Yuav ua li cas mus nrhiav tau lub qhov siab ntawm ib tug equilateral daim duab peb sab? Formula qhov chaw, qhov siab zog nyob rau hauv ib tug equilateral daim duab peb sab

Geometry - nws tsis yog ib lub tsev kawm kawm ntawm uas koj yuav tsum tau ib tug zoo meej tau. Nws kuj yog ib tug uas paub hais tias yog feem ntau yuav tsum tau nyob rau hauv lub neej. Piv txwv li, thaum lub tsev ib lub tsev nrog ib tug high school cov ru tsev yog tsim nyog los mus laij lub thickness ntawm lub cav thiab lawv tus xov tooj. Nws yog ib qho yooj yim yog tias koj paub yuav ua li cas nrhiav tau qhov siab ntawm ib tug equilateral daim duab peb sab. Architectural lug yog raws li kev txawj ntse ntawm lub thaj chaw ntawm geometric nuj nqis. Cov ntaub ntawv ntawm cov vaj tse yog feem ntau tsis pom kev zoo li lawv. Lub Egyptian pyramids, cov pob ntawm cov mis nyuj, artistic paj ntaub, sab qaum teb painting thiab txawm ncuav - tag nrho cov duab peb ceg uas lwm tus txiv neej. Raws li Plato hais tias, lub ntiaj teb no yog raws li nyob rau hauv cov vajvoos peb sab.

ceskaum daim duab peb sab

Kom nws dlaim phaj, raws li yuav tsum tau tham rau hauv qab no, nws yog ib tug nqi me ntsis rau koj nco ntsoov cov qauv rau kev ntsuas.

Daim duab peb sab yog ceskaum yog hais tias nws muaj ob tug sib npaug zos sab. Lawv yeej ib txwm hu sab. Tog uas nws qhov ntev txawv, hu ua bases.

tswv yim

Zoo li tej science, geometry nws muaj nws tus kheej kev cai thiab cov tswv yim. Ib tug ntau ntawm lawv. Xav txog xwb cov neeg uas tsis uas peb lub ntsiab yuav ua dog dig tsis meej.

Qhov siab - qhov no yog ib tug ncaj kab kos perpendicular mus rau sab nraud.

Theem nrab - ib ya qhia los ntawm txhua kab los sib ntsib ntawm daim duab peb sab tsuas mus rau nruab nrab ntawm qhov opposite sab.

Bisector - ib tug nqaj uas faib nyob rau hauv ib nrab lub kaum sab xis.

Bisector ntawm ib tug daim duab peb sab - nws yog ib tug ncaj, los yog es, lub ya bisector, txuas rau sab saum toj ntawm qhov opposite sab.

Nws yog ib qho tseem ceeb yuav tau nco ntsoov hais tias tus bisector ntawm lub kaum sab xis - nws yog obligatory ray thiab daim duab peb sab bisector - ib feem ntawm lub beam.

Lub hauv paus ces kaum ntawm

Lub theorem hais tias cov fab yog nyob rau ntawm lub hauv paus tej ceskaum daim duab peb sab yeej ib txwm sib npaug zos. Los ua pov thawj no theorem yog heev yooj yim. Yuav hais ib ceskaum daim duab peb sab ABC, nyob rau hauv uas AB = BC. Los ntawm ABC bisector lub tsim nyog los HP. Tam sim no ob tug ua daim duab peb sab yuav tsum tau suav hais tias. Nyob rau hauv mob AB = BC, lub HP sab ntawm lub duab peb ceg nyob rau hauv Feem ntau, thiab lub ces kaum AED thiab SVD yog muaj sib npaug, vim hais tias VD - bisector. Teebmeem thawj kos npe rau ntawm koob pheej ntawm lawv, peb yuav xyuam xim xaus uas lub duab peb ceg uas xam sib npaug zos. Thiaj li, tag nrho cov ces kaum muaj sib npaug. Thiab, ntawm chav kawm, lub tog, tab sis los ntawm lub sij hawm uas yuav rov qab mus rau yav tom ntej.

Lub qhov siab ntawm lub ceskaum daim duab peb sab

Cov yuav tsum muaj theorem, uas yog raws li cov tshuaj rau txhua kev pab raws qib, yog: qhov siab tsis pub dhau ib equilateral daim duab peb sab yog lub bisector thiab theem nrab. Yuav kom to taub nws cov tswv yim kev txiav txim zoo (los yog essence) yuav tsum tau ua kev pab txhawb nqa nyiaj. Ua li no, txiav daim ntawv ceskaum daim duab peb sab. Qhov yooj yim txoj kev uas yuav ua qhov no los ntawm ib tug dog dig ntawv ntawm phau ntawv sau nyob rau hauv lub thawv.

Quav lub resulting daim duab peb sab nyob rau hauv ib nrab, aligning sab. Yuav ua li cas tshwm sim? Ob tug sib npaug zos cov vajvoos peb sab. Tam sim no kos lub txoj kev fwv yees. Nthuav lub resulting origami. Kos ib tug quav kab. Nrog protractor xyuas lub kaum sab xis ntawm lub incised kab thiab ib daim duab peb sab puag. Yuav ua li cas puas lub kaum sab xis ntawm 90 degrees? Lub fact tias cov kab kos - perpendicular. Los ntawm txhais - qhov siab. Yuav ua li cas mus nrhiav tau lub qhov siab ntawm ib tug equilateral daim duab peb sab, peb tau to taub. Tam sim no rau cov fab rau saum. Siv tib daim tshev protractor ces kaum, yog tam sim no tsim twb siab. Lawv yog cov sib npaug. Qhov no txhais tau tias lub siab yog ob qho tib si bisector. Armed nrog ib tug kav, ntsuas lub feem mus rau hauv uas lub siab ntawm lub hauv paus. Lawv yog cov sib npaug. Thiaj li, lub qhov siab nyob rau hauv ib tug equilateral triangle bisects lub hauv paus thiab yog ib tug nruab nrab.

lub pov thawj

Visual pab kom meej meej qha lub validity ntawm cov theorem. Tab sis geometry - lub science tseeb txaus, li ntawd, nws tus kheej-tsheev.

Thaum lub sij hawm saib xyuas ntawm cov koob pheej ntawm lawv ntawm cov ces kaum nyob puag tau muaj pov thawj sib npaug zos cov vajvoos peb sab. Cov txheejtxheem, WA - bisector, thiab cov duab peb ceg AED thiab SVD yog muaj sib npaug. Qhov xaus yog hais tias cov coj sab ntawm lub duab peb sab thiab, ntawm chav kawm, cov ces kaum muaj sib npaug. Yog li ntawd AD = SD. Thiaj li, WA - median. Nws tseem mus ua pov thawj tias HP yog high school. Raws li cov koob pheej ntawm lawv ntawm cov vajvoos peb sab saib xyuas, nws hloov tawm hais tias ib lub sib npaug zos rau lub kaum sab xis ADV ADD. Tab sis cov no ob ces kaum yog nyob ib sab thiab tau lub npe hu mus ntxiv mus txog 180 degrees. Yog li ntawd, yog dab tsi lawv yog? Ntawm cov hoob kawm, 90 degrees. Yog li, HP - yog lub qhov siab nyob rau hauv ib tug equilateral triangle twv rau lub hauv paus. QED.

Ntsiab nta

• Yuav kom tau raws txoj kev sib tw, nws yuav tsum nco ntsoov lub ntsiab nta ntawm ceskaum cov vajvoos peb sab. Lawv zoo li yuav lub rov qab theorem.
• Yog hais tias nyob rau hauv lub chav kawm ntawm daws qhov teeb meem kuaj tau los ntawm lub koob pheej ntawm lawv ntawm ob ces kaum, nws txhais tau tias koj lis txog nrog ib tug ceskaum daim duab peb sab.
• Yog hais tias koj tsis muaj peev xwm los ua pov thawj hais tias theem nrab yog tseem lub qhov siab ntawm daim duab peb sab, xyuam xim vij - daim duab peb sab yog ceskaum.
• Yog hais tias lub bisector yog lub siab, ces, raws li nyob rau hauv lub ntsiab nta ntawm daim duab peb sab xa mus rau ib tug ceskaum daim duab peb sab.
• Thiab, ntawm chav kawm, yog hais tias tus theem nrab thiab ua hauj lwm pab raws li ib tug qhov siab, xws li ib tug daim duab peb sab - ceskaum.

lub qhov siab ntawm lub mis 1

Txawm li cas los, feem ntau paub tab, koj yuav tsum nrhiav tus xam qhov siab muaj nqis. Uas yog vim li cas peb xav txog yuav ua li cas nrhiav tau qhov siab ntawm ib tug equilateral daim duab peb sab.

Rov qab mus rau saum toj daim duab, ABC, nyob rau hauv uas ib tug - sab nyob rau hauv - hauv paus. HP - rau qhov siab ntawm daim duab peb sab, nws muaj lub h cim.

Yuav ua li cas yog daim duab peb sab AED? Txij li thaum HP - qhov siab, ces daim duab peb sab AED - lub ceg tias koj xav mus nrhiav tau. Siv cov Pythagorean mis, peb tau txais:

= + AV² AD² VD²

Txhais cov kev qhia VD thiab hloov designations saws ua ntej lawm, peb tau txais:

N² = a² - (a / 2) ².

Koj yuav tsum tshem tawm cov hauv paus:

H = √a² - v² / 4.

Yog hais tias koj ua ib tug ¼ ntawm lub kos npe rau ntawm lub hauv paus, ces cov mis yuav tsum:

H = ½ √4a² - v².

Li ntawd, yog lub qhov siab nyob rau hauv ib tug equilateral daim duab peb sab. Cov mis muab tau los ntawm cov Pythagorean theorem. Txawm hais tias peb tsis nco qab tus leb cim, ces, paub txog tus qauv ntawm nrhiav, koj yeej ib txwm coj nws.

lub qhov siab ntawm cov mis 2

Cov mis piav saum toj no yog cov yooj yim thiab feem ntau siv nyob rau hauv feem ntau geometrical teeb meem. Tab sis nws tsis yog tus tsuas yog ib qho. Tej zaum nws muab tsis ib lub hauv paus nqi muab kaum sab xis. Thaum cov ntaub ntawv xws li nrhiav ib tug qhov siab ntawm ib tug equilateral daim duab peb sab? Yuav kom daws tau cov teeb meem no nws yog advisable siv ib tug txawv mis:

H = ib tug / kev txhaum α,

qhov twg H - qhov siab, mus rau hauv lub hauv paus,

thiab - ib tug sab sab,

α - lub kaum sab xis ntawm lub hauv paus.

Yog hais tias qhov teeb meem yog muab lub kaum sab xis ntawm lub kab los sib ntsib, lub qhov siab tsis pub dhau ib equilateral daim duab peb sab yog raws li nram no:

H = ib tug / cos (β / 2),

qhov twg H - qhov siab, lowered mus rau hauv lub hauv paus ,,

β - lub kaum sab xis ntawm lub apex,

thiab - sab.

Txoj cai ceskaum daim duab peb sab

Heev ntawm nthuav cov khoom ntiag tug muaj ib tug daim duab peb sab, lub apex ntawm uas yog sib npaug zos rau 90 degrees. Xav txog ib tug txoj cai-angled daim duab peb sab ABC. Raws li nyob rau hauv dhau tus neeg mob, WA - qhov siab mus rau hauv lub hauv paus.

Lub hauv paus ces kaum muaj sib npaug. Xam lawv cov loj ua hauj lwm yuav tsis ua rau:

α = (180 - 90) / 2.

Yog li, cov ces kaum nyob rau ntawm lub hauv paus, yeej ib txwm nyob rau ntawm lub 45 degrees. Tam sim no xav txog ADV daim duab peb sab. Nws kuj yog ib. Peb nrhiav tau lub kaum sab xis AED. Los ntawm tej yam yooj yim suav peb tau txais 45 degrees. Thiab, yog li ntawd, qhov no daim duab peb sab tsis yog tsuas yog txoj cai, tab sis kuj yog ib tug ceskaum. Lub sab AD thiab VD yog cov sab thiab yog muaj sib npaug.

Tab sis sab AD nyob rau tib lub sij hawm yog ib nrab ntawm AU. Nws hloov tawm hais tias nyob rau hauv lub qhov siab ntawm ib tug equilateral daim duab peb sab yog sib npaug zos rau ib nrab hauv lub hauv paus, raws li yog hais sau rau hauv daim ntawv ntawm ib tug qauv, peb muab tau cov nram qab no qhia:

H = ib tug / 2.

Nws yuav tsum tsis txhob yuav tsis nco qab lawm hais tias qhov no mis tsuas yog ib tug tshwj xeeb cov ntaub ntawv, thiab muaj peev xwm tsuas yog siv rau lub lub ceskaum cov vajvoos peb sab.

Lub Golden daim duab peb sab

Heev ntawm nthuav cov yog cov golden daim duab peb sab. Nyob rau hauv no daim duab, tus piv ntawm lub sab ntawm lub hauv paus yog sib npaug zos rau cov nqi, hu ua lub xov tooj ntawm Phidias. Kaum nyob rau saum - 36 degrees, nrog lub hauv paus - 72 degrees. Qhov no daim duab peb sab admired Pythagoreans. Golden daim duab peb sab hauv paus ntsiab lus ua lub hauv paus ntawm ib tug plurality ntawm immortal masterpieces. Qhov zoo-paub tsib-taw lub hnub qub ua nyob hauv kev tshuam ntawm ceskaum cov vajvoos peb sab. Rau ntau tej hauj lwm ntawm Leonardo da Vinci siv cov hauv paus ntsiab lus ntawm lub "golden daim duab peb sab". Muaj pes tsawg leeg "Mona Lisa" yog raws li cia li nyob rau hauv cov nuj nqis, uas tsim ib txoj cai pentagram.

Painting "Cubism", ib tug ntawm Pablo Pikasso tej hauj lwm, fascinating saib ntaub ntawv lub hauv paus ntawm ib tug ceskaum daim duab peb sab.