Tsis tu ncua polygon. Cov nab npawb ntawm cov sab ntawm ib tug tsis tu ncua polygon

Daim duab peb sab, square, hexagon - cov nuj nqis yog lub npe hu rau yuav luag txhua leej txhua tus. Tiam sis ntawm no uas yog ib tug ib txwm polygon, paub tsis txhua leej txhua tus. Tab sis nws yog tag nrho cov tib geometric duab. Ib tug tsis tu ncua polygon yog hu ua ib tug uas muaj sib npaug zos ces kaum ntawm lawv tus kheej thiab lub sab. Cov nuj nqis ntau ntau, tab sis tag nrho lawv muaj tib lub zog, thiab siv tau rau lawv tib yam mis.

Thaj chaw ntawm cov kev uas

Tej kev polygon, seb square los yog Octagon, yuav inscribed nyob rau hauv ib lub voj voog. Qhov no yooj yim cuab yeej yog feem ntau siv nyob rau hauv kev tsim kho ntawm cov nuj nqis. Nyob rau hauv tas li ntawd, lub voj voog yuav tsum inscribed nyob rau hauv ib tug polygon thiab. Tus xov tooj ntawm kev sib cuag cov ntsiab lus yog sib npaug zos rau cov xov tooj ntawm nws cov sab. Nws tseem yog ib qho tseem ceeb uas lub voj voog inscribed nyob rau hauv ib tug ib txwm polygon yuav muaj nrog nws ib qho chaw. Cov duab cov nuj nqis yuav raug mus rau ib theorems. Txhua tog uas tseeb n-gon yog kev cob cog rua nrog lub voos kheej-kheej ntawm lub voj voog ib ncig nws R. Yog li ntawd, nws yuav tsum xam siv cov nram qab no: Muaj ib tug = 2R ∙ sin180 °. Los ntawm lub voos kheej-kheej ntawm lub vajvoog yuav pom tsis tau tsuas yog ob tog tab sis kuj ntawm lub perimeter ntawm ib tug polygon.

Yuav ua li cas mus nrhiav tau tus xov tooj ntawm cov sab ntawm ib tug tsis tu ncua polygon

Tej kev n-gon no yog muaj li ntawm ib tug xov tooj ntawm feem sib npaug zos rau txhua lwm yam, uas, thaum ua ke, tsim ib tug kaw kab. Nyob rau hauv cov ntaub ntawv no, tag nrho cov ces kaum tsim daim muaj nqi. Uas yog muab faib ua tej yam yooj yim thiab complex. Cov thawj pab pawg neeg no muaj xws li daim duab peb sab thiab lub square. Complex uas muaj ib tug loj tus naj npawb ntawm cov sab. Lawv kuj muaj xws li ib lub hnub qub zoo li tus daim duab. Nyob rau hauv txoj kev polygon sab no muaj nyob ntawm inscribing lawv nyob rau hauv ib lub voj voog. Ntawm no yog cov ntawv pov thawj. Kos ib txwm polygon nrog ib tug arbitrary tus naj npawb ntawm sab n. Piav ib lub voj voog ib ncig ntawm nws. Nug ib tug voos kheej-kheej R. Tam sim no xav txog tej yam uas ib txhia muab n-gon. Yog hais tias tus taw tes ntawm nws cov ces kaum dag rau ib lub voj voog thiab sib npaug zos rau txhua lwm yam, ces tus txhais tes yuav nrhiav tau los ntawm cov mis: a = 2R ∙ sinα: 2.

Nrhiav tus xov tooj ntawm ob lub inscribed kev daim duab peb sab

Equilateral triangle - yog ib tug tsis tu ncua polygon. Formula yuav tsum muaj ntaub ntawv tib yam li hais tias ntawm lub square, thiab cov n-gon. Daim duab peb sab yuav muab suav hais tias siv tau yog hais tias nws muaj tib lub raws qhov ntev ntawm ib sab. Lub ces kaum yog muaj sib npaug 60⁰. Tsim ib tug daim duab peb sab nrog sab ntawm predetermined ntev a. Paub nws theem nrab thiab qhov siab, koj yuav nrhiav tau tus nqi ntawm nws cov sab. Rau no peb siv ib txoj kev uas nrhiav tau lub mis los ntawm ib tug = x: cosα, qhov twg x - median los yog qhov siab. Txij li thaum tag nrho ob tog yog muaj sib npaug daim duab peb sab, peb nrhiav tau ib tug = b = c. Ces yuav muaj tseeb rau cov lus nram qab no ib tug = b = c = x: cosα. Ib yam li ntawd, peb yuav nrhiav tau tus nqi ntawm ob tog nyob rau hauv ib tug equilateral daim duab peb sab, tab sis yuav tsum muab x qhov siab. Nyob rau hauv cov ntaub ntawv no, nws yog npaj yuav nruj me ntsis rau ntawm lub hauv paus ntawm cov nuj nqis. Yog li ntawd, paub qhov siab qhov ntawm x, nrhiav tau ib tug sab ntawm ib tug ceskaum daim duab peb sab siv cov mis A = B = x: cosα. Tom qab nrhiav tau qhov tseem ceeb ntawm ib tug muaj peev xwm yuav xam los ntawm qhov ntev ntawm lub hauv paus. Peb thov lub theorem ntawm Pythagoras. Peb nrhiav ib lub hauv paus ib nrab nqi c: 2 = √ (x: cosα) ^ 2 - (x 2) = √x ^ 2 (1 - cos ^ 2α): cos ^ 2α = x ∙ tgα. Ces c = 2xtgα. Qhov ntawd yog qhov yooj yim txoj kev uas koj yuav nrhiav tau tej naj npawb ntawm cov sab ntawm lub inscribed polygon.

Muab xam los ntawm cov sab ntawm cov square inscribed nyob rau hauv ib lub voj voog

Zoo li lwm yam kev tu ncua polygon inscribed square muaj sib npaug zos sab thiab cov ces kaum. Yuav kom nws siv tib yam mis li hais tias ntawm ib tug daim duab peb sab. Xam rau sab ntawm lub square yog ua tau los ntawm tus nqi ntawm cov kab pheeb ces kaum. Xav txog qhov no txoj kev nyob rau hauv ntau yam. Nws yog lub npe hu hais tias tus kab pheeb ces kaum bisects kaum sab xis. Chiv cov nqi yog 90 degrees. Yog li, lub ob yog tsim tom qab faib lub lub daim duab peb sab. Lawv cov ces kaum nyob puag yuav ua ncaj rau 45 degrees. Raws li, txhua sab ntawm lub square yog sib npaug zos, uas yog: a = b = c = d = e e√2 ∙ cosα = 2, nyob qhov twg e - yog kab pheeb ces kaum ntawm ib tug square los yog ib lub hauv paus tsim tom qab division ntawm ib lub duab peb sab. Qhov no tsis yog tsuas yog txoj kev uas nrhiav tau lub sab ntawm cov square. Inscribe daim duab nyob rau hauv ib lub voj voog. Paub qhov voos kheej-kheej ntawm lub vajvoog R, peb nrhiav tau cov kev taw qhia ntawm ib tug square. Peb xam nws raws li nram no A4 = R√2. Lub radii ntawm kev uas yog xam los ntawm cov mis R = ib: 2tg (360 ^o: 2n), qhov chaw uas ib tug - sab ntev.

Yuav ua li cas los mus laij lub perimeter ntawm lub n-gon

Ntawm lub perimeter ntawm lub n-gon yog lub sum ntawm tag nrho nws cov sab. Nws yog ib qho yooj yim los mus laij. Koj yuav tsum paub qhov tseem ceeb ntawm tag nrho ob tog. Rau ib txhia hom uas, muaj tshwj xeeb cov qauv. Lawv cia koj mus nrhiav tau ntawm lub perimeter ntawm ib tug ceev heev. Nws yog lub npe hu hais tias tej kev polygon muaj sib npaug zos sab. Yog li ntawd, nyob rau hauv thiaj li yuav xam nws cov perimeter, nws suffices paub tsawg kawg yog ib tug ntawm lawv. Cov mis yuav nyob ntawm seb tus xov tooj ntawm ob lub lawm. Nyob rau hauv kev, nws zoo li no: R = ib tug, qhov chaw uas ib tug - tus nqi sab, thiab n - tus naj npawb ntawm cov ces kaum. Piv txwv li, mus nrhiav tau ntawm lub perimeter ntawm ib tug tsis tu ncua Octagon nrog ib tug sab ntawm 3 cm, koj yuav tsum muab nws los ntawm 8, uas yog, P = 3 ∙ 8 = 24 cm rau ib tug hexagon nrog ib tug sab ntawm 5 cm yog xam raws li nram no :. P = 5 ∙ 6 = 30 cm thiab li ntawd rau. txhua polygon.

Nrhiav lub perimeter ntawm ib tug parallelogram, square thiab pob zeb diamond

Nyob ntawm seb yuav ua li cas muaj ntau yam sab puas muaj kev polygon, xam nws perimeter. Qhov no zoo heev tswj neeg ua hauj lwm. Tseeb, nyob rau hauv sib piv rau rau lwm daim, nyob rau hauv cov ntaub ntawv no tsis yuav tsum tau saib rau tag nrho cov ntawm nws txhais tes, txaus ntawm ib tug. Nyob rau tib lub hauv paus ntsiab lus yog nyob ntawm lub perimeter ntawm lub quadrilateral, uas yog, square thiab pob zeb diamond. Txawm tias muaj tseeb hais tias lawv yog cov sib txawv cov nuj nqis, cov mis uas muaj ib tug P = 4a, qhov twg ib tug - sab. Ntawm no yog ib qho piv txwv. Yog hais tias ib tug neeg sab nrauv yog ib tug square los yog ib tug rhombus 6 cm, peb nrhiav puag ncig nram no: P = 4 ∙ 6 = 24 cm V parallelogram tsuas yog opposite qhia .. Yog li ntawd, nws puag ncig siv lwm txoj kev. Yog li ntawd, peb yuav tsum paub qhov ntev thiab dav ntawm ib daim duab. Tom qab ntawd peb thov cov mis P = (ib tug + b) ∙ 2. parallelogram uas nws sab tag nrho cov sib npaug thiab cov ces kaum nruab nrab ntawm lawv, hu ua pob zeb diamond.

Nrhiav lub perimeter ntawm ib tug equilateral daim duab peb sab thiab lub

Puag ncig txoj kev equilateral daim duab peb sab yuav pom los ntawm cov mis P = 3a, qhov twg ib tug - sab ntev. Yog hais tias nws tsis paub hais tias, nws muaj peev xwm yuav nrhiav tau los ntawm cov theem nrab. Nyob rau hauv ib txoj kev daim duab peb sab yog sib npaug zos rau cov nqi yog cia li muaj ob sab. Lub hauv paus yuav pom los ntawm cov Pythagorean theorem. Tom qab yuav paub qhov tseem ceeb ntawm tag nrho cov peb ob tog, peb xam lub perimeter. Nws muaj peev xwm yuav nrhiav tau siv cov mis R = ib + b + c, uas a thiab b - sib npaug zos sab, thiab nrog - ib lub hauv paus. Nco qab tias nyob rau hauv ib tug equilateral daim duab peb sab, ib tug = b = ib tug, ces ib tug + b = 2a, ces P = 2a + c. Piv txwv li, lub sab ntawm ib tug ceskaum daim duab peb sab yog sib npaug zos rau 4 cm, nrhiav nws puag thiab perimeter. Laij cov nqi Pythagorean hypotenuse nrog √a = ² + ² = √16 + 16 = √32 = 5,65 cm. Peb tam sim no xam ncig P = 2 ∙ 4 + 5.65 = 13.65 cm.

Yuav ua li cas mus nrhiav tau cov ces kaum ntawm ib lub polygon

Ib tug tsis tu ncua polygon yog pom nyob rau hauv peb lub neej txhua txhua hnub, piv txwv li, lub ib txwm square, daim duab peb sab, Octagon. Nws yuav zoo li uas tsis muaj dab tsi yooj yim dua rau tsim no daim rau koj tus kheej. Tab sis hais tias yog cia li thaum xub thawj siab ib muag. Nyob rau hauv thiaj li yuav tsim kom muaj tej n-gon, nws yog tsim nyog los paub qhov muaj nqis ntawm nws cov ces kaum. Tab sis ua li cas koj nrhiav tau lawv? Txawm ancient zaum muaj twb tau sim los tsim kom tau kev uas. Lawv xam kom haum lawv mus rau hauv ib lub voj voog. Thiab ces rau nws sau ntawv yuav tsum tau mus taw tes, txuas rau lawv nrog cov kab ncaj nraim. qhov teeb meem yog solved rau qhov kev siv ntawm tej yam yooj yim nrhiav. Qauv thiab theorems twb tau. Piv txwv li, lub Euclid nyob rau hauv nws nto moo ua hauj lwm "Tsev" rau tov ntawm cov teeb meem muab kev koom tes nyob rau hauv lub 3-, 4-, 5-, 6- thiab 15-gons. Nws pom txoj kev los tsim kom tau thiab nrhiav tau cov ces kaum. Cia peb kawm saib yuav ua li cas yuav ua rau nws rau lub 15-gon. Ua ntej, koj yuav tsum xam tag nrho ntawm nws sab hauv ces kaum. Nws yog tsim nyog los siv cov mis S = 180⁰ (n-2). Yog li ntawd, peb yuav muab ib tug 15-gon, li no, tus xov tooj n yog 15. pauv lub npe hu cov ntaub ntawv thiab muab tau cov mis S = 180⁰ (15 - 2) = 180⁰ x 13 = 2340⁰. Peb pom lub sum ntawm tag nrho cov sab hauv ces kaum ntawm ib tug 15-mog polygon. Tam sim no koj yuav tsum tau tus nqi ntawm txhua tus ntawm lawv. Tag nrho cov ces kaum 15 ua suav 2340⁰: 15 = 156⁰. Li no, txhua tus nyob hauv lub yog 156⁰, tam sim no nrog ib tug kav thiab compass muaj peev xwm tsim qhov tseeb 15-gon. Tab sis li cas txog ntau n-gon? Muaj ntau centuries zaum muaj tej yam nyuaj yuav daws tau qhov teeb meem no. Nws twb pom xwb nyob rau hauv lub 18th xyoo pua los ntawm Carl Fridrihom Gaussom. Nws muaj peev xwm los tsim kom tau ib tug 65537-square. Txij thaum ntawd los qhov teeb meem yog officially suav kiag li solved.

Muab xam los ntawm cov n-gon lub nyob rau hauv radians

Ntawm cov hoob kawm, muaj ob peb txoj kev uas nrhiav tau lub ces kaum ntawm polygons. Feem ntau cov feem ntau lawv yog xam nyob rau hauv degrees. Tab sis peb muaj peev xwm qhia rau lawv nyob rau hauv radians. Yuav ua li cas yuav ua rau nws? Taug raws li nram no. Ua ntej, peb yuav nrhiav tau tawm hauv lub xov tooj ntawm cov sab ntawm ib tug tsis tu ncua polygon, thiab ces rho therefrom 2. Li no, peb tau txais tus nqi: n - 2. Muab qhov txawv pom los ntawm tus xov tooj n ( "pi" = 3.14). Tam sim no koj cia li faib uas cov khoom los ntawm tus xov tooj ntawm cov ces kaum nyob rau hauv lub n-gon. Xav txog cov piv txwv ntawm kev xam cov ntaub ntawv ntawm tib pyatnadtsatiugolnika. Yog li, tus xov tooj n yog sib npaug zos rau 15. Peb thov cov mis S = n (n - 2): n = 3,14 (15 - 2): 15 = 3,14 ∙ 13: 15 = 2.72. Qhov no, ntawm chav kawm, tsis yog tib txoj kev uas yuav xam lub kaum sab xis nyob rau hauv radians. Koj muaj peev xwm tsuas faib qhov luaj li cas ntawm lub kaum sab xis nyob rau hauv degrees los ntawm tus xov tooj 57,3. Tom qab tag nrho, thiaj li muaj ntau degrees yog sib npaug rau ib radian.

Muab xam los ntawm cov ces kaum nyob rau hauv grads

Nyob rau hauv tas li ntawd mus degrees thiab radians, ces kaum ntawm ib lub polygon, koj muaj peev xwm sim nrhiav tus nqi nyob rau hauv degrees. Qhov no yog ua raws li nram no. Peb rho los ntawm tag nrho cov 2 ces kaum, faib lub resulting sib txawv los ntawm tus xov tooj ntawm cov sab ntawm ib tug tsis tu ncua polygon. Pom cov kev tshwm sim yog multiplied by 200. Los ntawm txoj kev, qhov no unit ntawm kev ntsuas ntawm cov ces kaum li grads, tsis yog siv.

Muab xam los ntawm sab nrauv ces kaum n-gon

Tej kev polygon, nyob rau hauv tas li ntawd mus domestic, peb yuav tau xam kuj sab ces kaum. Nws tus nqi yog tib yam li rau lwm yam nuj nqis. Yog li ntawd, mus nrhiav tau ib tug sab nraud kaum sab xis ntawm ib tug tsis tu ncua polygon, koj yuav tsum paub tus nqi ntawm Internal. Ntxiv mus, peb paub hais tias tus sum ntawm cov ob ces kaum yog ib txwm 180 degrees. Yog li ntawd, muab xam yog ua li cas raws li nram no: 180⁰ rho tawm lub puab ces kaum. Peb paub qhov sib txawv. Nws yuav ua tau tus nqi ntawm lub kaum sab xis uas nyob ib sab mus rau nws. Piv txwv li, lub puab ces kaum ntawm lub square yog 90 degrees, ces cov tsos yuav 180⁰ - 90⁰ = 90⁰. Raws li peb tau pom, nws yog ib qho yooj yim mus nrhiav tau. Sab nraud lub tej zaum yuav muab ib tug nqi los ntawm + 180⁰ rau, ntsig txog, -180⁰.