emi nehovor\u00ed. Nazve sa to jednoducho, matematika. To je trochu \u010dudn\u00e9. Vyzer\u00e1 to, akoby geometria bola nie\u010do, \u010do vlastne do matematiky celkom nepatr\u00ed. Tento dojem umoc\u0148uje aj umiestnenie geometrie na koniec u\u010debnice. Ke\u010f sa teraz pozer\u00e1m na synovu u\u010debnicu matematiky pre \u0161tvrt\u00e1kov, geometria je naozaj odsunut\u00e1 na posledn\u00fdch sedemn\u00e1s\u0165 str\u00e1nok. Minul\u00fd rok to bolo e\u0161te menej str\u00e1n. Smutn\u00e9.<\/p>\n\n\n\n

Jeden z mojich ob\u013e\u00faben\u00fdch u\u010dite\u013eov Du\u0161an Jedin\u00e1k hovorieval, \u017ee matematika, to s\u00fa po\u010dty a merba. To znie rozhodne lep\u0161ie. A ktor\u00fa \u010das\u0165 m\u00e1m rad\u0161ej? No, pravdupovediac, najrad\u0161ej m\u00e1m to, kde sa obe mie\u0161aj\u00fa v spr\u00e1vnom pomere. Je to ako, keby ste sa ma sp\u00fdtali, ktor\u00fa farbu m\u00e1m rad\u0161ej, modr\u00fa \u010di \u010derven\u00fa. A ja odpoviem, \u017ee fialov\u00fa. \ud83d\ude0f<\/p>\n\n\n\n

A kde sa po\u010dty a merba mie\u0161aj\u00fa? Ako prv\u00e9 v\u00e1m ur\u010dite napadne pou\u017e\u00edva\u0165 v\u00fdpo\u010dty na geometrick\u00e9 probl\u00e9my. Toto je celkom be\u017en\u00e9, naz\u00fdva sa to analytick\u00e1 geometria a na jej princ\u00edpe funguj\u00fa v\u0161etky geometrick\u00e9 softv\u00e9ry. Ke\u010f si spust\u00edte napr\u00edklad Geogebru a za\u010dnete v nej \u010doko\u013evek rysova\u0165, v\u013eavo v\u00e1m okam\u017eite nabiehaj\u00fa v\u00fdpo\u010dty, \u010d\u00edsla, rovnice, nerovnice,… Z kru\u017enice sa tak stane kvadratick\u00e1 rovnica, z priamky line\u00e1rna rovnica a pod. Je to fascinuj\u00face, ale trocha nuda.<\/p>\n\n\n\n

Menej sa u\u017e hovor\u00ed o tom, \u017ee aj v\u00fdpo\u010dty mo\u017eno robi\u0165 geometricky. Mysl\u00edm t\u00fdm, \u017ee ke\u010f chcem napr\u00edklad vypo\u010d\u00edta\u0165 s\u00fa\u010din dvoch \u010d\u00edsel, nemus\u00edm v\u00f4bec po\u010d\u00edta\u0165. Vytiahnem prav\u00edtko a kru\u017eidlo a za chv\u00ed\u013eku v\u00e1m poviem v\u00fdsledok. Never\u00edte? Tak \u010d\u00edtajte a predstavujte si.<\/p>\n\n\n\n

Pr\u00edklad je 3,4 x 8,7. Narysujem \u00fase\u010dku d\u013a\u017eky 3,4 cm. Nazvem ju AB. Pred\u013a\u017eim ju \u010falej za bod B. Potom narysujem polpriamku AX pod hocijak\u00fdm ostr\u00fdm uhlom a na \u0148u nanesiem d\u013a\u017eku 8,7 cm za\u010d\u00ednaj\u00fac v bode A, jej koniec ozna\u010d\u00edm p\u00edsmenom C. E\u0161te na \u0148u nanesiem aj d\u013a\u017eku 1 za\u010d\u00ednaj\u00fac od bodu A. Koniec nazvem J. Tento bod J spoj\u00edm s bodom B a urob\u00edm rovnobe\u017eku s JB id\u00facu bodom C. Tam, kde mi t\u00e1to rovnobe\u017eka pretne polpriamku AB (za bodom B), tam bude bod V, ako v\u00fdsledok. D\u013a\u017eka \u00fase\u010dky AV je toti\u017e s\u00fa\u010din 3,4 x 8,7.<\/p>\n\n\n\n

Tento postup (a mnoho in\u00e9ho) lep\u0161ie vysvetlen\u00fd n\u00e1jdete v mojej publik\u00e1ci\u00ed: Prech\u00e1dzka po svete geometrie https:\/\/pdf.truni.sk\/download?e-skripta\/fialova-geometria-2020.pdf<\/a><\/p>\n\n\n\n

Kon\u0161truk\u010dne m\u00f4\u017eeme po\u010d\u00edta\u0165 \u00falohy, kde sa s\u010d\u00edtava, od\u010d\u00edtava, n\u00e1sob\u00ed aj del\u00ed s klad\u00fdmi \u010d\u00edslami, tak\u017ee v podstate takmer cel\u00e1 z\u00e1kladn\u00e1 \u0161kola. V\u00fdsledky, samozrejme, nebud\u00fa \u00faplne presn\u00e9, preto\u017ee na\u0161a schopnos\u0165 presne rysova\u0165 je dos\u0165 \u00faboh\u00e1. Ale robi\u0165 nie\u010do inak je v\u017edy celkom osvie\u017euj\u00face.<\/p>\n\n\n\n

Podstatou geometrick\u00e9ho po\u010d\u00edtania je, \u017ee \u010d\u00edsla si predstavujeme ako d\u013a\u017eky \u00fase\u010diek. Pali\u010diek alebo p\u00e1sikov papiera, ak chcete by\u0165 \u00faplne konkr\u00e9tni. T\u00e1to predstava m\u00e1 jednu nesporn\u00fa v\u00fdhodu – predstavi\u0165 si \u010d\u00edsla, ktor\u00e9 nie s\u00fa cel\u00e9, \u010di\u017ee zlomky alebo desatinn\u00e9 \u010d\u00edsla alebo dokonca iracion\u00e1lne \u010d\u00edsla nie je \u017eiaden probl\u00e9m. Nev\u00fdhodou je, \u017ee je trochu probl\u00e9m predstavi\u0165 si \u010d\u00edsla z\u00e1porn\u00e9. Tak\u00e1to geometrick\u00e1 predstava \u010d\u00edsla je \u00faplne nez\u00e1visl\u00e1 od nejak\u00fdch zau\u017e\u00edvan\u00fdch sp\u00f4sobov z\u00e1pisu. Mo\u017eno, keby sme objavili civiliz\u00e1ciu, ktor\u00e1 zapisuje \u010d\u00edsla diametr\u00e1lne odli\u0161ne, pr\u00e1ve cez geometriu by sme sa vedeli dohodn\u00fa\u0165…<\/p>\n\n\n\n

\"\"
Mimozem\u0161\u0165an a \u010dlovek v priate\u013eskom rozhovore o matematike<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"

Kdesi som kedysi po\u010dula alebo \u010d\u00edtala, \u017ee matematik je \u010dlovek, ktor\u00fd h\u013ead\u00e1 odpovede na ot\u00e1zky, ktor\u00e9 nikto nepolo\u017eil. Mne nikto nepolo\u017eil ot\u00e1zku, ktor\u00fa oblas\u0165 matematiky m\u00e1m najrad\u0161ej. A ke\u010f\u017ee som tak trochu matematik, idem ju sk\u00fasi\u0165 zodpoveda\u0165. V \u0161kole sa matematika oby\u010dajne del\u00ed na dve ve\u013ek\u00e9 oblasti – geometria a t\u00e1 druh\u00e1, ktor\u00e1 sa ozna\u010duje […]<\/p>\n","protected":false},"author":2,"featured_media":1947,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-71","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nezaradene"],"yoast_head":"\nGeometrick\u00e9 po\u010d\u00edtanie - jankafialka<\/title>\n<meta name=\"description\" content=\"Geometrick\u00e9 po\u010d\u00edtanie je \u00favaha o vz\u0165ahu medzi dvoma najstar\u0161\u00edmi oblas\u0165ami matematiky - geometriou a aritmetikou.\" \/>\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=71\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Geometrick\u00e9 po\u010d\u00edtanie - 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