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 chichawedzerwa. Kana 0 < k < 1, chinhu chichaderedzwa. Semuenzaniso, kana tiine triangle ine mapoinzi A(2, 3), B(4, 6), na C(6, 5), uye tichida kuwedzera triangle ne scale factor ye2, ipapo mapoinzi matsva etriangle ndiA'(4, 6), B'(8, 12), na C'(12, 10).
Mashandiro Anoita Kupatsanura Kuti tinzwisise mashandiro anoita kupatsanura, tinofanira kufunga nezvezvinhu zviviri zvakakosha: 1. Nzvimbo yeKupatsanura: Nzvimbo yakatarwa iyo daro remapoinzi ese pachinhu rinowanziridzwa nechiyero. Nzvimbo iyi inogona kuva mukati, kunze, kana pane imwe yenzvimbo dzechinhu. 2. Chiyero cheChikero (k): Kukosha kunoshandiswa kuwanziridza daro kubva pakati pekuwedzera kusvika kumapoinzi ese ari muchinhu. Semuenzaniso, kana chiyero chiri 2, saka daro rese kubva pakati pekuwedzera kusvika kumapoinzi echinhu richapetwa kaviri. Ngatitii nzvimbo yekuwedzera iri pakutanga (0,0). Kana poindi A(x, y) pachinhu chekutanga yakawedzerwa nechiyero k, saka macoordinates matsva eA' achava (kx, ky). Muchiitiko ichi, mutsetse unobatanidza nzvimbo yekuwedzera kusvika panzvimbo pachinhu chekutanga uye poindi pachinhu chakapatsanura uchagara wakatwasuka, zvichiratidza kuti chinhu chakawedzerwa kana kuderedzwa zvakaenzana. Mashandisirwo eKuwedzera kweNzvimbo muHupenyu hweZuva Nezuva 1. Kugadzira Mepu uye Kukwanisa Kukura: Kugadzira Mepu kunowanzo shandisa pfungwa yekukudza. Semuenzaniso, mepu yeguta kana nyika. Mepu yakadaro kuwedzera kwenzvimbo chaiyo nechiyero chakati, zvichibvumira kuratidzwa kwedata renzvimbo nenzira inogayiwa zviri nani. 2. Kutora Mifananidzo neKugadzira Mifananidzo: Munyika yekutora mifananidzo nekugadzira mifananidzo, kuwedzera kunoshandiswa zvakanyanya mukuchinja saizi yemifananidzo nemifananidzo. Maitiro aya anofanira kuitwa pasina kuchinja chiyero (zvikamu) zvemufananidzo kudzivirira kukanganisa. 3. Kugadzira Masvomhu: Mukugadzira masvomhu, kunyanya mufizikisi neinjiniya, kuwedzera kunoshandiswa kutevedzera mamiriro akasiyana pasina kuchinja chimiro chemuenzaniso. Semuenzaniso, mukutevedzera zvivakwa, kushandiswa kwekuwedzera kunogona kubatsira kuona mhedzisiro yekuwedzera chiyero pasina kuchinja huwandu hwezvikamu zvega zvega. Muenzaniso Matambudziko neMhinduro Dambudziko 1: Funga nezve poindi P(3, 4) mu coordinate plane. Wedzera poindi iyi nepakati pa (0,0) uchishandisa scale factor ye3. Mhinduro: Poindi P ine coordinate (3,4). Kana tikashandisa scale factor ye3, tinowedzera coordinate ne3: \[ P'(x', y') = (3 3, 3 4) = (9, 12) \] Saka, poindi itsva P' mushure mekuwedzera i (9,12). Mubvunzo 2: Katatu kane mapoinzi A(1, 2), B(3, 4), uye C(5, 6). Isa dilation ine pakati pa (0,0) uye scale factor ye 0.5. Mhinduro: Point A(1,2): \[ A'(x', y') = (0.5 1, 0.5 2) = (0.5, 1) \] Point B(3,4): \[ B'(x', y') = (0.5 3, 0.5 4) = (1.5, 2) \] Point 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 Nemamwe Mashanduko Kunze kwekuwedzerwa, mamwe mashanduko akasiyana anozivikanwa mu geometry akadai sekushandura, kutenderera, uye kufungisisa. Asi chii chinosiyanisa kuwedzera kubva pakuchinja uku? - Shanduro inotamisa chinhu kubva panzvimbo imwe kuenda kune imwe mu coordinate plane pasina kuchinja saizi, chimiro, kana kurongeka kwacho. - Kutenderera kunotenderera chinhu chakatenderedza pakati pekutenderera neimwe angle, kuchengetedza saizi nechimiro chacho asi kuchinja kurongeka kwacho. - Kufungisisa kunoshandura nzvimbo yechinhu zvichibva pamutsetse wekuratidzira, senge kuratidza chinhu pamutsetse kuti chigadzire chimiro chakaenzana. Panguva imwecheteyo, kuwedzera, kunyanya, kunochinja saizi chete uku uchichengetedza chimiro nekutungamira kwacho. Mhedziso Kuwedzeredza ipfungwa yakakosha yemasvomhu mukunzwisisa kuti zvinhu zvinogona sei kuderedzwa saizi zvakaenzana. Kuwedzera kana kuderedza chinhu pasina kuchinja chimiro chacho chepakutanga ndiyo hwaro hwemashandisirwo akasiyana-siyana muminda yakasiyana-siyana, kubva pakugadzira mamepu kusvika pakugadzira mifananidzo, uye simulation yeinjiniya. Kunzwisisa nekushandisa kuwedzera kunovhura mukana wekuchinja kwakaoma kunzwisisa kwejometri uye mashandisirwo azvo muhupenyu chaihwo. Sechimwe chezvishandiso zvakawanda zvinoshandiswa mumasvomhu nesainzi, pfungwa iyi inotiyeuchidza nezvechokwadi chakakosha: saizi inogona kuchinja, asi chimiro uye hunhu zvinoramba zvakafanana.