color math

Mumwe muverengi akandipomera mhosva yekutaura zvematongerwo enyika mumapepa angu esvomhu. Zvakanaka, ndanga ndichingotaura nezvekudzidziswa. Chikoro chagara chiri nyaya yezvematongerwo enyika, kunyangwe payaifanirwa kuve yezvematongerwo enyika maererano nesoftware. Mukutanga kwaKubvumbi, mushure mekuiswa kwezvirambidzo zvekadhidhi muhupenyu hwedu hweveruzhinji, kudiwa kwekudzidza kure kwakawedzera zvakanyanya. Chikamu chechinyorwa changu kuita kune imwe hurukuro yeTV yevadzidzi vepuraimari. Vakakonzera dutu munyika yevadzidzisi vesvomhu - vakange vakazara zvisina maturo, sedhiramu remvura rakakandwa mugungwa. Kuti pasave nemunhu anondipomera kuita zvematongerwo enyika, ini handisi kuzonyora kuti yaive chiteshi cheTV ripi.

Rugwaro rwacho rwakapatsanurwa - ndinotanga nehurukuro yevana vadiki, asi enderera mberi nekufunga kune vakuru uye zvinopesana. Izvi hazvisi zvekukufinha. Kutanga kuvana. Iri ndiro izwi rangu muhurukuro pamusoro pekuti (zvakanaka, iwe unogona sei) kutaura nevana nezve "Queen of Sciences".

Exercise 1. Tarisa padandemutande rangu rekutanga. Unoonei pairi?

Unogara kupi? Mark. Iwe unofunga kuti ndakasarudza mavara emiganhu yedu nemukana, kana iwe unogona kuwana tsananguro nei "pamusoro" iri bhuruu-girinhi, uye "pasi" chimiro chichena? Asi sei ndakanyora "pamusoro" uye "pasi"? Mushure mezvose, nzvimbo idzi dzenyika dzinonzi ... zvakanaka, chii chaizvo? Uye mamwe maviri? Kana kuti pamwe unoziva chikonzero nei mazita epasi rese emakadhinari mapoinzi ari N, E, W, S?

Chiitwa 2. Tarisa zvikwangwani zvemumugwagwa (1). Ndechipi chatingadaidza kuti square? Uye nei makona ekutanga nechitatu akatenderedzwa? Tsvaga kuti ndeapi masaini emumugwagwa ane triangular, denderedzwa (denderedzwa), uye octagonal muchimiro. Neiko chiratidzo chimwe chemativi matatu chakasiyana nezvimwe? Sei chiratidzo chimwe chete octagonal?

1. Ndechipi chezviratidzo chine mativi mana?

Exercise 3. Enda online. Simudza chero browser. Nyora "square", wozosarudza "mifananidzo" uye ... tarisa mifananidzo iripo. Kwete zvese, asi gumi nemaviri chete. Sarudza yaunoda zvakanyanya. Wakasarudza? Zvino edza ndinyengetedzesei ichi. Zvichida hauzvizivi iwe pachako? Kana kuti pamwe unoziva?

Exercise 4. Zvino tarisa nhamba yangu yepuzzle nhamba yechipiri. Unoona masikweya mairi? Chaizvo - yakatsvuka mukati. Vanokura. Yekutanga, diki, kuruboshwe ine ziso rimwe, "bhatani" rimwe.

Ndichapindura ipapo ipapo. Mashiripiti sikweya chikwere umo huwandu hwenhamba dzakachinjika, dzakadzika uye nediagonally dzakafanana. Ngatitarisei: ungangotaura kuti yechipiri yakakura zvakapetwa kaviri nekuti ine mabhatani maviri kudivi rega rega…. Oh, yakakura zvakapetwa kaviri here? Verenga mabhatani mangani ana mana! Ngationei zvichazoitika. Yechitatu yakafara uye zvishwe zvitatu pakureba. Verengai seams. Vangani variko? 25. Yechina ina yakareba uye yakafara (kana yakakwirira) ina. Kana ina ina ine gumi nenhanhatu. Hongu, ine misono gumi nematanhatu. Uye yechishanu? Kune matinji mashanu kudivi rimwe nerimwe, saka vangani varipo pamwe chete? Bravo, 25. Isu tinoti sikweya iyi ine nzvimbo yeXNUMX. Asi pamwe waizviziva. Saka, sezvakaratidzwa mutafura iri kurudyi.

4+9+2=3+5+7=8+1+6=4+3+8=9+5+1=2+7+6= 4+5+6=8+5+2=15.

Wikipedia inonyora nenzira kwayo kuti mashiripiti masikweya haabatsiri musainzi. Vanongonakidza chete. Asi mavakirwo avakaitwa anonakidza kupfuura masikweya pachawo. Zvakafanana nekushanya: kazhinji chinangwa chiri chechipiri, nzira yekuenda nayo yakakosha. Ngatitarisei nzira yekuvaka sikweya yemamita makumi maviri neshanu. Isu tinoisa iyo pakati uye tinoyeuka iyo yakatokanganwa "mutambo wehumambo", ndiko kuti, chess. Tichasvetuka takananga kuNNE (North-North-East). Iko kare "troika" inowira kunze kwekona. Tinoenda nayo kunzvimbo yayo (yekupedzisira mumutsara wechipiri kubva pasi). Inondiyeuchidza nezvemumhanzi "kudzikiswa kune yekutanga octave". Isu tinoshandisa musimboti uyu nguva dzose ... kwenguva yakareba sezvinobvira. Anomira paXNUMX. Hazvina mhosva, tinoisa zvitanhatu pasi pezvishanu zvitsvuku, izvo zvatova mukati mechikwere chedu.

2. Sei sikweya iyi iri "magic"?

Kudzokera kusvomhu dzevana. Zvino tarisa kumusoro kwepikicha yangu # 2. Pane mativi mana here? Kwete! Nhamba idzi dzinonzi chii? Beata, uri sei? Wataura chokwadi, rectangles. Nei vachidaidzwa kudaro? Nokuti vane makona chaiwo? Tichazotaura nezvazvo gare gare, asi parizvino ngatirangarirei kuti kona yekurudyi chii. Bartek, ungatsanangura sei izvi kune mumwe munhu asingazive? Pamwe ikona yakadaro. Zvakanaka, ngazvive zvakadaro. Kana isu tiri kutyaira motokari uye kutendeuka pakona yakarurama, saka kwete kure zvakanyanya mberi kana kure zvakanyanya kumashure, asi chaizvoizvo kudivi. Selina, simuka utendeuke pakona chaipo. Kuruboshwe kana kurudyi? chero nzira yaunoda.

Ngatitaureiwo nezve maumbirwo ari pamusoro, kureva, rectangles. Ndeupi wakakora, mutete, mutete, murefu, mupfupi, mupfupi, mutete, wakarebesa? Iwe unobvuma zvechokwadi kuti yero kurudyi kureba, kutetepa uye kureba. Asi chenjera. Kana iyo yakarara padivi payo, ichavawo yakareba, asi ipfupi. Ungamuti "akakora" here?

3. Tanga kuvaka 5 by 5 magic square.

4. Nzira yekuvaka 5x5 magic square?

Iye zvino zvakare maviri anoisa evaverengi vakuru. Yekutanga ndeye 100. Ndinofunga kuti zana izana mune chero mutauro wechiSlavic. Izvi zvakakosha kune nyanzvi dzemitauro. Zita renhamba iyi rinosiyanisa mapoka maviri emitauro yeIndo-European, iyo inosanganisira mitauro yose mukondinendi yedu, kunze kweFinnish, Hungarian, Estonian Basque uye Breton isinganyanyozivikanwa.

Mumitauro yakatanga mukutanga kutama, izwi rezana rakagadzirwa kuita (chiGiriki) uye (Latin), kwakabva French neGerman (uye, chokwadi, Chirungu). Ndiko kusaka tichidaidza mitauro iyi kuti mazana.

Mutauro wedu ndeweboka remitauro yepakati kana yesatemic, nekuti mushure mekunyorovesa (kunyorovesa) mutauro wevabereki wakatora iyi yakanaka uye pfupi fomu yezana. Makore zana, zana remakore, kurarama kwenguva refu ...

5. Zvevanoziva. Magic square inoumbwa nenhamba huru.

Yechipiri inopinza yakarebesa, asi yakanyatso papoindi.

Mathematician uye

Pointer BMI Ndakabvunza zvangu. Rega ndikuyeuchidze kuti ichi chiratidzo chinofananidza uye kuongorora kutevedza kwehuremu hwemurwere mukuru ane dzidziso yakasimbiswa. Iyo fomula yemasvomhu iri nyore: Kamura huremu hwako (mumakirogiramu) neskweya yehurefu hwako (mumamita). Muganhu wehuremu hwepamusoro unofungidzirwa kuva quotient ye 25. Pachiyero ichi, mutambi weTennis ane mukurumbira weSpanish Rafael Nadal anenge akawandisa (185 cm, 85 kg), achipa BMI ye24,85. Skinny sechip, mukwikwidzi wake weSerb Novak Djokovic ane 21,79 uye anokwana nyore mumiganho yakajairika. Munyori wemashoko aya ... handingatauri kuti nhamba iyi yakakwirira sei. Zvisinei, semuganho wakaderera wehuremu hwakakodzera kwandiri (180 cm), iyi ... 61 kg. Mukomana ane huremu hwemakirogiramu 180 ane huremu hwemakirogiramu makumi matanhatu nerimwe aizodonha nemhepo ipi zvayo. Ini ndinotenda kuti kunyangwe iyo musimboti wechiratidzo pachayo wakarurama, iyi yekumisikidza yeparamita ingangove yakatemerwa nemakambani emishonga (mapiritsi ekudya).

Vanachiremba pachavo vanoziva kuti chiratidzo ichi hachifungi nezvehutano hwemunhu murwere. Ndichawedzerawo math chokwadi. Vanhu vakura vari kuonda. Muzongoza wavo unodonha. Muhuduku hwangu, ndakanga ndakareba 184 cm, ikozvino 180 cm. Kana ndaiyera 100 kg, ipapo "ipapo", kureva, nehupamhi hwe 184 cm, izvi zvaizopa chiratidzo che 29,5 (I degree overweight), uye ikozvino. kuti nehupamhi hwemasendimita 180, ichava 30,9 (yakawandisa yedhigirii yechipiri). Uye zvakadaro "ini" haina kuderera, chete musana wakamonyoroka.

Ngatitarisei iyo BMI index ye "constancy of indicators." Icho chiripo ndechekuti hazvifanirwe kuve nebasa kana iyo data yakapihwa mune metric system (makirogiramu nemamita) kana, semuenzaniso, muChirungu mapaundi netsoka. Ehe, nhamba dzichave dzakasiyana, sezvichaita nhamba dzinoratidza kumhanya kwekufamba mumamaira nemakiromita. Asi mumwe anogona nyore kushandura imwe kuita imwe pasina kupokana. Heino kupatsanurwa. Mamaira anogona kushandurwa nyore kuita makiromita. Asi paakabvunzwa kuti firiji yakakura sei, shamwari yangu yeCanada yakapindura, "27 cubic feet." Uye chenjera pano. Mamiriro acho akanyanya kuipa pakusarudza mashandisirwo emafuta emotokari. MuUnited States neCanada vanozviti "Ndichatyaira mamaira mangani pagaloni?" Muverengi, pamwe unogona kutonga (kuverenga) kana 60 mpg yakawandisa kana kuti idiki? Imwe gorosi yeUnited States yakasiyana neCanada (inonziwo imperial) gallon. Chokwadi, zviyero zvemetric zvave zvichishanda muCanada kwemakore akawanda, asi kuchinja maitiro hakusi nyore.

Asi neBMI zvese zviri mugwara. Sezvo tsoka yechirungu iri 30,48 cm uye pondo iri 0,454 kg, mhedzisiro yeChirungu BMI (inotaridzwa mumapaundi ehuremu paskweya tsoka yehurefu) inofanira kuwanda ne0,454 uye 0,30482, iyo yakaenzana ne4,88. Munhu 180 cm anorema 220,26 pounds uye 5,9 tsoka. Nzira mbiri dzekuverenga BMI dzakafanana, 30,9.

Iye zvino inonyanya kufadza (kubva pakuona kwemasvomhu). Mune rimwe remabhuku angu, ndakatsanangura "roundness index" - kuti maumbirwo akatenderedzwa akaita sedenderedzwa. Zvakawanda sei - kureva, masvomhu "ingani muzana." Vhiri, hongu, 100 muzana kutenderera. Uye dzimwe nhamba? Nzira yekuiyera sei?

Ngatishandisei pfungwa iyi kuyera kuti rectangle "inotaridzika" yakaita sei sikweya. Ngatitii "destruction measure". Sikweya inofanirwa kuve 100% yakatsemuka, handiti? Nyanzvi yemasvomhu inofarira kutaura kuti kutsemuka kweskweya i1, uye kutsemuka kwemarectangles akatetepa kunoda kudiki.

Ngatiisei chimwe chinhu senge body mass index kumarectangles. Gurai nzvimbo yacho ne square ye perimeter. Sikweya ine side A ingani? Ingori 1/16 yemaakaundi. Kuti tiwane indekisi ya1, ngatiwande negumi nematanhatu. Saka body mass index yemarectangles ndeye

Zvino fungidzira kuti rectangles kuenda kuna chiremba. “Ndichaverenga BMI yako,” chiremba anodaro. Ndapota, mumwe nomumwe. Hedzinoi mhinduro dzako. Ndeipi yekuderedza uremu?

6. Nderipi rectangle ndeyekuonda, uye ndeipi inorexic? Zviverengere

Chirevo. BMI inobata vanhu sezvisikwa zvakapfava! Ichi chiratidzo chinoshanda zvakanaka (pasina kurangarira marongero emazinga emuganhu). Zvisinei, nyanzvi dzemasvomhu hadzina chokwadi nazvo. Zviri nyore kuita generic. Maformula akapfava emasvomhu ekutsanangura biological and social phenomena anofanirwa kubatwa nekuchenjerera kukuru.

Tadzoka kuzokurukura nevana vadiki. Ngatimbotarisaizve dambanemazwi nhamba 2. Takabvumirana vana vadiwa kuti ichokwadi kuti rectangle ine makona chaiwo chete. Zvaizoshamisa kudai zvaisaita. Asi iwo manhamba ari pazasi (yebhuruu piramidhi), yepepuru "monyoroka" uye yebhuruu pinwheel inewo makona chaiwo. Pamwe vane rectangular? Kwete, vanhu vakabvumirana kuti rectangles ndeavo vane makona mana ekurudyi, hapasisina.

Dzidza kufunga zvakanaka. Tarisa:

Kana chimwe chinhu chiri rectangle, saka chine makona chaiwo chete. Izvi hazvina kufanana ne:

Kana chimwe chinhu chine makona chaiwo chete, irectangle.

Sei? Panzvimbo yerectangle, tora kati nembwa, panzvimbo yekona yakarurama, tora paws. Manzwisisa zvino? Zvirokwazvo!

Mhinduro yevakuru (uye kwete chete). Muhuduku hwangu pakanga pane sirogani: Kufunga kune remangwana rakakura! Dai zvadaro kare.

Nzwisisa. Mubvunzo wakakosha. Sikweya irectangle here? Pane! Ine makona mana ekurudyi! Tinogona kutaura kuti sikweya ndiyo inonyanya kuenzana nerectangle. Rutivi rumwe norumwe rwakafanana kureba.

Ticharamba tichigadzira mapikicha akanaka. Unonyatsoziva kuti even number chii. Kana kirasi yaiswa paviri, zvino mumwe munhu achasara asina peya, kana ... asina kusiiwa. Ko 12 inhamba yakaenzana here? Ehe. Kana vanhu gumi nevaviri vachida kutamba volleyball, zviri nyore kwavari kuumba zvikwata zviviri. Kaviri nhanhatu igumi nembiri. Uye kana vanhu vakafanana vachida kutamba ping-pong, vanogona kugadzira mapaya matanhatu. Katanhatu kakapetwa kaviri zvakare gumi nembiri.

Chii chavakafanana: mutambo, muchato, duel, girazi uye mari? Chechipiri. Mumutambo, zvikwata zviviri, murume nemukadzi vanoroora (hongu, murume nemukadzi - anoroora, anoroora). Vapikisi vaviri vari kurwisana mu duel, mugirazi tinoona zvakasiyana "" ini. Menduru ine mativi maviri. Mazita avo ndivanaani? Misoro kana miswe. Tine gondo pamari yekuPoland. Pane waunoziva ane mapatya here? Kare kare, "mapatya" aishandiswa mumisha - midziyo miviri yakabatana, imwe yesobho, imwe ye ... yechipiri.

Kana kuti pamwe unonzwisisa mazwi: kaviri, symmetry, inversion, hunyambiri, zvakapesana, mapatya, duet, tandem, imwe nzira, yakaipa, kuramba?

Kana imba iine mabudiro maviri (kana kuti kupinda nekubuda, chero kwaunoda), tingati ine "masuo maviri" here? Kwete, hazvina kunaka. Zvakanaka sei? Nei tichidaro? Uye kana tikawedzera rimwe suo rekamuri rine madhoo maviri ndokuisa musuo imomo, madhoo mangani achavapo? Tatu? Aiwa kwete….

"Kumberi" kunofambidzana ne "kumashure". Apo pane "kuruboshwe", panewo "kurudyi", kana chimwe chinhu chisiri "pamusoro", zvino chinogona kuva "pasi". Dai pasina kuwedzera, iyo minus yaisazodiwa. Nhamba yechipiri yakanaka.

Vanoimba: “Imbwa mbiri…” Unoziva rwiyo rwacho here? Kana zvisina kudaro, dzidza.

Mabhuroko mangani ari mupikicha inotevera? Handizivi, isu hatitomboverenge. Ndinoreva pasina kuverenga, ndinoziva kune imwe nhamba. Sei? Kasper, ndinozviziva sei izvi? Oo, iwe unotoziva? Sezvaunotaura? Kuti munhu wese akaenzana? Zvimwechetezvo!

Zvinyoro. Kune vaviri. Hazvikunetse here kuti pink iri kuruboshwe yakasviba pane iri kurudyi?

Izvo zvisipo kana zviripo. Ndinoyeuka kuti ndichiri mudiki ndaitamba nhabvu, paigara paine dambudziko kana paine vanomwe, vapfumbamwe, gumi nerimwe, gumi nevatatu vedu ... Zvakanga zvisingaite kukamura kuita zvikwata zviviri zvakaenzana. Mhinduro yaive yekuti takatamba chinangwa chimwe chete. Mutambi wepagedhi uyu aisave wechikwata chipi zvacho. Aifanira kuzvidzivirira pakurova kwose.

Dambudziko…kwete revakuru chete. Ipa mienzaniso yemotokari dzine nhamba isinganzwisisike yemavhiri (hativerenge vhiri remotokari mumotokari). Rimwe zuva ndakaona kuti inogona kunge iri ... mota yetambo kuKasprowy Wierch - mota yakakungurutswa patambo pamavhiri manomwe. Asi ikozvino handizivi kuti zvaita sei.

Mabhuroko mangani ari mupikicha yechina? Pane nhamba yakaenzana kana isinganzwisisike here? Petrek, izvi ndezvenyu! Uchazvigadzirisa sei? Unoda kuverenga wobva waziva? Zvakanaka, uri kukanganisa here pakuverenga uku? Ona kana zvisina basa.

Munguva dzekare, nhamba dzisinganzwisisiki dzaionekwa sedzakanakisisa. Nhasi tinoda kuenzana. Wanga uchiziva here kuti kana tikapa mumwe munhu maruva, saka panofanira kunge paine odd nhamba yawo? Ehe, izvi hazvishande kune hofori bouquets.

Dambudziko rinofungidzirwa ... pamwe kwete revakuru chete. Ndiani akakodzera mashoko okuonga, maruva uye ruremekedzo kubva kwatiri tose (uye ngatirege kutya izvi - mubairo wakasimba!) Nokuda kwekuzvipira, kuneta, kushanda kwenguva refu, yakaoma uye ine ngozi kuitira kuti tisarwara, uye kana tinorwara, topora nekukasika?