Kukura Kwemasvomhu: Kuchinja Saizi Pasina Kuchinja Chimiro
Pendauluan
Mumasvomhu, pfungwa yekuwedzera simba ine basa rakakosha, kunyanya mu geometry. Kuwedzera simba, kana kushanduka kwehuwandu, inzira yekuwedzera kana kuderedza chinhu pasina kushandura chimiro chayo chepakutanga. Maitiro aya anosanganisira kushandisa chikero chakati kuti chiwedzere kana kuderedza chinhu chose zvakaenzana. Chinyorwa chino chichaongorora pfungwa, mashandisirwo, uye mienzaniso yekuwedzera simba mumasvomhu zvakadzama.
Tsanangudzo nepfungwa dzinokosha
Kuchinja chimiro (dilation) imhando yekuchinja chimiro (geometric change) kunochinja saizi yechimiro zvichibva pane scale factor, ukuwo kuchichengetedza kufanana kwechimiro. Muchidimbu, kuwedzera chimiro kunoreva kushanduka uko saizi yechinhu inowedzerwa kana kuderedzwa, asi chimiro nekwakatarisana nechinhu zvinoramba zvisina kuchinja.
Kana tikatsanangura chinhu muzvikamu zviri muzvikamu zviviri (2D), saka kushanduka kwekuwedzera kunogona kuratidzwa nefomura iri nyore yemasvomhu. Ngatitii tine poindi ine zvikamu (x, y) yatinoda kushandura nechikamu chek. Zvikamu zvitsva zvepoindi ndeizvi (kx, ky).
Kana k > 1, chinhu chacho chichakudzwa. Kana 0 < k < 1, chinhu chichaderedzwa muhukuru. Semuenzaniso, kana tine triangle ine mapoinzi A(2, 3), B(4, 6), uye C(6, 5), uye tichida kuwedzera triangle ne scale factor ye2, saka mapoinzi matsva etriangle ndiA'(4, 6), B'(8, 12), uye C'(12, 10). Mashandiro Anoita Kuwedzeredza Kuti tinzwisise mashandiro anoita kuwedzeredza, tinofanira kufunga nezvezvinhu zviviri zvakakosha: 1. Nzvimbo yeKukura: Nzvimbo yakatarwa iyo daro remapoinzi ese pachinhu rinowanziridzwa nechiyero. Pakati apa panogona kunge pari mukati, kunze, kana kuti pane imwe nzvimbo chaiyo yechinhu chacho. 2. Chiyero cheScale (k): Kukosha kunoshandiswa kuwanza daro kubva pakati pekuwedzerwa kusvika kumapoinzi ese ari muchinhu chacho. Semuenzaniso, kana chiyero chiri 2, saka daro rese kubva pakati pekuwedzera kusvika kune mapoinzi echinhu richapetwa kaviri. Ngatitii pakati pekuwedzera kwehuwandu pane mavambo (0,0). Kana poindi A(x, y) pachinhu chekutanga ikawedzeredzwa nechiyero k, saka macoordinates matsva eA' achava (kx, ky). Muchiitiko ichi, mutsetse unobatanidza pakati pekupatsanurwa nepfungwa pachinhu chekutanga uye pfungwa pachinhu chakapatsanurwa ucharamba wakatwasuka, zvichiratidza kuti chinhu chacho chakakura kana kuderedzwa zvakaenzana. Mashandisirwo eKuwedzera Kwesimba Muhupenyu Hwezuva Nezuva 1. Kugadzira Mepu uye Kukwanisa Kukura: Kugadzira mepu kunowanzo shandisa pfungwa yekuwedzera. Semuenzaniso, mepu yeguta kana nzvimbo yekumaruwa. Mepu iyi inobatanidza nzvimbo chaiyo nechikamu chakati, zvichibvumira kuratidzwa kwedata renzvimbo nenzira inogayiwa zviri nyore. 2. Kutora Mifananidzo uye Kugadzira Mifananidzo: Munyika yekutora mifananidzo uye kugadzira mifananidzo, kuwedzera kunoshandiswa zvakanyanya mukuchinja saizi yemifananidzo nemifananidzo. Maitiro aya anofanira kuitwa pasina kuchinja chiyero chemufananidzo (proportions) kuti pasave nekukanganiswa. 3. Kuenzanisa Masvomhu: Mukuenzanisa kwemasvomhu, kunyanya mufizikisi neinjiniya, kuwedzera kunoshandiswa kutevedzera mamiriro akasiyana pasina kuchinja chimiro chemuenzaniso. Semuenzaniso, mukutevedzera zvivakwa, kushandiswa kwekuwedzera kunogona kubatsira kuona mhedzisiro yekuwedzera chiyero pasina kushandura huwandu hwezvikamu zvega zvega. Muenzaniso weMibvunzo neMhinduro Mubvunzo 1: Ngatitii poindi P(3, 4) iri mu coordinate plane. Wedzera nzvimbo iyi nepakati pa (0,0) uchishandisa chiyero che3. Mhinduro: Point P ine macoordinates (3,4). Kana tikashandisa chiyero che3, tinowanza ma coordinates ne3: \[ P'(x', y') = (3 3, 3 4) = (9, 12) \] Saka, poindi itsva P' mushure mekuwedzerwa ndeye (9,12). Mubvunzo 2: Katatu ine mapoinzi A(1, 2), B(3, 4), uye C(5, 6). Isa dilation ine pakati pa (0,0) uye scale factor ye0.5. Mhinduro: Poindi A(1,2): \[ A'(x', y') = (0.5 1, 0.5 2) = (0.5, 1) \] Poindi B(3,4): \[ B'(x', y') = (0.5 3, 0.5 4) = (1.5, 2) \] Poindi C(5,6): \[ C'(x', y') = (0.5 5, 0.5 6) = (2.5, 3) \] Saka, kuverenga mushure mekuwedzerwa kwetriangle kuchava nemapoinzi A'(0.5,1), B'(1.5,2), uye C'(2.5,3). Hukama Nezvimwe Zvishanduko Kunze kwekuwedzerwa, mu geometry zvimwe zvishanduko zvakasiyana-siyana zvinozivikanwa zvakaita sekushandura, kutenderera, uye kufungisisa. Asi chii chinosiyanisa kuwedzera kubva pakushanduka? - Shanduro inotamisa chinhu kubva panzvimbo imwe kuenda kune imwe mu coordinate plane pasina kuchinja saizi yacho, chimiro, kana kuti kwachinongedzera. - Kutenderera kunotenderedza chinhu pakati pekutenderera nekona yakatarwa, kuchengetedza saizi nechimiro asi kuchichinja mafambiro echinhu chacho. - Kufungisisa kunochinja nzvimbo yechinhu zvichibva pamutsetse wekufungisisa, zvakaita sekuratidza chinhu pamutsetse kuti chigadzire chimiro chakaenzana. Panguva iyi, kuwedzera kwehukuru kunongochinja saizi chete ukuwo kuchichengetedza chimiro uye kurongeka. Mhedziso Kupatsanurwa kwehuwandu ipfungwa inokosha yemasvomhu mukunzwisisa kuti zvinhu zvinogona sei kuenzaniswa zvakaenzana. Kuwedzera kana kuderedza zvinhu pasina kuchinja chimiro chazvo ndiyo hwaro hwemashandisirwo akawanda muminda yakasiyana-siyana, kubva pakugadzira mamepu kusvika pakugadzira mifananidzo, uye kutevedzera mainjiniya. Kunzwisisa nekushandisa kuwedzera kunovhura mukana wekuchinja kwakaoma kunzwisisa kwejometri uye mashandisirwo azvo muhupenyu chaihwo. Sechimwe chezvishandiso zvakawanda zvinoshandiswa mumasvomhu nesainzi, pfungwa iyi inotiyeuchidza nezvechinhu chakakosha: saizi inogona kuchinja, asi chimiro uye hunhu zvinoramba zvakafanana.
