Ntawm lub perimeter ntawm lub square peb nrhiav tau ib tug ntau yam ntawm txoj kev

Tej zaum, ua ntej tus txiv neej twg thiaj li raug mus kaw qhov yuav tsum tau mus nrhiav lub perimeter ntawm lub square. Piv txwv li, koj yuav tau ua ib tug laj kab ncig ntawm lub square cheeb tsam, wallpapered square chav tsev los yog muab ib lub phab ntsa ntawm square seev cev nrog daim iav. Yuav kom xam tus nqi ntawm cov ntaub ntawv uas yuav tsum tau, nws yog tsim nyog los ua tshwj xeeb suav. Thiab nws yog ces, tsis paub yuav ua li cas nrhiav tau ntawm lub perimeter ntawm lub square, yuav muaj mus kis tau cov ntaub ntawv uas "los ntawm qhov muag". Okay, yog hais tias nws yog pheej yig wallpaper, tab sis tus ntxiv iav uas ces muab tso rau? Thiab nrog ib tug tsis txaus ntawm cov khoom ces nws yog heev yooj yim mus nrhiav tau ib tug ntxiv ntawm cov zoo tib yam.

Yog li ntawd, yuav ua li cas koj puas paub yog dab tsi ntawm lub perimeter ntawm lub square? Peb paub tias tag nrho cov tog yog muaj sib npaug mus rau lub square. Thiab yog hais tias tus puag ncig - lub sum ntawm tag nrho cov sab ntawm lub polygon, ntawm lub perimeter ntawm lub square yuav sau raws li (q + q + q + q), qhov chaw uas q - tus nqi qhia qhov ntev ntawm ib sab ntawm lub square. Lawm, lub feem ntau yooj yim yog siv cov npaug. Yog li, ntawm lub perimeter ntawm lub square - ib tug quadruple nqi coj mus rau qhov ntev ntawm nws sab los yog 4q, qhov twg q - sab.

Tab sis yog hais tias peb paub tus tsuas yog thaj tsam ntawm lub square, ntawm lub perimeter ntawm uas koj xav kom nrhiav tau tawm - yuav ua li cas nyob rau hauv cov ntaub ntawv no? Thiab ces txhua yam yog yooj yim heev! Los ntawm lub zoo-paub cov nuj nqis, uas qhia thaj tsam ntawm lub square, koj yuav tsum ua lub extraction ntawm square cov hauv paus hniav. Yog li tus nqi ntawm cov square yuav tsum pom. Tam sim no saib rau ntawm lub perimeter ntawm lub square yog tsim nyog raws li cov mis muab saum toj no.

Lwm lo lus nug, yog tias koj yuav tau mus nrhiav lub perimeter ntawm lub square nyob rau hauv kab pheeb ces kaum. Ntawm no yog peb yuav tsum nco ntsoov lub Pythagorean theorem. Xav txog ib tug square nrog ib tug kab pheeb ces kaum wert WR. WR muab faib cov square mus rau hauv ob txoj kev-angled ceskaum daim duab peb sab. Yog hais tias peb paub qhov ntev ntawm lub kab pheeb ces kaum (conditionally txais nws rau z, thiab sab - rau u), ces tus nqi ntawm cov square yuav tsum tau nrhiav rau lub hauv paus ntawm lub mis: lub square ntawm z yog sib npaug zos rau ob zaug lub square ntawm u, los ntawm uas peb deduce: u yog sib npaug zos rau cov square hauv paus, fetched ib nrab ntawm lub hypotenuse ntawm ib tug square . Tom ntej no yog nce cov los ntawm 4 lub sij hawm - uas yog koj thiab lub perimeter ntawm lub square!

Nrhiav cov kev taw qhia ntawm cov square yuav ua tau lub voos kheej-kheej ntawm lub vajvoog inscribed nyob rau hauv nws. Tom qab tag nrho, lub inscribed vajvoog nphav tag nrho cov sab ntawm cov square, nyob qhov twg lub xaus yog - lub lub cheeb ntawm ib lub voj voog sib npaug zos rau qhov ntev ntawm lub square. Ib tug kab uas hla - nws yog lub npe hu mus rau tag nrho - ob npaug rau voos kheej-kheej.

Yog hais tias koj paub lub voos kheej-kheej los yog txoj kab uas hla ntawm ib lub voj voog circumscribed nyob ib ncig ntawm ib tug square, ntawm no peb pom hais tias tag nrho cov plaub vertices ntawm ib tug square cov txheej txheem ntawm nyob rau hauv ib lub voj voog. Li no, lub lub cheeb ntawm lub circumscribed lub voj voog yog sib npaug zos rau qhov ntev ntawm lub kab pheeb ces kaum ntawm lub square. Noj qhov teeb meem no raws li ib tug muab, ua raws li los ntawm xam xyuas ntawm lub perimeter ntawm lub mis nrhiav puag ncig ntawm nws diagonals, sib tham saum toj no.

Tej zaum ib tug neeg ua hauj lwm nyob rau hauv uas koj yuav tau mus nrhiav seb yog dab tsi yog ntawm lub perimeter ntawm lub square, uas yog inscribed nyob rau hauv ib tug ceskaum txoj cai daim duab peb sab li hais tias ib tug ces kaum ntawm lub square coincides nrog rau hauv tib neeg kaum sab xis ntawm daim duab peb sab. Paub yog lub ceg ntawm cov geometrical daim duab. Txhais li daim duab peb sab wer, wherein E yog ib qho kab los sib ntsib.

Inscribed square yuav tsum khij ETYU. ET sab yog nyob rau sab ntawm PEB, thiab sab ntawm EU - nyob rau sab ntawm lub ER. Y kab los sib ntsib lies nyob rau hauv hypotenuse WR. Xav ntxiv duab, cov lus xaus yuav tsum kos:

1. WTY - ceskaum daim duab peb sab, vim hais tias ntawm cov mob wer - ceskaum txhais tau tias, EWR lub yog 45 degrees, thiab lub resulting daim duab peb sab - nrog lub kaum sab xis ntawm lub hauv paus thiab 45 degrees, uas tso cai rau peb mus qhia nws ceskaum. Nws hais ntxiv hais tias lub WT = Ty.
2. Ty = ET li ob lub square.
3. Ua raws li cov tib algorithm, peb neeg hauv qab no: Yu = UR, thiab UR = EU.
4. Sab ntawm koj lub daim duab peb sab yuav tuaj raws li lub sum ntawm cov feem. EW = ET + TW, thiab ER = EU + UR.
5. Hloov sib npaug zos theem, peb deduce: EW = ET + Ty, thiab ER = EU + UY.
6. Yog hais tias ntawm lub perimeter ntawm lub inscribed square yog qhia los ntawm cov mis mos (ET + Ty) + (EU + UY), nyob rau hauv tej txoj kev nws yuav raug sau cia, lub ntsiab lus tias tsuas yog tus muab tau tus nqi ntawm daim duab peb sab sab, raws li EW + ER. Uas yog, ntawm lub perimeter ntawm lub square inscribed nyob rau hauv ib lub duab peb sab uas muaj ib tug txuam cai kaum yog sib npaug zos rau qhov tawm ntawm cov qhov lwm ob sab.

Qhov no, ntawm chav kawm, tsis yog txhua txhua kev xaiv rau xam ntawm lub perimeter ntawm lub square, tiam sis tsuas yog lub feem ntau. Tiam sis tag nrho cov ntawm lawv raug raws li nyob rau hauv lub fact tias lub perimeter ntawm lub quadrilateral - ib tug sau ua ke nqi ntawm tag nrho nws cov sab. Thiab muaj tsis muaj khiav dim!