Yuav ua li cas yog ib tug square? Yuav ua li cas mus nrhiav tau vertices sectional dav hlau kab zauv, ntim thiab hneev taw ntawm ib tug square lub?

Nug txog qhov tseeb hais tias xws li ib tug square, yuav tau teem caij. Nws tag nrho cov nyob rau uas koj tau nyob no qhov teeb meem. Lub tshuab raj hais tias lub square - ib tug 4, 8, 16, 32 tuav los yog jazz improvisation. Tus me nyuam - nws yog ib tug kev ua si nrog ib tug pob los yog ib tug me nyuam txoj kev magazine. Cov tshuab luam ntawv yuav xa koj mus rau kawm font loj thiab cov khoom siv - hlau-profile hom.

Muaj ntau ntau lwm yam tseem ceeb nyob rau hauv cov lus no, tab sis hnub no peb yuav nug ib lo lus nug ntawm kev kawm txog zauv. Yog li ntawd ...

Yuav kom nrog no daim duab, peb yuav maj mam, los ntawm tej yam yooj yim mus, thiab pib nrog cov keeb kwm ntawm lub square. Raws li nws tshwm sim, raws li ntaus nqi los ntawm cov neeg, zaum los ntawm ntau lub teb chaws thiab civilizations?

Keeb kwm kev tshawb square

Ancient lub ntiaj teb no perceives lub square, tsuas yog raws li cov plaub cardinal cov ntsiab lus. Nyob rau hauv kev, txawm ntau quads, cia li nyob hauv lub ntsiab square ntawm tus xov tooj - plaub. Rau cov Axilia thiab lub Peruvian square - lub ntiaj teb no, uas yog, nws nruab nrab yog cov plaub lub ntsiab lus qhia ntawm lub compass.

Txawm lub qab ntuj khwb yog zoo li ib tug square, tseem muab faib ua plaub qhov chaw - lub zeem muag ntawm North America. Rau cov Celts, lub ntug - nws yog ntau npaum li raws li peb cov square, nested, thiab los ntawm qhov chaw ntawm lub plaub dej ntws (!). Thiab tag nrho cov Egyptians pe hawm no daim duab!

Thawj piav los ntawm cov formulas lej square Greeks. Tab sis rau lawv, qhov no polygon muaj tsuas tsis zoo yam ntxwv. Pythagoras tsis nyiam txooj, pom lawv li tsis muaj zog thiab hais txog poj niam.

Txawm kev ntseeg tam sim no square. Nyob rau hauv Islam, cov Kaaba - lub puj ntaws ntawm lub ntiaj teb - tsis yog ib co kheej kheej, namely ib tug nyhav zoo.

Nyob rau hauv Is Nrias teb, lub ntsiab grapheme sawv cev lub ntiaj teb, los yog lub ntiaj teb lub cim, tau rebaptized square. Ib zaug ntxiv, peb yuav tau tham txog lub plaub cardinal cov ntsiab lus, cov plaub cheeb tsam ntawm lub ntiaj teb.

Nyob rau hauv Tuam Tshoj, lub square - ib lub ntiaj teb kev sib raug zoo thiab kev txiav txim. Chaos yog vanquished tsev square Pauv. Ib tug square inscribed nyob rau hauv ib lub voj voog, yog lub hauv paus ntawm pom lub ntiaj teb no, symbolizing txoj kev sib sau thiab kev twb kev txuas ntawm lub cosmos thiab lub ntiaj teb.

Pagan Russia - Square Svarog. Qhov no cim yog tseem hu ua Svarog Star los yog Star ntawm Russia. Nws tseem zoo nkauj tham, raws li tau ua los ntawm kev sib tshuam thiab kaw kab. Svarog - Vaj tswv blacksmiths, lub ntsiab creator, tus creator thiab lub ntuj nws tus kheej nyob rau hauv qhov kev nthuav qhia ntawm Rus. Qhov no cim yog ib tug rhombus, uas rov hais lus ntawm lub ntiaj teb thiab nws cov plaub cov lus qhia. Thiab lub hnub qub nrog plaub rays - 4 fab ntawm lub ntiaj teb, Lika Svaroga 4 - nws omniscience. Ib tug duab tshav tshuam - center.

Nthuav lus tseeb hais txog tus square

Cov feem nrov kab lus hais tias los rau lub siab ntawm peb protagonist - "Black Square".

Malevich daim duab yog tseem nrov heev. Tus sau tom qab nws creation tau ntev raug kev txom nyem rau lo lus nug ntawm yog dab tsi nws yog ib thiab yog vim li cas ib tug yooj yim dub square nyob rau hauv ib tug dawb keeb kwm yav dhau li ntawd, thim xim rau nws tus kheej.

Tiam sis yog tias koj noj ib los ze zog saib zoo, koj mam li paub hais tias cov square dav hlau yog tsis du, thiab nyob rau hauv cov kab nrib pleb ntawm cov dub number case yog ib tug txheej ntawm multi-kob ntxoov. Thaj, nyob rau hauv thaum pib muaj ib tug tej yam muaj pes tsawg leeg, uas tus sau tsis nyiam, thiab nws kaw tau nws los ntawm peb lub qhov muag mus rau qhov daim duab. Dub square raws li dab tsi - ib tug dub qhov, tsuas yog cov khawv koob square zoo lawm. Ib tug tsis muaj dabtsis yog paub tias yuav nyiam ...

Lwm nrov heev "khawv koob squares". Nyob rau hauv qhov tseeb nws yog - ib lub rooj, ntawm chav kawm, lub square uas muaj cov xov tooj nyob rau hauv txhua lub thawv. Lub sum ntawm cov zauv yog tib yam rau tag nrho cov kab, kab thiab diagonals (cais). Yog hais tias lub diagonals yog tshem tawm los ntawm lub kab zauv, lub square - semimagic.

Albrecht Dürer nyob rau hauv 1514 tsim lub painting "Melancholia kuv", uas depicted ib 4x4 khawv koob square. Nws zaum ntawm cov xov tooj ntawm txhua, kab, diagonals, thiab txawm lub puab square yog peb caug-plaub.

Nyob rau lub hauv paus ntawm cov ntxhuav heev nthuav thiab nrov puzzle - "Sudoku".

Lub Egyptians yog cov ua ntej mus nqa tawm interconnection kab xov tooj (hnub yug) thiab cov ua cim sijhawm, muaj peev xwm thiab kev txawj ntse ntawm tus neeg. Pythagoras coj txawj ntse no, ob peb ua thiab muab tso rau hauv lub square. Cov tshwm sim yog ib tug square ntawm Pythagoras.

Nws muaj ib tug nyias muaj nyias ib cheeb tsam nyob rau hauv numerology. Los ntawm cov hnub yug ntawm ib tug neeg xam los ntawm kev ntxiv lub plaub lub ntsiab xov tooj uas muab tso rau hauv Pythagoras Square (square). Thiab pw tawm tag nrho cov thaum cov lus qhia txog koj lub zog, noj qab haus huv, txuj ci, muaj hmoo, siab luv thiab lwm yam nyob rau hauv lub txee. Nyob rau nruab nrab, cov neeg ntawm cov ntawv tshawb fawb yog 60% -80%.

Yuav ua li cas yog ib tug square?

Square hu ua lub geometric duab. Zoo square - quadrilateral, uas muaj sib npaug zos sab thiab cov ces kaum. Ntau precisely, lub quadrangle hu ua tseeb.

Lub square muaj nws cov cim. Lawv yog:

• sab sib npaug ntev;
• sib npaug zos ces kaum ntawm lawv tus kheej - ncaj (90 degrees).

Vim hais tias ntawm cov yam ntxwv thiab nta ntawm lub squared vajvoog yuav inscribed, thiab piav txog nws nyob ib ncig ntawm nws. Lub circumscribed lub voj voog yog tangent rau tag nrho cov ntawm nws vertices inscribed - nruab nrab ntawm nws sab. Lawv ua kom pom tseeb yuav coincide nrog qhov chaw ntawm lub square thiab yuav muab tag nrho nws diagonally nyob rau hauv ib nrab. Cov yav tas, nyob rau hauv lem, yog muaj sib npaug thiab faib lub ces kaum ntawm lub square rau hauv sib npaug zos qhov chaw.

Ib tug kab pheeb ces kaum cais lub square mus rau hauv ob ceskaum cov vajvoos peb sab, ob tug - mus rau plaub.

Yog li, Yog hais tias qhov ntev ntawm lub sab ntawm ib tug square - t, qhov ntev ntawm lub voos kheej-kheej ntawm lub circumscribed lub voj voog - R, thiab ib tug inscribed - r, ces

• ib tug square puag cheeb tsam los yog square cheeb tsam (S) yog sib npaug zos rau S = t ² = 2R ² = 4r ^2;

• ib tug square puag ncig P yuav tsum tau xam los ntawm cov mis P = 4t = 4√2R = 8r;

• qhov ntev ntawm lub voos kheej-kheej ntawm lub vajvoog R = (√2 / 2) t;

• inscribed - r = t / 2.

Ib tug square puag cheeb tsam tseem yuav xam paub nws sab (a) los yog qhov ntev ntawm nws cov kab pheeb ces kaum (c), ces cov mis yuav tshwm sim feem: S = ib tug ² thiab S = 1 / 2C ^2.

Yuav ua li cas yog lub square, peb pom. Cia wb mus ze zog saib kom paub meej, vim hais tias cov duab ntawm lub square yog lub symmetrical duab plaub. Nws muaj tsib axes ntawm symmetry, nrog ib tug (plaub txiav txim) kis tau los ntawm qhov chaw thiab yog lawv mus rau lub dav hlau ntawm lub square, thiab plaub rau lwm tus neeg - ob symmetry axis, ob tug ntawm lawv yog thaum uas tig mus rau lub sab, thiab ob ntau pass los ntawm cov kab pheeb ces kaum ntawm lub square.

Txoj kev ntawm constructing ib lub square

Raws li lub ntsiab txhais, nws nkawd hais tias muaj yog tsis muaj dab tsi yooj yim dua rau tsim ib tug zoo meej square. Qhov no yog muaj tseeb, tab sis nyob rau hauv lub mob uas koj muaj tag nrho cov kev ntsuas cov cuab yeej. Thiab yog hais tias ib yam dab tsi yog tsis muaj?

Cia saib cov uas twb muaj lawm txoj kev, uas yuav pab kom peb tsim no daim duab.

Xab kav thiab teem square - cov no yog cov tseem ceeb cov cuab yeej los ntawm kev uas koj muaj peev xwm feem ntau yooj yim tsim ib tug square.

Thaum xub thawj, kos tus cim rau taw tes, hais A, peb yuav tsim rau nws ib tug square puag.

Siv ib tug kav, ib sab ntawm nws mus rau sab xis ib tug deb sib npaug zos rau qhov ntev ntawm lub sab, piv txwv li 30 mm, thiab teem lub point B.

Tam sim no, los ntawm lub ob lub ntsiab lus, siv gon perpendiculars los so mus rau 30 mm txhua. Thaum lub xaus ntawm lub perpendiculars set ntsiab lus C thiab D, uas yog kev cob cog rua rau txhua lwm yam, siv ib tug pas ntsuas - tag nrho cov square abcd nrog rau sab 30 mm npaj txhij!

Siv ib tug pas ntsuas thiab protractor yog tseem heev yooj yim mus tsim ib tug square. Pib, raws li nyob rau hauv lub yav dhau los cov ntaub ntawv nyob rau hauv cov nqe lus, piv txwv li N, ib cag los ntawm nws cov kab rov tav luv, piv txwv li 50 mm. Muab tus taw tes O.

Tam sim no qhov chaw ntawm lub protractor txuas nrog lub point H, lub checkbox nyob rau hauv lub kaum sab xis ⁰ 90, therethrough thiab ib tug taw tes H muaj ntsug ya 50 mm nyob rau hauv nws xaus nrog ib tug taw tes P. Ntxiv mus, nyob rau hauv no txoj kev tsim lub thib peb ya los ntawm tus taw tes O los ntawm lub kaum sab xis ntawm 90 ⁰ 50 hli, cia nws xaus point P. Connect lub dots R thiab R. koj tau muab OGMF square nrog ib tug sab ntev ntawm 50 mm.

Nws yog ua tau los mus tsim ib tug square, siv xwb compass thiab straightedge. Yog hais tias koj muaj ib qho tseem ceeb luaj li cas ntawm cov square thiab yog lub npe hu rau qhov ntev ntawm lub sab, nws yuav tsum tau ntau thiab tswvyim.

Yog li ntawd, muab lub thawj point E - qhov no yuav ua tau nws ntawm lub vertices ntawm lub square. Tom ntej no, xaiv qhov chaw uas nws yuav tsum tau nyob yam txawv kab los sib ntsib F, piv txwv li tos kab pheeb ces kaum Hedgehog koj daim duab. Yog hais tias koj tsim ib square nyob rau hauv loj, nrog qhov ntev ntawm lub sab, xam qhov ntev ntawm lub kab pheeb ces kaum ntawm lub mis:

d = √2 * ib tug, qhov chaw uas ib tug - sab ntev.

Thaum koj paub tias qhov ntev ntawm lub kab pheeb ces kaum ntev ntawm hedgehog tsim no tus nqi. Los ntawm taw tes E nrog ib tug caliper nyob rau hauv cov kev taw qhia ntawm taw tes F kos ib lub voj voog ntawm lub vojvoog hedgehog. On qhov tsis tooj, los ntawm tus taw tes F - lub voj voog rau tus taw tes E, tib voos kheej-kheej. Los ntawm cov kev tshuam taw tes ntawm cov semi-voj voog, siv ib tug pas ntsuas, kos ib ya link. Hedgehog thiab GI tshuam ntawm txoj cai ces kaum thiab diagonals yog yav tom ntej los ntawm ib tug square. Txuas lub tsuas me me UOM, IL, ZHZ thiab PEB nrog ib tug kav, koj yuav tau txais ib inscribed square EIZHZ.

Nws yog tseem tau los mus tsim ib tug square nrog ib txoj kab. Yuav ua li cas yog ib tug square? Qhov no dav hlau feem bounded by sib tshuam feem (kab rays). Li no, peb muaj peev xwm tsim ib tug square nyob rau hauv coordinates ntawm nws vertices. Thawj kos co. Sab ntawm koj lub square yuav pw rau lawv, los yog cov kev tshuam ntawm lub diagonals ntawm qhov chaw coincides nrog lub point ntawm keeb kwm - nws yog nyob ntawm koj muaj lub siab xav los yog teeb meem tej yam kev mob. Tej zaum koj daim duab yuav tsum spaced los ntawm lub axis ntawm ib yam nrug. Nyob rau hauv txhua rooj plaub, lub thawj cim ntawm numeric qhov tseem ceeb (across los yog conditionally), lub ob lub ntsiab lus, ces koj yuav tsum paub sab ntev ntawm ib tug square. Peb yuav tam sim no xam lub coordinates ntawm qhov seem uas ob vertices, nco ntsoov tias lub sab ntawm cov square yog muaj sib npaug rau txhua tus lwm yam thiab yog thaum uas tig mus. Qhov kawg kauj ruam - txuas tag nrho cov dots nyob rau hauv series nrog txhua lwm yam nrog rau ib tug kav.

Yuav ua li cas yog cov squares?

Square - ib daim duab kom meej meej tseg thiab nruj me ntsis txwv lawv cov ntsiab lus txhais, li ntawd lub hom squares tsis txawv ntau haiv neeg.

Lub square Euclidean geometry yog pom ntau lug - ib tug quadrilateral nrog sib npaug sab thiab cov ces kaum, tab sis cov neeg kawm ntawv ntawm cov ces kaum yog tsis teev. Qhov no txhais tau tias lub ces kaum tej zaum yuav 120 degrees ( "convex" square), thiab, piv txwv li, 72 degrees ( "concave" square).

Yog hais tias koj nug dab tsi yog qhov square nyob rau hauv geometry los yog science, lawv mam li qhia rau koj tias - nws yog ib tug ua kom tiav los yog planar teeb (kab K ₁ los ntawm K _4). Thiab nws yog kiag li tiag tiag. Lub count muaj vertices thiab sawv. Thaum lawv tau txais nyob rau hauv lub kom khub, tsim ib tug teeb. Tus nab npawb ntawm vertices - qhov no yog qhov kev txiav txim ntawm lub teeb, tus xov tooj ntawm npoo - nws loj. Yog li, lub square - ib tug planar teeb nrog plaub vertices thiab rau sawv, los yog K _4: 6.

sab ntawm lub square

Ib tug ntawm lub ntsiab yam kev mob rau lub hav zoov ntawm cov square - lub muaj vaj huam sib luag-ntev sab - ua lub sab tseem ceeb heev rau ib tug ntau yam ntawm suav. Tab sis nyob rau tib lub sij hawm muaj ntau yam txoj kev mus rau lub square sab ntev twb xam nyob rau hauv lub xub ntiag ntawm ib tug ntau yam ntawm qhov chaw cov ntaub ntawv.

Yog li ntawd, yuav ua li cas nrhiav tau tus nqi ntawm cov square?

• Yog hais tias koj paub xwb qhov ntev ntawm lub kab pheeb ces kaum ntawm lub square d, ces koj yuav xam cov kev taw qhia ntawm cov nram qab no: Muaj ib tug = d / √2.
• Cov kab uas hla ntawm lub inscribed vajvoog yog lub sab ntawm ib tug square thiab, yog li ntawd, ob zaug lub voos kheej-kheej, uas yog: a = D = 2R.
• Lub voos kheej-kheej ntawm lub vajvoog kuj pab tau xyuas seb dab tsi yog sab ntawm lub square. Peb yuav nrhiav tau cov voos kheej-kheej R ib lub cheeb D, uas, nyob rau hauv lem, yog sib npaug zos rau cov kab pheeb ces kaum ntawm ib tug square d, thiab cov mis rau tus kab pheeb ces kaum ntawm lub square los ntawm peb paub: a = D / √2 = d / √2 = 2R / √2.
• Los ntawm cov koob pheej ntawm lawv ntawm nws implies tias kawm sab ntawm ib tug square (a) yog tau los ntawm kev txhais tau tias ntawm nws ncig P thiab cheeb tsam S: a = √S = P / 4.
• Yog hais tias peb paub qhov ntev ntawm txoj kab uas mus los ntawm lub ces kaum ntawm lub square thiab crosses rau hauv nruab nrab ntawm nws ib sab sab C, tus peb kuj yuav tau mus nrhiav seb yog dab tsi yog qhov ntev ntawm lub sab ntawm lub square: a = 2C / √5.

Qhov ntawd yog yuav ua li cas muaj ntau txoj kev muaj pom tej kev ib qho tseem ceeb parameter raws li qhov ntev ntawm lub square.

ntim square

Cov kab lus nws tus kheej yog absurd. Yuav ua li cas yog ib tug square? Qhov no yog ib lub dav hlau daim duab muaj tsuas yog ob tug tsis - qhov ntev thiab dav. Thiab lub ntim? Qhov no yog ib quantitative characterization ntawm qhov chaw nyob los ntawm cov tus kwv, uas yog, nws yuav tsum xam xwb nyob rau hauv volume lub cev.

Puag ncig lub cev, tag nrho cov ntawm uas nws ntsej muag yog squares - lub thawv muaj rau sab. Dua li ntawm qhov enormous thiab siv qhov sib txawv, cov tub ntxhais kawm feem ntau sim mus xam qhov ntim ntawm ib tug square. Yog hais tias nws tus ib tug neeg nca muab tsis tau, cov Nobel nqi zog yog muab.

Thiab mus nrhiav tau tawm qhov ntim ntawm ib lub voos xwmfab V, nws yog txaus muab tag nrho peb ntawm nws tav - ib tug, b, c: V = ib * b * c. Thiab txij li thaum lawv yog los ntawm txhais sib npaug zos, cov mis tej zaum yuav zoo sib txawv: V = ^3.

Hwm qhov chaw thiab cov yam ntxwv

Lub square, raws li zoo raws li tej polygon, muaj lub sab saum toj - qhov no yog qhov point uas tus ntoo khaub lig ntawm nws. Lub sab saum toj ntawm lub square dag rau ib lub voj voog piav nyob ib ncig ntawm nws. Los ntawm lub sab saum toj chaw ntawm lub square nyob rau hauv lub kab pheeb ces kaum ncua, uas yog tseem lub bisector thiab ib voos ncig ntawm lub circumscribed lub voj voog.

Txij li thaum lub square - ib tug ca daim duab, ces txiav thiab tsim kom muaj ib tug square ntoo khaub lig-section yog tsis tau. Tab sis tej zaum nws yuav tshwm sim ntawm cov kev tshuam ntawm ntau loj lub cev dav hlau. Piv txwv li, ib tug tog raj kheej. Axial seem ntawm ib tug kheej kheej - ib tug duab plaub los yog square. Txawm square yuav tshwm sim ntawm cov kev tshuam ntawm lub dav hlau ntawm lub cev ntawm tej lub!

Tab sis lub square muaj lwm yam ntxwv rau tus ntoo khaub lig seem, tab sis tsis tau ib co, tab sis rau cov golden seem.

Peb txhua tus yeej paub hais tias tus Golden piv - ib tug piv nyob rau hauv uas ib tus nqi koom mus rau lwm lub raws li zoo raws li lawv sum rau ib tug loj tus nqi. Nyob rau hauv txoj kev, qhov no feem pua yog raws li nram no: cov kev siv tus nqi (nqi) yog muab faib los ntawm 62 thiab 38 feem pua.

Tus Golden seem yog heev nrov. Nws yog siv nyob rau hauv tus tsim, architecture, yog nyob qhov twg, txawm nyob rau hauv kev khwv nyiaj txiag. Tab sis qhov no yog tsis yog tib ratio, muab tau los ntawm Pythagoras. Muaj, rau Piv txwv li, txawm lub qhia "√2". Nyob rau nws cov hauv paus tsim kho ntawm lub dynamic voos, uas nyob rau hauv lem yog founders hom pab pawg neeg A (A6 ntawm A5, A4, etc.). Vim li cas peb yuav tau tham txog dynamic voos? Vim hais tias lawv siv pib nrog ib tug square.

Yog, ua ntej koj yuav tsum tau tsim ib tug square. Nws sab yuav ua ncaj rau tus me sab ntawm lub duab plaub ntawm lub neej yav tom ntej. Ces koj yuav tau tuav lub kab pheeb ces kaum ntawm lub square thiab siv cov compass, qhov ntev ntawm lub kab pheeb ces kaum laug sij hawm mus lub continuation ntawm lub square. Ntawm tus taw tes tau rau cov kev tshuam yog tsim tau ib tug duab plaub uas nws kab pheeb ces kaum dua tsim thiab ncua nws kav ntev npaum rau qhov yuav ncua ntxiv sab. Yog hais tias koj tseem ua hauj lwm nyob rau hauv no cov tswvyim, yuav tau txais cov heev dynamic voos.

Qhov ratio ntawm ntev sab kom luv luv thawj duab plaub yog 0.7. Nws yog ze li ntawm 0,68 nyob rau hauv lub Golden seem.

Lub ces kaum ntawm lub square

Ua tau, ib yam dab tsi tshiab hais txog cov ces kaum yog ib qhov nyuaj. Tag nrho cov khoom, lawv kuj yog tej yam tshwm sim ntawm lub square, peb tau sau tseg. Raws li rau cov fab, plaub ntawm lawv (raws li nyob rau hauv tej quadrangle), txhua lub ces kaum ntawm lub square - ib tug ncaj kab, uas yog, muaj ib tug loj ntawm cuaj caum degrees. Los ntawm txhais, muaj yog ib lub square. Yog hais tias cov chaw ti ntawm lub loj los yog me me - qhov no yog ib tug txawv daim duab.

Kab pheeb ces kaum ntawm ib tug square yog muab faib nyob rau hauv ib nrab nws cov ces kaum, piv txwv li lawv yog cov bisectors.

square kab zauv

Yog hais tias tsim nyog los xam tus nqi sib txawv ntawm cov tshaj nyob rau hauv ib tug square (square puag ncig lengths ntawm lub sab los yog lub diagonals) siv ntau sib npaug, uas yog muab los ntawm cov khoom ntawm ib tug square, thiab qhov yooj yim cov kev cai ntawm geometry cai.

1. kab zauv square cheeb tsam

Los ntawm qhov sib npaug los mus laij lub quadrilateral cheeb tsam, peb paub hais tias nws (tus cheeb tsam) yog qhov khoom ntawm ntev thiab dav. Thiab raws li lub square sab sib npaug zos nyob rau hauv ntev, lub cheeb tsam nws yuav ua ncaj rau qhov ntev ntawm tog, ua nyob rau hauv lub thib ob degree

S = ^2.

Siv cov Pythagorean theorem, peb yuav tau xam lub cheeb tsam ntawm ib tug square paub qhov ntev ntawm lub kab pheeb ces kaum.

S = d ^2/2.

2. Cov kab zauv ntawm lub square puag ncig

Ntawm lub perimeter ntawm lub square, raws li zoo raws li tag nrho cov quadrangles, sib npaug zos rau cov sum ntawm cov lengths ntawm nws sab, thiab txij li thaum lawv muaj tag nrho cov tib yam, nws yuav tau hais tias lub square ntawm tus puag ncig yog qhov ntev ntawm ib sab, multiplied by plaub

P = ib + ib + ib + a = 4a.

Dua Pythagorean theorem yuav pab peb nrhiav tau cov puag ncig los ntawm tus kab pheeb ces kaum. Peb yuav tsum value kab pheeb ces kaum ntev khoo los ntawm ob cag ntawm ob

P = 2√2d

3. kab zauv kab pheeb ces kaum ntawm lub square

Kab pheeb ces kaum ntawm ib tug square yog sib npaug zos rau tshuam ntawm txoj cai ces kaum thiab muab faib cov kev tshuam taw tes ntawm ob tug.

Koj yuav nrhiav tau lawv nyob rau hauv lub hauv paus ntawm lub saum toj no sib npaug ntawm cheeb tsam thiab puag ncig ntawm ib tug square

d = √2 * ib tug, d = √2S, d = P / 2√2

Muaj ntau txoj kev mus nrhiav seb yog dab tsi yog qhov ntev ntawm lub kab pheeb ces kaum ntawm ib tug square. Lub voos kheej-kheej ntawm lub vajvoog inscribed nyob rau hauv ib tug square nws yog sib npaug zos rau ib nrab ntawm cov kab pheeb ces kaum, li no

d = √2D = 2√2R, qhov twg D - txoj kab uas hla, thiab R - lub voos kheej-kheej ntawm lub inscribed voj voog.

Paub qhov voos kheej-kheej ntawm lub circumscribed lub voj voog, xam kab pheeb ces kaum txawm yooj yim, vim hais tias nws yog txoj kab uas hla, i.e. d = D = 2R.

Nws yog tseem tau mus laij tau qhov ntev ntawm lub kab pheeb ces kaum, paub txog qhov ntev ntawm txoj kab los ntawm lub ces kaum rau hauv qhov chaw ntawm lub square C: d = √8 / 5 * C.

Tab sis tsis txhob hnov qab tias cov square - ib tug dav hlau zajlus, ciaj los ntawm plaub sib tshuam kab.

Rau cov kab (thiab tsim qauv duab rau) muaj txaus sib npaug tsis yuav tsum tau ntxiv cov hauj lwm, tab sis cov kab yog kev txom. Ib tug limited uas kab sib tshuam. Rau lawv nws yog tau siv linear equations ua ke nyob rau hauv defining kab ncaj nraim. Tab sis nws yog tsim nyog los qhia kom meej ntxiv tsis, tej yam kev mob.

Yuav kom txiav txim seb qhov uas nws yog tsim nyog los ua xws li ib qho kev uas yuav piav tsis yog ib tug kab tab sis ib tug nyias muaj nyias ib arbitrary luv tsis muaj cuam tshuam rau ntxiv cov ntsiab lus thiab piav qhia.

_{[X / x i] * [} x i / x] * y kuv - uas yog ib tug tshwj xeeb kab zauv rau cov uas.

Lub square nkhaus nyob rau hauv nws taw tes rau ib qho kev zam mob yog ib tug fractional ib feem ntawm tus xov tooj, uas yog, peb yuav tsum tau tawm xwb rau tag nrho cov xov tooj. y _kuv - ib tug muaj nuj nqi uas yog nyob rau hauv ntau ntawm cov parameter x rau x _i.

Siv cov kab zauv, peb yuav neeg ib tug tshiab kab zauv los mus laij lub lengths thiab kab muaj ob peb theem. Nws yog ib tug yooj yim, universal rau polygons.

Nco ntsoov hais tias lub square - nws yog ib feem ntawm lub dav hlau, yog li nws cov hauj lwm ntawm lub hom y = f (x) yuav sawv cev, feem ntau tsuas yog raws li ib tug multi-muaj nuj nqis muaj nuj nqi, uas, nyob rau hauv lem, yuav qhia nyob rau hauv unambiguous yog qhia lawv parametrically, uas yog nyob rau ntawm lub ib tug parameter t:

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

Yog li ntawd, yog tias siv tau universal kab zauv thiab parametric sawv cev, nws yog tiag tiag ua tau rau neeg ib tug kab zauv rau lub qhia txog polygons:

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

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

qhov twg

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],

qhov twg P - kab pheeb ces kaum ntawm lub duab plaub, L - lub kaum sab xis ntawm inclination rau cov kab rov tav, kab pheeb ces kaum P, T - parameter ua nyob rau hauv ntau P rau 5P.

Yog hais tias L = 3,14 / 4, ces lub kab zauv yuav piav qhia txog plaub fab ntawm txawv ntau thiab tsawg, nyob ntawm seb qhov loj ntawm lub kab pheeb ces kaum P.

Kev siv cov square

Nyob rau hauv hnub no lub ntiaj teb no ntawm technology tso cai rau koj mus muab ntau yam khoom square zoo lawm, los yog ntau tshaj precisely ib tug square ntoo khaub lig seem.

Qhov no yog kev lom zem ntau paaj, pheej yig dua, ntau check thiab kev ruaj ntseg. Yog li ntawd, tam sim no ua square kav, pawg, hlau (thaiv), thiab txawm ib tug square thread.

Main zoo yog cuab kev, lawv mus tawm ntawm elementary geometry. Nrog tus nqi qub inscribed vajvoog ib tug square cheeb tsam me me tshaj lub cheeb tsam nyob rau hauv uas nws nkag mus hauv, thiaj li, tus bandwidth ntawm ib tug square raj los yog ib tug square hlau zog noj yuav tsum muaj ntau tshaj hais tias ntawm lub round analogs.

Feem ntau Consumables square ntau aesthetically pleasing thiab yooj yim rau siv, nruab, mount.

Thaum xaiv cov ntaub ntawv nws yog ib qho tseem ceeb kom raug xam lub square ntoo khaub lig-section mus rau ib tug hlau los yog cov yeeb nkab tau tiv thaiv cov tsim nyog load. Nyob rau hauv txhua rooj plaub, ntawm chav kawm, yuav tsum tau tsis xws li tam sim no lub dag lub zog los yog siab, tab sis tsis muaj yooj yim geometric cai ntawm lub square tsis tau ua ntawm no. Txawm tias qhov luaj li cas ntawm square seem yog tsis yog li ntawd ntau npaum li cas xam raws li xaiv los ntawm qhov muab ciaj ciam ntawm lub rooj teem tawm qhua rau ntau yam industries.