Mene ne wani square? Yadda za a sami vertices bangaranci jirgin lissafi, girma da kuma sawun wata square kwana?

Answers zuwa ga tambaya game da abin da yake cikin square, za a iya kafa. A duk ya dogara a kan waɗanda ka yi jawabi wannan batun. A mawaki ya ce da square - mai 4, 8, 16, 32 sanduna ko jazz improvisation. The yaro - yana da wani wasan da ball ko yara mujallar. Firintar zai aika ka yi nazarin font size da kuma kayan aiki - da karfe-profile jinsunan.

Akwai su da yawa wasu dabi'u a cikin wannan kalmar, amma a yau za mu tambaya na lissafi. Saboda haka ...

Magance wannan adadi, za mu sannu a hankali, daga sauki ga hadaddun, da kuma fara da tarihin square. Kamar yadda ya bayyana, kamar yadda ya gane da mutane, masana kimiyya daga kasashe daban-daban da kuma wayewar?

A tarihin na nazarin square

Ancient duniya tsinkayen square, yafi a matsayin hudu manyan maki. A general, duk da yawa quads, kawai a babban square na lamba - hudu. Domin Assuriyawa da kuma Peru square - da dukan duniya, da cewa shi ne, shi wakiltar hudu main kwatance da kamfas.

Ko sararin samaniya ne kamar square, kuma zuwa kashi hudu sassa - mafarkinsa na Arewacin Amirka. Domin da Celts, duniya - shi ne kamar yadda uku square, nested, kuma daga cibiyar na hudu na gudãna daga ƙarƙashinsu (!). Kuma dukan Masarawa bauta wa wannan adadi!

Da farko aka bayyana da ilmin lissafi dabarbari square Helenawa. Amma ga su, wannan polygon yana da kawai korau halaye. Pythagoras bai so ko lambobi, ganin su a matsayin mai rauni, kuma na mata.

Ko addinai ba square. A Musulunci, qwarai da gaske - da cibiya na duniya - ba wasu siffar zobe, wato wani cubic siffar.

A India, babban grapheme wakiltar duniya, ko da ƙasa, alama ce, da aka rebaptized square. Sa'an nan, muna magana ne game da hudu manyan maki, da hudu yankuna na duniya.

A China, da square - a duniya jituwa da oda. Hargitsi aka rinjãye su a ginin square bambanta. A square rubũtacce a cikin da'irar, shi ne tushen ganin duniya, NUNA da hadin kai da kuma dangane da halittu da kuma Duniya.

Pagan Rasha - Square Svarog. Wannan alama ce kuma ake kira Svarog Star ko Star na Rasha. Yana kyawawan rikitarwa, kamar yadda ya tashi daga intersecting da rufaffiyar Lines. Svarog - bautãwa na maƙera, babban mahalicci, mahaliccin kuma sama kansa a gabatar da Rus. Wannan alama ce shi ne wani rhombus, wanda kuma yayi magana da Duniya da kuma ta hudu kwatance. Kuma da star tare da hudu haskoki - 4 kusurwa ta duniya, Lika Svaroga 4 - ya sanin kome da kome. A ray mahada - cibiyar.

Ban sha'awa abubuwa game da square

Mafi mashahuri magana zuwa rai na mu protagonist - "Black Square".

Malevich ta hoto ne har yanzu Popular. Marubucin bayan halittarsa sun dogon sha wahala da tambaya na abin da shi ne da kuma dalilin da ya sa wani sauki baki square a kan wani farin baya haka fa, tã da hankali ga kanta.

Amma idan ka dauki mukalli a hankali, za ka lura da cewa square jirgin sama ne ba sumul ba ne, kuma a fasa daga cikin baki tawada ne mai sa na Multi masu launin tabarau. A fili, a farkon akwai wani abun da ke ciki, wanda marubucin bai so, kuma ya rufe shi daga idanun mu ga wannan adadi. Black square a matsayin wani abu - a baki rami, kawai sihiri square siffar. A wõfintattu da aka sani ya jawo hankalin ...

Wani Popular "sihiri murabba'ai". A gaskiya ma shi ne - a tebur, ba shakka, da square cika da lambobin a kowane shafi. Jimlar wadannan lambobin shi ne guda ga duk layuka, ginshikan da diagonals (dabam). Idan diagonals an shafe ta daga lissafi, da square - semimagic.

Albrecht Dürer a shekarar 1514 halitta zanen "Melancholia I", wanda aka nuna a 4x4 sihiri square. Yana takaice daga cikin lambobin ginshikan, layuka, diagonals, har ma da ciki square ne da talatin da huɗu.

Bisa ga wadannan alluna kasance sosai ban sha'awa da kuma rare wuyar warwarewa - "Sudoku".

Masarawa suka farko a gudanar da musayar line lamba (ranar haihuwa) kuma halayya, damar iya yin komai, kuma talanti na mutum. Pythagoras ya dauki wannan ilmin, 'yan sarrafa da kuma sanya shi a cikin square. A sakamakon haka shi da wani square na Pythagoras.

Yana yana da wani raba yankin a numerology. Daga ranar haihuwa na wani mutum lissafi ta ƙara da hudu babban lambobin da aka sanya a Pythagoras Square (square). Kuma dage farawa daga duk boye bayanai game da makamashi, kiwon lafiya, iyawa, sa'a, halin da sauran abubuwa a kan shelves. A kan talakawan, daidaito da safiyo ne 60% -80%.

Mene ne wani square?

Square kira da lissafi adadi. Siffar square - quadrilateral, wanda yana daidai tarnaƙi, kuma kusassari. More daidai, da quadrangle kira daidai.

A square yana ta ãyõyi. Su ne:

• bangarorin na daidaita tsawon;
• daidai kusassari tsakãninsu - mike (90 digiri).

Saboda wadannan halaye da kuma siffofin da Squared da'irar za a iya rubũtacce, da kuma bayyana shi a kusa da shi. A circumscribed da'irar ne tangent to duk da vertices rubũtacce - tsakiyar sãsanninta. Su mayar da hankali zai zo daidai da cibiyar da square da zai raba dukan diagonally a cikin rabin. A karshen, bi da bi, su ne daidai da raba sasanninta na square a cikin daidai sassa.

Daya diagonal da rababben square cikin biyu isosceles triangles, biyu - zuwa hudu.

Saboda haka, idan da tsawon da bangarorin na wani square - t, da tsawon da radius daga cikin circumscribed da'irar - R, kuma an rubũtacce - r, sa'an nan

• wani square tushe yanki ko square area (S) shi ne daidai S = t ² = 2R ² = 4r ^2;

• wani square kewaye P ya kamata a lasafta ta da dabara P = 4t = 4√2R = 8r.

• da tsawon da radius daga cikin da'irar R = (√2 / 2) t;

• rubũtacce - r = t / 2.

A square tushe yanki ne har yanzu yiwuwa yin lissafi, sanin ya gefe (a) ko da tsawon da diagonal (c), sa'an nan da dabara zai bayyana bi da bi: S = ² da kuma S = 1 / 2c ^2.

Mene ne square, muna samu. Bari mu dauki wani kusa look at cikakken bayani, saboda da siffa daga cikin square ne tsakaitã murabba'i mai dari. Ya na da biyar da gatura da fasali, tare da daya (hudu-domin) ya wuce ta tsakiyar da kuma shi ne perpendicular da jirgin saman na square, da wasu mutum hudu - amfãninta ninki biyu fasali axis, su biyu a layi daya ga bangarorin, da kuma biyu mafi izinin tafiya a cikin diagonal na square.

Hanyar na gina wani square

Bisa ga definition, ga alama cewa babu wani abu sauki fiye da gina wani m square. Wannan gaskiya ne, amma bisa sharadin cewa kana da dukan ji dasu. Kuma idan wani abu ne ba samuwa?

Bari mu dubi data kasance hanyoyin, wadda za ta taimake mu mu gina wannan adadi.

Aunawa m da kuma saita square - Waɗannan su ne babban kayan aikin ta hanyar abin da za ka iya mafi saukin gina wani square.

A farko, alama batu, ce A, za mu gina a kan shi a square tushe.

Amfani da wani m, bijirẽwa daga gare ta ga dama a nesa daidai da tsawon gefe, misali 30 mm, da kuma kafa batu B.

Yanzu, daga cikin maki biyu, ta amfani gon perpendiculars Doke shi gefe har zuwa 30 mm kowane. A iyakar da perpendiculars sa maki C da D, wanda suna da alaka da juna, ta amfani da wani m - duk square ABCD da gefen 30 mm shirye!

Amfani da shugaba da protractor ma quite sauki shirya wani square. Fara, kamar yadda a baya harka a sharuddan, misali N, kau da kai daga ta a kwance tazara, misali 50 mm. Saka batu O.

Yanzu tsakiyar protractor gama da maki H, akwati a cikin kwana ⁰ 90, therethrough da wani batu H ginawa a tsaye kashi 50 mm a ƙarshensa tare da wani batu P. Bugu da ari, a cikin wannan hanya gina da uku kashi daga cikin aya Yã ta wani kwana na 90 ⁰ 50 mm, bar shi kawo karshen aya P. Haša dige R kuma R. kun juya OGMF square da wani gefe tsawon 50 mm.

Yana yiwuwa a yi wani square, ta amfani kawai kamfas da straightedge. Idan kana da muhimmanci girman da square da aka sani na da tsawon gefe, shi zai bukatar karin da kalkaleta.

Saboda haka, sa batu na farko E - wannan zai zama shi da vertices na square. Next, zaɓi wuri inda za a located gaban kokuwa F, watau jira diagonal bushiya your adadi. Idan ka gina wani square a size, tare da tsawon gefe, lissafi da tsawon na diagonal da dabara:

d = √2 * a, inda wani - gefe tsawon.

Da zarar ka san tsawon na diagonal tsawon bushiya gina wannan darajar. Daga aya E tare da wani caliper a cikin shugabanci na ma'ana F zana wani rabin zoɓe na radius bushiya. A akasin wannan, daga aya F - rabin zoɓe wajen auna E, wannan radius. Ta hanyar mahada batu na wadannan Semi-da'ira, ta amfani da mai mulki, a zana kashi mahada. Bushiya da GI rarraba a dama kusassari da diagonals ne nan gaba na wani square. Haša dige UOM, il, ZHZ kuma mun da wani mai mulki, za ka sami wani rubũtacce square EIZHZ.

Shi ne har yanzu yiwu ga shirya wani square da daya line. Mene ne wani square? Wannan jirgin sama rabo a daure da intersecting segments (Lines haskoki). Saboda haka, za mu iya yi wani square a kan tsarawa daga ta vertices. Da farko Draw gatura. Gefen da square iya karya a kan su, ko da mahada na diagonals na cibiyar daidai da batu na asalin - ya dogara a kan so ko matsalar yanayi. Zai yiwu your adadi za a spaced daga axis a wani nesa. A cikin wani hali, na farko alamar Tazarar dabi'u (da ka ko yanaye), da maki biyu, sa'an nan za ku zama sananne a gefen tsawon wata square. Yanzu muna iya lissafi da tsarawa daga biyun da suka rage vertices, ambata cewa tarnaƙi daga cikin square daidai suke da juna da kuma suna layi daya. A karshe mataki - gama duk dige a jerin da juna tare da wani m.

Mene ne murabba'ai?

Square - wani adadi fayyace kuma tsananin iyakance su fassarorin, don haka da irin murabba'ai ba su bambanta ba bambancin.

A square Euclidean lissafi aka gani mafi yadu - a quadrilateral tare da daidaita bangarorin da sasanninta, amma digiri na kusassari da aka ba a kayyade ba. Wannan yana nufin cewa kusassari iya zama 120 darajõji ( "convex" square), da kuma, alal misali, 72 digiri ( "concave" square).

Idan ka tambaye abin da yake cikin square a lissafi ko kimiyya, da suka ji gaya muku cewa - shi ne mai cikakken ko planar jadawali (ginshikan K ₁ ta hanyar K _4). Kuma yana da cikakken gaskiya. A count yana da vertices da gefuna. Idan suka tashi a umurce biyu, samar da wani jadawali. Yawan vertices - wannan ne domin na jadawali, yawan gefuna - ta size. Saboda haka, square - a planar jadawali da hudu vertices da shida gefuna, ko K _4: 6.

gefe na square

Daya daga cikin manyan yanayi na zama na square - gaban daidai-tsawon bangarorin - sa gefe ne da muhimmanci sosai ga dama lissafin. Amma a lokaci guda samar da hanyoyi da yawa da square gefe tsawon aka lasafta a gaban wani m iri-iri na tushen bayanan.

Saboda haka, yadda za a sami darajar da square?

• Idan ka san kawai da tsawon da diagonal da square d, sa'an nan za ka iya lissafta da shugabanci na wadannan dabara: a = d / √2.
• A diamita na rubũtacce da'irar ne gefen wani square da kuma, sabili da haka, sau biyu da radius, cewa shi ne: wani = D = 2R.
• A radius daga cikin da'irar kuma iya taimaka gane abin da yake a gefen square. Mun iya samun radius R diamita D, wanda, bi da bi, shi ne daidaita da diagonal da wani square d, kuma da dabara domin diagonal da murabba'i ta hanyar da muka sani: a = D / √2 = d / √2 = 2R / √2.
• Daga cikin daidaici da shi ya nuna cewa koyon gefen wani square (a) shi ne zai yiwu, ta hanyar da kewaye P da kuma yankin S: a = √S = P / 4.
• Idan muka sani da tsawon layin da ke daga kusurwar square da crosses tsakiyar ta m gefen C, da mu ma su iya gano abin da ke da tsawon gefen square: a = 2C / √5.

Wannan yadda da yawa hanyoyi akwai ganin irin wannan muhimmanci siga a matsayin tsawon na square.

girma square

A jumlar da kanta ne m. Mene ne wani square? Wannan shi ne wani jirgin saman adadi da ciwon kawai biyu sigogi - da tsawon da nisa. Kuma da girma? Wannan shi ne gwada yawa faye hali na sarari sun shagaltar da abu, wato, shi za a iya lasafta kawai a juz'i na jikinsu.

Kewaye da jiki, duk da fuskokinsu suke murabba'ai - da shigen sukari. Duk da babban kuma bambancin, dalibai sau da yawa kokarin yin lissafi da girma na wani square. Idan ta wani nasara, da Nobel Prize aka bayar.

Kuma don gano girma na wani shigen sukari V, shi ne isa ya ninka duk uku daga cikin hakarkarinsa - a, b, c: V = a * b * c. Kuma tun suna da definition daidai, da dabara iya duba daban-daban: V = wani ^3.

Dabi'u sassa da halaye

A square, kazalika da wani polygon, akwai saman - wannan shi ne batu a da giciye shi. A saman square ƙarya a kan wani da'irar da aka bayyana a kusa da shi. Ta hanyar saman cibiyar da square a cikin diagonal kara, wanda kuma bisector da radius daga cikin circumscribed da'irar.

Tun da square - wani lebur adadi, sa'an nan a yanka da kuma gina wani square giciye-kashi ne da ba zai yiwu. Amma kuma zai iya zama sakamakon da rarrabawa da yawa ƙato jiki jirgin sama. Alal misali, a Silinda. Axial sashe na wani Silinda - wani murabba'i mai dari ko square. Ko square iya faruwa a yankunan da jirgin sama na jiki a kowane kusurwa!

Amma da square akwai wani ra'ayi zuwa giciye sashe, amma ba don wasu, amma da zinariya sashe.

Dukanmu mun san cewa Golden rabo - wani rabo a cikin abin da daya darajar da dangantaka da wani kazalika da Miliyan Xari to ya fi girma darajar. A takaice, wannan kashi ne kamar haka: tunani darajar (adadin) aka raba da 62 da kuma 38 bisa dari.

A zinariya sashe ne Popular. Ana amfani da a cikin zane, gine-gine, a ko'ina, ko da a cikin tattalin arzikin kasar. Amma shi ne ba kawai da rabo samu ta Pythagoras. Akwai, misali, ko da da magana "√2". A ta da asali da gina tsauri rectangles, wanda bi da bi ne suka kafa tsare-tsaren kungiyar A (A6, A5, A4, da dai sauransu). Me muna magana ne game da tsauri rectangles? Saboda su yi farawa da wani square.

Eh, na farko kana bukatar ka gina wani square. Gefe zai zama daidai da karami gefen murabba'i mai dari na nan gaba. Sa'an nan kuma ka bukatar ka rike da diagonal da square da kuma amfani da kamfas, da tsawon da diagonal ya fasa ci gaba da square. Daga cikin aya samu a yankunan da ake gina wani murabba'i mai dari wanda diagonal sake gina da kuma jinkirta ta tsawon a kan tsawo gefe. Idan ka ci gaba da yin aiki a kan wannan makirci, za su sami da sosai tsauri rectangles.

A rabo daga dogon gefen to short farko murabba'i mai dari ne 0.7. Yana da kusan 0,68 a cikin zinariya sashe.

A kusurwoyin square

A gaskiya, wani abu sabo a ce game da kusassari ne wuya. Duk da kaddarorin, su ne kuma alamun da square, da muka lissafa. Amma ga sasanninta, hudu daga cikinsu (as a wani quadrangle), kowane kusurwa na square - a mike layin, wato, yana da girman da casa'in digiri. By definition, akwai wani rectangular square. Idan sasanninta na ya fi girma ko karami - wannan shi ne wani daban-daban adadi.

Diagonal na wani square da aka raba a rabin cikin sasanninta, watau sũ ne mãsu bisectors.

square lissafi

Idan dole yin lissafi da darajar daban-daban magnitudes a wani square (square kewaye tsawo na bangarorin ko diagonals) amfani da daban-daban lissafai, wanda ake samu daga cikin kaddarorin da wani square, kuma ka'idojin lissafi dokoki.

1. lissafi square yankin

Daga cikin lissafai yin lissafi da quadrilateral yanki, mun san cewa shi (cikin yankin) ne samfurin na tsawon da nisa. Kuma a matsayin square gefen daidaita a tsawon, yankin zai kasance daidai da tsawon ko dai gefe, gina a karo na biyu digiri

S = ^2.

Amfani da Pythagorean Theorem, za mu iya lissafta da yanki na wani square da sanin tsawon na diagonal.

S = d ^2/2.

2. A lissafi na square kewaye

A kewaye da square, kazalika da dukan quadrangles, daidai da Naira Miliyan Xari da tsawo daga sãsanninta, kuma tun suna duk wannan, yana iya bayyana cewa, cikin square da kewaye ne da tsawon part, ta tara da hudu

P = wani + a + a + mai = 4A.

Sake Pythagorean Theorem taimaka mana mu samu kewaye ta da diagonal. Wajibi ne a daraja diagonal tsawon yawaita ta biyu Tushen na biyu

P = 2√2d

3. lissafi diagonal da murabba'i

Diagonal na wani square ne daidai da rarraba a dama kusassari da kuma raba mahada batu na biyu.

Za ka iya nemo su a kan tushen da sama lissafai na yankin da kuma kewaye wani square

d = √2 * A, D = √2S, d = P / 2√2

Akwai hanyoyi don gano abin da ke da tsawon da diagonal da wani square. A radius daga cikin da'irar rubũtacce a wani square shi ne daidai da rabin diagonal, Saboda haka

d = √2D = 2√2R, inda D - diamita, da kuma R - da radius daga cikin rubũtacce da'irar.

Sanin radius daga cikin circumscribed da'irar, lissafi diagonal ko da sauki, domin shi ne diamita, Ina nufin d = D = 2R.

Shi ne kuma zai yiwu yin lissafi da tsawon da diagonal, da sanin tsawon na line fitowa daga kusurwa da cibiyar da square C: d = √8 / 5 * C.

Amma kar ka manta da cewa square - wani jirgin saman mãkirci, a daure da hudu intersecting Lines.

Domin Lines (da kuma kafa siffofi to) akwai isasshen lissafai ba ya bukatar kara bayanin, amma line ne m. A iyaka polygons Lines mahada. Domin su yana yiwuwa a yi amfani da mikakke lissafai hade a fassara da madaidaiciya Lines. Amma wajibi ne don saka ƙarin sigogi, yanayi.

Don sanin polygons shi wajibi ne don ya yi irin wannan lissafi da cewa zai bayyana ba a layi amma raba sabani tazara ba tare da tsangwama ga ƙarin sharuddan da kwatancin.

_{[X / x i] * [} x i / x] * y i - wannan shi ne na musamman lissafi ga polygons.

A square baka a shi nuna wani togiya yanayin ne fractional ɓangare na lamba, cewa shi ne, dole ne mu bar kawai dukan lambar. y _i - wani aiki wanda yake a cikin kewayon na siga x zuwa x _i.

Amfani da wannan lissafi, za mu iya samu wani sabon lissafi yin lissafi da tsawo da kuma line kunsha da dama segments. Yana da wani asali, duniya domin polygons.

Ka tuna cewa square - shi ne wani ɓangare daga cikin jirgin sama, saboda haka ta bayanin da irin y = f (x) za a iya wakilta, mafi sau da yawa ne kawai a matsayin wani Multi-mai daraja aiki, wanda, bi da bi, za a iya bayyana a unambiguous idan gabatar da su parametrically, cewa shi ne dogara a kan mai siga t:

x = f (t), y = f (t).

Saboda haka, idan amfani a tare da duniya lissafi da kuma parametric misali, yana da gaske yiwu ga samu wani lissafi ga magana daga polygons:

x = ((A2 + A3) * A5 + A4 * P) * cos (L)

y = ((A1 + A4) * A5 + A3 * P) * Zunubi (L),

inda

A1 = [1 / [T / P]] * [T / P]. A2 = [2 / [T / P]] * [[T / P] / 2]. A3 = [3 / [T / P]] * [[T / P] / 3]; A4 = [4 / [T / P]] * [[T / P] / 4]; A5 = TP * [T / P],

inda P - diagonal da murabba'i mai dari, L - da kwana na son zuwa a kwance, diagonal P, T - siga sãɓãwar launukansa a cikin kewayon P to 5P.

Idan L = 3,14 / 4, sa'an nan da lissafi zai bayyana murabba'ai daban-daban masu girma dabam, dangane da girman da diagonal P.

A amfani da square

A yau duniya da fasaha ba ka damar hašawa daban-daban kayan square siffar, ko fiye daidai wani square giciye sashe.

Wannan shi ne sun fi mayar da m, mai rahusa, mafi m, kuma mafi aminci. Saboda haka, yanzu aikata square bututu, tara, waya (wayoyi), da kuma ko da wani square thread.

Main abũbuwan amfãni ne bayyananne, suka zo daga na farko lissafi. Tare da wannan adadin na rubũtacce da'irar wani square yanki karami fiye da yanki a wadda ta shiga, sakamakon haka, kayan da aka samar ko ikon amfani da square tube na square wayoyi don zama ya fi da cewa da zagaye analogs.

Sau da yawa wasu kaya square mafi aesthetically m da sauki don amfani, shigar, hawa.

A lokacin da zabar wadannan kayan yana da muhimmanci a daidai lissafi da square giciye-kashi ga wani waya ko bututu msa da zama dole load. A kowane hali, ba shakka, za a bukata sigogi kamar yanzu ƙarfi, ko matsa lamba, amma ba tare da asali na lissafi dokoki na square ba zai iya yi a nan. Ko da yake size of square sashe ba sosai lasafta a matsayin zaba da ba sigogi na alluna kafa daga baƙi for daban-daban da masana'antu.