Nzira yekuwana sei mativi ekatatu yakanaka? Zvinhu zvinokosha zve geometry

Makumbo uye mhedziso ndiwo mapande emakona matatu. Yokutanga ndiyo zvikamu zviri pedo nekona yakarurama, uye chikonzero ndechokuti chikamu chakareba kwazvo chechimiro uye chinopesana nekona re 90 ^° . I triangle yePythagorane ndiyo iyo mazamu ayo akaenzana nenhamba dzepanyama; Kureba kwavo munyaya iyi kunonzi "Pythagorean Troika".

The Triangle Triangle

Kuti chizvarwa chemazuva ano chizive geometry nenzira iyo inodzidziswa kuchikoro ikozvino, yakashanduka kwemazana emakore akawanda. Pfungwa huru ndeyedzidziso yePythagoras. Mativi emakona matatu emakona matatu (iyo nhamba inozivikanwa kunyika yose) ndeye 3, 4, 5.

Vanhu vashomanana havazive nemutsara wekuti "Pythagorean pants kumativi ose akaenzana." Zvisinei, chaizvoizvo, theorem inonzwika seyiyi: c ² (sarotenususe yembiru) = ² + b ² (chiyero chemakumbo emakumbo).

Pakati pemasvomhu, hutatu huine mapofu 3, 4, 5 (cm, mamita, etc.) anonzi "Egypt". Zvinofadza kuti radius yendenderedzwa, iyo yakanyorwa mumufananidzo, yakaenzana nemumwe. Zita racho rakasimuka kumativi ezana remakore rechi5 BC, apo vazivi veGreece vakaenda kuEgipita.

Pakuvaka mapiramidhi, vavakadzi vezvivako uye vaongorori vakashandisa chiyero che3: 4: 5. Zvisungo zvakadaro zvakazove zvakaenzana, zvinonakidza pakuonekwa uye zvakakura, uyewo kazhinji hazvina kuwira.

Kuti vave nekona yakarurama, vavaki vakashandisa tambo, iyo mafundo gumi nemaviri akasungirirwa. Muchiitiko ichi, mukana wekuvaka kona katatu yakasimudzirwa yakasimudzwa kusvika 95%.

Kuenzana zviratidzo

• Nhengo yakaoma mune katatu yakanyatsotenderera uye rutivi rukuru runofanana nezvinhu zvakafanana mumutsara wechipiri chiratidzo chisingaoneki chekuenzana kwezvifananidzo. Tichifunga nezvehuwandu hwemakumbo, zviri nyore kuratidza kuti chechipiri inopinza mairi yakafananawo. Nokudaro, zviduku zvitatu zvakafanana muchiratidzo chechipiri.
• Apo mifananidzo miviri yakakonzerwa kune mumwe nemumwe, tinovashandura kuitira kuti ivo, vabatanidzwa, vave imwe yechipfuva chesosceles. Maererano nenzvimbo dzayo, mashizha, kana zvakanyanyisa, iyo inofungidzira, yakaenzana, seyiyo makona ari pasi, izvo zvinoreva kuti izvi zviyero zvakafanana.

Nechiratidzo chekutanga chiri nyore kwazvo kuratidza kuti zviduku zvitatu zvakaenzana zvakaenzana, chinhu chikuru ndechokuti mapoka maduku maviri (kureva, makumbo) akaenzana.

Zviratidzo zvichave zvakafanana muchiratidzo chechipiri, icho chinokosha icho chiri kuenzana kwegumbo uye yakaoma angle.

Zvigaro zvekona katatu yakarurama

Kureba kwakaderedzwa kubva kurudyi, kunoparadzanisa mufananidzo muzvikamu zviviri zvakaenzana.

Mativi edenderedzwa rakatenderedzwa zvakanaka uye mamiririri aro anenge ari nyore kuziva nemitemo: iyo miviri, iyo inoderedzwa kusvika pakufungidzira, yakaenzana nehafu yayo. Nharaunda yemufananidzo inogona kuwanikwa pamwe chete nemarangariro aHeron uye neshoko rokuti yakaenzana nehafu yezvibereko zvemakumbo.

Mune katatu yakarurama-angled, nzvimbo yemakona iri 30 ^° , 45 ^°, uye 60 ^° .

• Pakona ye 30 ^° , inofanira kuyeukwa kuti gumbo rinopikisa richava chikamu chechikamu chikuru.
• Kana kona iri 45 ^о , ipapo chikamu chechipiri chinowanikwawo kune 45 ^о . Izvi zvinoratidza kuti katatu ndeye isosceles, uye makumbo acho akafanana.
• Imba yekona ye 60 ° ndeyokuti kona yechitatu ine chiyero chechidimbu che 30 °.

Nharaunda yacho inonyatsozivikanwa neimwe yevatatu mazano:

1. Kupfurikidza nehupamhi uye nechemberi, pane iyo inonyura;
2. Nechirevo chaHeron;
3. Pamativi uye kona pakati pavo.

Mativi emakona matatu akangwara, kana kupfuura kunyanya makumbo, anotenderera nezvikamu zviviri. Kuti uwane chechitatu, zvakakosha kufunga nezvenguva yekatatu yakagadzirwa, uye zvakare, neyedzidziso yePythagorean, kuverenga urefu hunoda. Mukuwedzera kune chimiro ichi, panewo chiyero chepamusoro pepakati uye urefu hwechikonzero. Nzira inowanzozivikanwa pakati pevadzidzi ndeyekutanga, sezvo inoda kuverenga shoma.

Zvinyorwa zvinoshandiswa kune katatu yakarurama

Ijiometri yekona katatu yakarurama inosanganisira kushandiswa kwemaoremu akadai se:

1. The Pythagorean Theorem. Chinokosha chayo chiri muchokwadi chokuti chikamu chekufungidzira kwakaenzana nemari yemakumbo emakumbo. MuEuclidean geometry, ichi chiyero ndicho chinhu. Iwe unogona kushandisa rondedzero kana iwe uine katatu, somuenzaniso, SNH. SN - hypotenuse, uye inofanira kuwanikwa. Ipapo SN ² = NH ² + HS ² .
2. The cosine theorem. Inokonzera dzidziso yePythagoras: g ² = f ² + s ² -2fs * cos the angle between them. Somuenzaniso, DOB triangle inopiwa. Anozivikanwa DB cathete uye asinganzwisisi DO, zvakakosha kuwana OB. Zvadaro chirevo chacho chinotora chimiro chakapiwa: OB ² = DB ² + DO ² -2DB * ITA * yekona D. Pane migumisiro mitatu: kona yekatatu inenge yakaoma, kana chikamu chechitatu chiri kubviswa kubva pachiyero chezvikwata zvemaviri maviri, chigumisiro chinofanira kunge chisina kupfuura zero. Nzira yacho inoputika, kana kutaura kwakanyanya kudarika zero. Nzira yacho yakarurama kumutsara we zero.
3. The sine theorem. Inoratidza kuvimba kwemativi kumativi akasiyana. Mune mamwe mazwi, ichi ndicho chiyero chehurefu hwemativi kumakona emakona. Muchikamu chetatu HFB, uko kuve neHF, kunenge kuine: HF / chitadzo chezvivi B = FB / sin angle H = HB / sin angle F.