Ikufanana ndi ndege: chikhalidwe ndi katundu

Likufanana ndi ndege ndi mfundo koyamba anaonekera mu Masamu Euclidean kwa zaka zoposa zikwi ziwiri zapitazo.

Main makhalidwe a masamu chakale

Kubadwa chilango katswiriyu ndi Ntchito wotchuka wakale Greece dzina Euclid, amene analemba m'zaka za zana lachitatu BC, kapepalako "Zochitika". Ogaŵikana khumi mabuku, "Zochitika" ndiko Kupambana apamwamba a masamu onse wakale ndi kumufotokozera mfundo lofunika kugwirizana ndi katundu wa kanjedza ndege.

Chakale chikhalidwe cha ndege kufanana anali anakonza motere: ndege ziwiri angatchedwe yomweyi ngati wina alibe mfundo wamba. Werengani Euclidean chachisanu zopanda ntchito.

Katundu wa ndege kufanana

The Euclidean Masamu akutali, kawirikawiri zisanu:

• chuma ndi woyamba (ndipo limafotokoza kufanana kwa ndege ya apadera). Kudzera mfundo imodzi, lomwe lili kunja ndege imeneyi, tingayandikire wina ndi chimodzi chokha kufanana ndege

• Chuma chachiwiri (amatchedwanso katundu triplicate). Ngati kumene ndege ziwiri zikufanana ndi kulemekeza wachitatu, pakati pawo, iwo amagwiritsidwa ikufanana.

• chuma ndi wachitatu (mwa kulankhula kwina, umatchedwa chuma mzere intersecting kufanana kwa ndege). Akamwedwa mzere payokha molunjika mitanda mmodzi wa ndege izi analemba kuti awoloka ndi mzake.

• katundu wachinayi (chuma cha mizere molunjika chosema pa ndege ikufanana ndi mnzake). Pamene ndege awiri kufanana intersect wachitatu (mbali iliyonse), ndi mzere awo a mphambano kukhala kufanana

• katundu kachisanu (chuma limene limalongosola zigawo zosiyanasiyana mizere kufanana molunjika, amene kugona pakati pa ndege ikufanana ndi mnzake). The zigawo za mizere analemba zimene akachita pakati pa ndege awiri kufanana kwenikweni ofanana.

Kufanana kwa ndege sanali Euclidean Masamu

Chotero njira ndi makamaka Masamu Lobachevsky ndi Riemann. Ngati Euclidean Masamu akuyendera pa malo athyathyathya, ndiye Lobachevsky mu malo zoipa yokhota kumapeto (yokhota kumapeto kunena mwachidule), pamene Riemann kuti wapeza kuzindikira ake mu malo ndithu yokhota kumapeto (mwa kulankhula kwina - m'madera). Pali sizachilendo stereotypical view kuti Lobachevsky kufanana kwa ndege (ndi mzere) intersect. Komabe, zimenezi si zoona. Inde kubadwa kwa Masamu hyperbolic anali kugwirizana ndi umboni wa zopanda Euclid ndi wachisanu ndi kusintha maganizo pa izo, koma tanthauzo kwambiri a ndege kufanana ndi mizere molunjika zikutanthauza kuti iwo sangathe kuwoloka kapena Lobachevsky kapena Riemann, kulikonse mipata iwo akuyendera. Kusintha mtima ndi mawu ali motere. M'malo mwa zopanda kuti munthu mmodzi yekha kufanana ndege angaonere mwa mfundo osati ndege kuperekedwa, anadza chiphunzitso china kudzera mfundo imene sanama ndege imeneyi akhoza kutenga awiri, osachepera, molunjika, amene ali ndege imodzi ndi zimenezi ndipo simudutsa izo.