{"id":34,"date":"2023-04-26T12:10:59","date_gmt":"2023-04-26T10:10:59","guid":{"rendered":"https:\/\/www.jankafialka.sk\/?page_id=34"},"modified":"2024-12-30T18:03:20","modified_gmt":"2024-12-30T17:03:20","slug":"vselico-z-geometrie","status":"publish","type":"page","link":"https:\/\/www.jankafialka.sk\/?page_id=34","title":{"rendered":"V\u0161eli\u010do z geometrie"},"content":{"rendered":"\n<p>\u010co by ste narysovali, ak dostanete prv\u00fdkr\u00e1t do ruky rysovacie potreby a m\u00e1te narysova\u0165 nie\u010do z geometrie? Sk\u00fasite mo\u017eno v\u0161eli\u010do, ale kruhy bud\u00fa pravdepodobne to, \u010d\u00edm sa budete zab\u00e1va\u0165 najdlh\u0161ie. Preto prv\u00fdm na\u0161\u00edm po\u010dinom v s\u00favislosti s geometriou v rovine s\u00fa pr\u00e1ve kruhy obohaten\u00e9 o prvok n\u00e1hody. Tak\u017ee v\u00fdsledok je v\u017edy origin\u00e1lny.<\/p>\n\n\n\n<p>Ka\u017ed\u00e9 kliknutie na obrazovku prid\u00e1 desa\u0165 n\u00e1hodn\u00fdch kruhov. N\u00e1hodn\u00e9 je umiestnenie, ve\u013ekos\u0165 aj farba ka\u017ed\u00e9ho kruhu.<\/p>\n\n\n\n<canvas id=\"platnoKruhy\"><\/canvas>\n<script>\n{function random(n){\nreturn Math.floor(n*Math.random());}\nconst platno= document.getElementById(\"platnoKruhy\");\nplatno.width=0.9*document.documentElement.clientWidth;\nplatno.height=0.9*document.documentElement.clientHeight;\nconst w1=platno.width;\nconst h1=platno.height;\n\nconst ktx = platno.getContext(\"2d\");\nktx.fillStyle=\" rgb(250,250,250)\";\nktx.fillRect(0,0,w1,h1);\nktx.strokeStyle=\"black\";\nktx.strokeRect(0,0,w1,h1);\n\nfunction kresliKruhy(){\nfor(i=0;i<10;i++){\nktx.fillStyle=`rgb(${random(256)}, ${random(256)}, ${random(256)})`;\nktx.beginPath();\nktx.arc(random(w1),random(h1),random(Math.min(w1,h1)\/5),0,2*Math.PI);\nktx.fill();\n}}\nkresliKruhy();\nkresliKruhy();\n\nplatno.addEventListener (\"click\",kresliKruhy);}\n<\/script>\n\n\n\n<button id=\"saveButton1\">Ulo\u017e ako obr\u00e1zok<\/button>\n<script>\n{\nconst canvas = document.getElementById(\"platnoKruhy\");\nconst saveButton = document.getElementById('saveButton1');\n\n\/\/ Zaregistruj udalos\u0165 kliknutia na tla\u010didlo\nsaveButton.addEventListener('click', () => {\n  \/\/ Z\u00edskaj URL reprezent\u00e1ciu aktu\u00e1lneho obr\u00e1zka z canvas\n  const dataURL = canvas.toDataURL();\n\n  \/\/ Vytvor odkaz na s\u0165ahovanie s n\u00e1zvom \"canvas-obrazok.png\"\n  const link = document.createElement('a');\n  link.href = dataURL;\n  link.download = 'canvas-obrazok.png';\n\n  \/\/ Kliknut\u00edm na odkaz automaticky stiahne\u0161 obr\u00e1zok\n  link.click();\n});}\n<\/script>\n\n\n\n<h3 class=\"wp-block-heading\">Vo\u013en\u00fd p\u00e1d<\/h3>\n\n\n\n<p>V tejto uk\u00e1\u017eke m\u00f4\u017eeme sledova\u0165 pohyb simuluj\u00faci vo\u013en\u00fd p\u00e1d lopty na podlo\u017eku. Pri ka\u017edom p\u00e1de sa lopta odraz\u00ed sp\u00e4\u0165 so zmen\u0161enou silou. Farba a umiestnenie s\u00fa vyberan\u00e9 n\u00e1hodne. Nov\u00fa loptu mo\u017eno prida\u0165, aj ke\u010f p\u00f4vodn\u00e1 e\u0161te nedosk\u00e1kala.<\/p>\n\n\n\n<button id=\"tlac\"><b><i>Pridaj loptu !<\/i><\/b><\/button><br><br>\n<canvas id=\"platno\"><\/canvas>\n\n\n\n <script type=\"module\">\n        import * as THREE from 'https:\/\/unpkg.com\/three@0.154.0\/build\/three.module.js';\n        import { OrbitControls } from 'https:\/\/unpkg.com\/three@0.154.0\/examples\/jsm\/controls\/OrbitControls.js';\n\n\n\/\/ tu uz mozno upravovat\nconst camera = new THREE.PerspectiveCamera( 70, window.innerWidth \/ window.innerHeight, 0.01, 10 );\ncamera.position.z = 1;\n\nconst scene = new THREE.Scene();\n\nconst svetlo = new THREE.DirectionalLight(0xffffff, 5);\nsvetlo.position.set(-0.6, 1.5, 1);\nconst svetlo2 = new THREE.DirectionalLight(0xffffff, 3);\nsvetlo2.position.set(0.5,2,-1);\nscene.add(svetlo, svetlo2);\n\nconst gula = new THREE.SphereBufferGeometry(0.05);\nconst matGula = new THREE.MeshPhongMaterial({color:\"rgb(17,17,80)\", shininess: 10});\n\nconst meshGula = new THREE.Mesh(gula, matGula);\n\nmeshGula.translateY(0.05);\n\nscene.add(meshGula );\n\/\/scene.add(new THREE.AxesHelper(20));\nscene.add(new THREE.GridHelper(1,50));\n\nconst renderer = new THREE.WebGLRenderer( { canvas: platno, antialias: true } );\nrenderer.setSize( 0.9*window.innerWidth, window.innerHeight );\nrenderer.setClearColor(\"rgb(174,227,245)\",1);\n\nconst kontrol = new OrbitControls(camera, renderer.domElement);\nkontrol.addEventListener(\"change\", ()=> renderer.render(scene, camera));\n\nrenderer.render(scene, camera);\n\nfunction pridaj(){\nconst r= Math.random()*0.03+0.02;\nconst gulaN = new THREE.SphereBufferGeometry(r);\nconst mat = new THREE.MeshPhongMaterial({color:`rgb(${Math.floor(Math.random()*100)},${Math.floor(Math.random()*100)},${Math.floor(Math.random()*100)})`, metalness: 0.8, shininess: 20, transparent: true, opacity: 0.9});\n\nconst meshgulaN = new THREE.Mesh(gulaN, mat);\n\nmeshgulaN.translateX(Math.floor(9*Math.random())\/10-0.4);\nmeshgulaN.translateZ(Math.floor(9*Math.random())\/10-0.4);\n\nmeshgulaN.translateY (0.5-r);\n\/\/t je aktualny cas, a zrychlenie pri prvom pade, t1 cas prveho dopadu\nlet t=0;\nconst a= 0.0002;\nconst t1= Math.sqrt((1-4*r)\/a);\n\nfunction pad(){\nt++;\n\/\/tf pomocna premenna vid posledna vetva programu\nlet tf=0;\nif(t<=t1){\nmeshgulaN.translateY(-a*t);\nscene.add(meshgulaN);\nrenderer.render(scene, camera);\n}\n\n\/\/zrychlenie sa skracuje na 70 percent pri kazdom odraze, hore a dole ide rovnako\n\nelse if (t<3*t1)\n{\nmeshgulaN.translateY(0.7*a*(2*t1-t));\nscene.add(meshgulaN);\nrenderer.render(scene, camera);}\n\nelse if (t<5*t1)\n{\nmeshgulaN.translateY(0.7*0.7*a*(4*t1-t));\nscene.add(meshgulaN);\nrenderer.render(scene, camera);}\nelse if (t<7*t1)\n{\nmeshgulaN.translateY(0.7*0.7*0.7*a*(6*t1-t));\nscene.add(meshgulaN);\nrenderer.render(scene, camera);}\nelse if (t<9*t1)\n{\nmeshgulaN.translateY(Math.pow(0.7,4)*a*(8*t1-t));\nscene.add(meshgulaN);\nrenderer.render(scene, camera);\n}\n\nelse if (t<11*t1)\n{\nmeshgulaN.translateY(Math.pow(0.7,5)*a*(10*t1-t));\nscene.add(meshgulaN);\nrenderer.render(scene, camera);\n}\nelse if (t<13*t1)\n{\nmeshgulaN.translateY(Math.pow(0.7,6)*a*(12*t1-t));\nscene.add(meshgulaN);\nrenderer.render(scene, camera);\n}\n\nelse if (t<15*t1)\n{\nmeshgulaN.translateY(Math.pow(0.7,7)*a*(14*t1-t));\nscene.add(meshgulaN);\nrenderer.render(scene, camera);\n}\n\/\/vyrovnanie nepresnosti, tf je tam preto, aby prebehla len raz\nelse if(tf==0) {\ntf=1;\nmeshgulaN.translateY(r-meshgulaN.position.y);\nscene.add(meshgulaN);\nrenderer.render(scene, camera);\n}\nrequestAnimationFrame (pad);\n}\nrequestAnimationFrame (pad);\n}\n\nlet tlac= document.getElementById (\"tlac\");\ntlac.addEventListener (\"click\", pridaj);\n<\/script>\n\n\n\n<h3 class=\"wp-block-heading\">Rota\u010dn\u00e9 teles\u00e1<\/h3>\n\n\n\n<p>Rota\u010dn\u00e9 teles\u00e1 - to nie je len valec, ku\u017ee\u013e a gu\u013ea. Tu vid\u00edme uk\u00e1\u017eky in\u00fdch telies vzniknut\u00fdch rot\u00e1ciou \u010dasti kruhu. Teles\u00e1 s\u00fa mierne priesvitn\u00e9, tak\u017ee si pri ur\u010ditom uhle m\u00f4\u017eeme vn\u00fatri telesa v\u0161imn\u00fa\u0165 \u00fatvar, ktor\u00e9ho rot\u00e1ciou teleso vzniklo.<\/p>\n\n\n\n<canvas id=\"platno2\"><\/canvas>\n<script type=\"module\">\nimport * as THREE from 'three';\nimport { OrbitControls } from 'three\/addons\/controls\/OrbitControls.js';\nconst camera = new THREE.PerspectiveCamera( 70, window.innerWidth \/ window.innerHeight, 0.01, 10 );\ncamera.position.z = 1;\n\nconst scene = new THREE.Scene();\n\/\/nastavim svetla, posledne cislo je intenzita\nconst svetlo = new THREE.DirectionalLight(0xffffff, 5);\nsvetlo.position.set(-0.6, 1.5, 1);\nconst svetlo2 = new THREE.DirectionalLight(0xffffff, 1);\nsvetlo2.position.set(0.5,2,-0.2);\nconst svetlo3 = new THREE.DirectionalLight(0xffffff, 1);\nsvetlo3.position.set(0,-1,0);\nscene.add(svetlo, svetlo2, svetlo3);\n\/\/niekolko materialov, mat2 je pre prierez\nconst mat = new THREE.MeshPhongMaterial({color:0x111150, shininess: 40, transparent: true, opacity: 0.8});\nconst mat2 = new THREE.MeshPhongMaterial({color:0xff0010, shininess : 40, transparent: true, opacity: 0.8});\nconst mat3 = new THREE.MeshPhongMaterial({color:0x003020, shininess: 40, transparent: true, opacity: 0.8});\nconst mat4 = new THREE.MeshPhongMaterial({color:0x111100, shininess: 40, transparent: true, opacity: 0.8});\nconst mat5 = new THREE.MeshPhongMaterial({color:0x222225, shininess: 40, transparent: true, opacity: 0.8});\nconst mat6 = new THREE.MeshPhongMaterial({color:0x255000, shininess: 40, transparent: true, opacity: 0.8});\n\/\/mriezka a osi\n\/\/scene.add(new THREE.AxesHelper(20));\n\/\/scene.add(new THREE.GridHelper(10,100));\n\nconst renderer = new THREE.WebGLRenderer( { canvas: platno2, antialias: true } );\nrenderer.setSize( 0.9*window.innerWidth, window.innerHeight );\nrenderer.setClearColor(\"rgb(174,227,245)\",1);\n\nconst kontrol = new OrbitControls(camera, renderer.domElement);\nkontrol.addEventListener(\"change\", ()=> renderer.render(scene, camera));\n\n\/\/cesta pre extr\u00faziu v tvare kruhu okolo osi y. R je polomer.\nconst R= 0.08;\nconst cesta = new THREE.CurvePath();\nlet BodyKr = [];\nlet i,x, z;\n\nfor (i=0; i<100*R; i++){\n    x = (100*R-i)\/100;\n    z = Math.sqrt(R*R-x*x);\n    BodyKr.push(new THREE.Vector3(x, 0, -z));\n}\nfor (i=0; i<100*R; i++){\n    x = i\/100;\n    z = Math.sqrt(R*R-x*x);\n    BodyKr.push(new THREE.Vector3(-x, 0, -z));\n}\nfor (i=0; i<100*R; i++){\n    x = (100*R-i)\/100;\n    z = Math.sqrt(R*R-x*x);\n    BodyKr.push(new THREE.Vector3(-x, 0, z));\n}\nfor (i=0; i<100*R; i++){\n    x = i\/100;\n    z = Math.sqrt(R*R-x*x);\n    BodyKr.push(new THREE.Vector3(x, 0, z));\n}\nconst first= new THREE.CatmullRomCurve3(\n     BodyKr, true); \/\/ true bude uzavreta\n      cesta.add(first);\n\nconst extrudeSettings = {\n    steps: 100,\n    extrudePath: cesta,\n    bevelEnabled: false\n};\n\/\/ tvar sa kresli do roviny x, y, ale vzdy sa otoci o 90 nadol\nconst shape = new THREE.Shape();\nshape.moveTo(0,0);\nshape.arc(0,0,0.1,Math.PI,Math.PI*5\/4, false);\/\/true false je smer otacania\nshape.lineTo(0, 0);\n\/\/ Vytvor\u00edme geometriu\nconst geometry = new THREE.ExtrudeGeometry(shape, extrudeSettings);\n\/\/const prierez = new THREE.ExtrudeGeometry(shape, {depth:0.01, bevelEnabled: false});\nconst meshExt = new THREE.Mesh(geometry, mat);\nmeshExt.translateY(0.2);\n\/\/const meshPrierez = new THREE.Mesh(prierez, mat2);\n\/\/druhe teleso\nconst shape2 = new THREE.Shape();\nshape2.moveTo(0,0);\nshape2.arc(0,0,0.05,Math.PI,Math.PI*2, false);\/\/true false je smer otacania\nshape2.lineTo(0, 0);\n\nconst geometry2 = new THREE.ExtrudeGeometry(shape2, extrudeSettings);\nconst meshExt2 = new THREE.Mesh(geometry2, mat2);\nmeshExt2.translateX(0.3);\n\n\/\/tretie teleso\nconst shape3 = new THREE.Shape();\nshape3.moveTo(0,0);\nshape3.arc(0,0,0.05,-Math.PI\/4,Math.PI\/4, false);\/\/true false je smer otacania\nshape3.lineTo(0, 0);\n\nconst geometry3 = new THREE.ExtrudeGeometry(shape3, extrudeSettings);\nconst meshExt3 = new THREE.Mesh(geometry3, mat3);\nmeshExt3.translateZ(0.3);\n\nconst shape4 = new THREE.Shape();\nshape4.moveTo(0,0);\nshape4.arc(0,0,0.05,Math.PI*3\/2,Math.PI*2, false);\/\/true false je smer otacania\nshape2.lineTo(0, 0);\n\nconst geometry4 = new THREE.ExtrudeGeometry(shape4, extrudeSettings);\nconst meshExt4 = new THREE.Mesh(geometry4, mat4);\nmeshExt4.translateX(-0.3);\nmeshExt4.translateY(0.1);\n\nconst shape5 = new THREE.Shape();\nshape5.moveTo(0,0);\nshape5.arc(0,0,0.05,Math.PI*3\/2,Math.PI*3, false);\/\/true false je smer otacania\nshape5.lineTo(0, 0);\n\nconst geometry5 = new THREE.ExtrudeGeometry(shape5, extrudeSettings);\nconst meshExt5 = new THREE.Mesh(geometry5, mat5);\nmeshExt5.translateZ(-0.3);\n\nconst shape6 = new THREE.Shape();\nshape6.moveTo(0,0);\nshape6.arc(0,0,0.06,0,Math.PI, false);\/\/true false je smer otacania\nshape6.lineTo(0, 0);\n\nconst geometry6 = new THREE.ExtrudeGeometry(shape6, extrudeSettings);\nconst meshExt6 = new THREE.Mesh(geometry6, mat6);\nmeshExt6.translateY(-0.2);\n\nscene.add(meshExt, meshExt2, meshExt3, meshExt4, meshExt5, meshExt6);\nrenderer.render( scene, camera );\n<\/script>\n\n\n\n<h3 class=\"wp-block-heading\">Mnohosten<\/h3>\n\n\n\n<p>Vedeli ste, \u017ee ak spo\u010d\u00edtate po\u010det vrcholov a po\u010det stien, odpo\u010d\u00edtate po\u010det hr\u00e1n, tak v\u017edy, v \u00faplne ka\u017edom mnohostene, dostanete v\u00fdsledok 2? Plat\u00ed to pre be\u017en\u00e9 mnohosteny, ako je kocka, hranoly, ihlany, ale aj v\u0161elijak\u00e9 in\u00e9 \u010dud\u00e1, ktor\u00e9 s\u00fa tvoren\u00e9 iba rovn\u00fdmi stenami.<\/p>\n\n\n\n<canvas id=\"platno3\"><\/canvas>\n<script type=\"module\">\nimport * as THREE from 'three';\nimport { OrbitControls } from 'three\/addons\/controls\/OrbitControls.js';\nconst camera = new THREE.PerspectiveCamera( 70, window.innerWidth \/ window.innerHeight, 0.01, 10 );\ncamera.position.z = 1;\n\nconst scene = new THREE.Scene();\n\/\/nastavim svetla, posledne cislo je intenzita\nconst svetlo = new THREE.DirectionalLight(0xffffff, 2);\nsvetlo.position.set(-0.6, 1.5, 1);\nconst svetlo2 = new THREE.DirectionalLight(0xffaaaa, 1);\nsvetlo2.position.set(0.5,2,-0.2);\nconst svetlo3 = new THREE.DirectionalLight(0xaaffaa, 2);\nsvetlo3.position.set(0.5,-1,0);\nscene.add(svetlo, svetlo2, svetlo3);\n\nconst renderer = new THREE.WebGLRenderer( { canvas: platno3, antialias: true } );\nrenderer.setSize( 0.9*window.innerWidth, window.innerHeight );\nrenderer.setClearColor(\"rgb(174,227,245)\",1);\n\n\/\/doubleside musi byt, aby boli steny vidiet z oboch stran.\nconst mat = new THREE.MeshStandardMaterial({color:0x505050, shininess: 40, transparent: true, opacity: 0.9,  emmisive: 0x505050, side: THREE.DoubleSide});\n\nconst kontrol = new OrbitControls(camera, renderer.domElement);\nkontrol.addEventListener(\"change\", ()=> renderer.render(scene, camera));\n\n\/\/vrcholy su suradnice, steny su po trojiciach vrcholy, ktore tvoria steny.\n\/\/ robi to len mnohosteny vpisane do gule.\n\nconst vrcholy =new Float32Array([\n0,0.3,0,   0,-0.4,0,   0.5,0.1,0,   Math.sqrt(3)\/4,-0.1,0.25,  0.25,0.1,Math.sqrt(3)\/4,   0,-0.1,0.5,   -0.25,0.1,Math.sqrt(3)\/4,   -Math.sqrt(3)\/4,-0.1,0.25,  -0.5,0.1,0,   -Math.sqrt(3)\/4,-0.1,-0.25,   -0.25,0.1,-Math.sqrt(3)\/4,   0,-0.1,-0.5,   0.25,0.1,-Math.sqrt(3)\/4,   Math.sqrt(3)\/4,-0.1,-0.25\n]);\nconst steny = new Uint32Array([\n\/*0,2,4,   0,4,6,   0,6,8,   0,8,10,   0,10,12,   0,12,2,    \n1,3,5,   1,5,7,   1,7,9,   1,9,11,   1,11,13,   1,13,3,\n2,3,4,   3,4,5,   4,5,6,   5,6,7,   6,7,8,   7,8,9,   8,9,10,   9,10,11,   10,11,12,   11,12,13,   12,13,2,   13,2,3*\/\n0,2,3,  0,3,4,  0,4,5,  0,5,6,  0,6,7,  0,7,8,  0,8,9,  0,9,10,  0,10,11,  0,11,12,  0,12,13, 0,13,2,\n1,2,3,  1,3,4,  1,4,5,  1,5,6,  1,6,7,  1,7,8,  1,8,9,  1,9,10,  1,10,11,  1,11,12,  1,12,13,  1,13,2\n]);\n\/\/ 0.4 je polomer gule, 0 hladkost\n\n\/*const geometry = new THREE.BufferGeometry();\ngeometry.setAttribute('position', new THREE.BufferAttribute(vrcholy, 3));\n\ngeometry.setIndex(new THREE.BufferAttribute(steny, 1));*\/\n\nconst geometry = new THREE.PolyhedronGeometry (vrcholy, steny, 0.2, 0);\n\nconst mesh = new THREE.Mesh(geometry, mat);\n\nscene.add(mesh);\n\nrenderer.render( scene, camera );\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>\u010co by ste narysovali, ak dostanete prv\u00fdkr\u00e1t do ruky rysovacie potreby a m\u00e1te narysova\u0165 nie\u010do z geometrie? Sk\u00fasite mo\u017eno v\u0161eli\u010do, ale kruhy bud\u00fa pravdepodobne to, \u010d\u00edm sa budete zab\u00e1va\u0165 najdlh\u0161ie. Preto prv\u00fdm na\u0161\u00edm po\u010dinom v s\u00favislosti s geometriou v rovine s\u00fa pr\u00e1ve kruhy obohaten\u00e9 o prvok n\u00e1hody. Tak\u017ee v\u00fdsledok je v\u017edy origin\u00e1lny. Ka\u017ed\u00e9 kliknutie na [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-34","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>V\u0161eli\u010do z geometrie - jankafialka<\/title>\n<meta name=\"description\" content=\"Str\u00e1nka V\u0161eli\u010do z geometrie obsahuje tvorbu n\u00e1hodn\u00fdch kruhov, simul\u00e1ciu padaj\u00facich gu\u013e\u00f4\u010dok, zop\u00e1r rota\u010dn\u00fdch telies a jeden pekn\u00fd mnohosten.\" \/>\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\/?page_id=34\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"V\u0161eli\u010do z geometrie - jankafialka\" \/>\n<meta property=\"og:description\" content=\"Str\u00e1nka V\u0161eli\u010do z geometrie obsahuje tvorbu n\u00e1hodn\u00fdch kruhov, simul\u00e1ciu padaj\u00facich gu\u013e\u00f4\u010dok, zop\u00e1r rota\u010dn\u00fdch telies a jeden pekn\u00fd mnohosten.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.jankafialka.sk\/?page_id=34\" \/>\n<meta property=\"og:site_name\" content=\"jankafialka\" \/>\n<meta property=\"article:modified_time\" content=\"2024-12-30T17:03:20+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Predpokladan\u00fd \u010das \u010d\u00edtania\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 min\u00faty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.jankafialka.sk\\\/?page_id=34\",\"url\":\"https:\\\/\\\/www.jankafialka.sk\\\/?page_id=34\",\"name\":\"V\u0161eli\u010do z geometrie - jankafialka\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.jankafialka.sk\\\/#website\"},\"datePublished\":\"2023-04-26T10:10:59+00:00\",\"dateModified\":\"2024-12-30T17:03:20+00:00\",\"description\":\"Str\u00e1nka V\u0161eli\u010do z geometrie obsahuje tvorbu n\u00e1hodn\u00fdch kruhov, simul\u00e1ciu padaj\u00facich gu\u013e\u00f4\u010dok, zop\u00e1r rota\u010dn\u00fdch telies a jeden pekn\u00fd mnohosten.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.jankafialka.sk\\\/?page_id=34#breadcrumb\"},\"inLanguage\":\"sk-SK\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.jankafialka.sk\\\/?page_id=34\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.jankafialka.sk\\\/?page_id=34#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/www.jankafialka.sk\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"V\u0161eli\u010do z geometrie\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.jankafialka.sk\\\/#website\",\"url\":\"https:\\\/\\\/www.jankafialka.sk\\\/\",\"name\":\"jankafialka\",\"description\":\"O matematike\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.jankafialka.sk\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"sk-SK\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"V\u0161eli\u010do z geometrie - jankafialka","description":"Str\u00e1nka V\u0161eli\u010do z geometrie obsahuje tvorbu n\u00e1hodn\u00fdch kruhov, simul\u00e1ciu padaj\u00facich gu\u013e\u00f4\u010dok, zop\u00e1r rota\u010dn\u00fdch telies a jeden pekn\u00fd mnohosten.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.jankafialka.sk\/?page_id=34","og_locale":"sk_SK","og_type":"article","og_title":"V\u0161eli\u010do z geometrie - jankafialka","og_description":"Str\u00e1nka V\u0161eli\u010do z geometrie obsahuje tvorbu n\u00e1hodn\u00fdch kruhov, simul\u00e1ciu padaj\u00facich gu\u013e\u00f4\u010dok, zop\u00e1r rota\u010dn\u00fdch telies a jeden pekn\u00fd mnohosten.","og_url":"https:\/\/www.jankafialka.sk\/?page_id=34","og_site_name":"jankafialka","article_modified_time":"2024-12-30T17:03:20+00:00","twitter_card":"summary_large_image","twitter_misc":{"Predpokladan\u00fd \u010das \u010d\u00edtania":"2 min\u00faty"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.jankafialka.sk\/?page_id=34","url":"https:\/\/www.jankafialka.sk\/?page_id=34","name":"V\u0161eli\u010do z geometrie - jankafialka","isPartOf":{"@id":"https:\/\/www.jankafialka.sk\/#website"},"datePublished":"2023-04-26T10:10:59+00:00","dateModified":"2024-12-30T17:03:20+00:00","description":"Str\u00e1nka V\u0161eli\u010do z geometrie obsahuje tvorbu n\u00e1hodn\u00fdch kruhov, simul\u00e1ciu padaj\u00facich gu\u013e\u00f4\u010dok, zop\u00e1r rota\u010dn\u00fdch telies a jeden pekn\u00fd mnohosten.","breadcrumb":{"@id":"https:\/\/www.jankafialka.sk\/?page_id=34#breadcrumb"},"inLanguage":"sk-SK","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.jankafialka.sk\/?page_id=34"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.jankafialka.sk\/?page_id=34#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.jankafialka.sk\/"},{"@type":"ListItem","position":2,"name":"V\u0161eli\u010do z geometrie"}]},{"@type":"WebSite","@id":"https:\/\/www.jankafialka.sk\/#website","url":"https:\/\/www.jankafialka.sk\/","name":"jankafialka","description":"O matematike","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.jankafialka.sk\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"sk-SK"}]}},"_links":{"self":[{"href":"https:\/\/www.jankafialka.sk\/index.php?rest_route=\/wp\/v2\/pages\/34","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.jankafialka.sk\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.jankafialka.sk\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.jankafialka.sk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.jankafialka.sk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=34"}],"version-history":[{"count":5,"href":"https:\/\/www.jankafialka.sk\/index.php?rest_route=\/wp\/v2\/pages\/34\/revisions"}],"predecessor-version":[{"id":2248,"href":"https:\/\/www.jankafialka.sk\/index.php?rest_route=\/wp\/v2\/pages\/34\/revisions\/2248"}],"wp:attachment":[{"href":"https:\/\/www.jankafialka.sk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}