Pimanyika

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Pimanyika[chinja | edit source]

Pimanyika (Geometry in English) chidzidzo chinowongorora mibvunzo pamusoro pezvinotevera:


  • Kaumbirwo kakaitwa zviumbwa tichitarisa kupimwa kwemativi nemagonyo;
  • Kupa mitemo inotsanangudza, kufananidza, nokusiyanisa chiumbwa chimwe nechimwe;
  • Kududza kuti chiumbwa chiri papi zvichifananidzwa nepane chimwe chiumbwa.
  • Kukura kwakaita nzvimbo;
  • Kududza kuti nzvimbo iri papi zvichifananidzwa nepane imwe nzvimbo;


Chinangwa[chinja | edit source]

Chinangwa chechinyorwa chino kuparura nhaurwa yezvidzidzo zvePimanyika tichitaura neChiShona. Pakutanga mazita achapiwa kune izvo zvatinosangana nazvo pakupima nzvimbo nezviumbwa. Mazita eShona achadudzirwa zvakare pachishandiswa mazwi ariko kuChirungu. Nokuda kwekuti mamwe mazwi haasati aveko kuChiShona pachange pachipiwa mazita matsva, zvichibatsira kuumba mutauro wedu takatarisana neumhizha Pimanyika.

Mashoko Anowanikwa Muzvidzidzo zvePimanyika[chinja | edit source]

Chiyero chekupimisa (Unit of measure)- pakupimwa kunoitwa zvinopimwa pane mwero yakatarwa pamutemo (pasirose) kuti ishandiswe kupima mipimo yakasiyana inodaidzwa nemazita akasiyana. Sokuti kana tichipima nhambwe tinoshandisa chiyero chinonzi mita (metre).

Mutsetse kana kuti mutsara (line) - iri izwi rinotsanangudza mutaro wakanyorwa ungave wakati twasa kana kuti une minyongo.

Chiumbwa (Shape)- chiumbwa chinogona kunge chine nzenda mbiri kana nzenda nhatu. Tsanangudzo yokuti nzenda chii iri kutevera mberi

Hurefu (length) - shoko iri rinoreva kureba kwenzvimbo kana ichipimwa

Hwasha (width) - shoko iri rinoreva kupamhama kwenzvimbo kana ichipimwa

Hudzamu (depth) - shoko rinoreva kudzika kwenzvimbo kana ichipimwa

Hukwidza (altitude, height) - shoko iri rinoreva kukwirira kwakaita nzvimbo.

Mukwava (mugwava) - iri izwi rapiwa rinoreva panosangana mitsetse miviri kana uso huviri (where two surfaces or lines meet to form an angle)

Gonyo (angle) iri izwi rapiwa rinoreva kushama kwakaita mukwava uri pakati pemitsetse miviri kana uso huviri. gonyo kana ichipimwa inopimwa nechiyero chinonzi dhigirii

Sambamba (parallel) - izwi iri rapiwa rinotsangangudza mitsetse miviri yakati twasa yakataramukana nhambwe dzakaenzana panzvimbo dzose kana nhambwe ichipimwa pakati pemitsetse iyi. Apa nhambwe inofanirwa kunge iri kupimwa kuchitevedzwa mitsetse wechitatu unocheka mitsetse miviri yokutanga. Mutsetse wechitatu unofanirwa kunge uchicheka miviri yokutanga pamukwava une gonyo rakaenzana panzvimbo dzose. Muenzaniso wemitsetse wakati sambamba isimbi mbiri dzenjanji nokuti dzinofamba dzakayererana asi dzisingapesane.

Twasuka (straight) - izwi rinotsanangudza mutsetse kana kuti uso hwakatichechetere kunge pamusoro pemvura yakagadzikana isina masaisai. Mutsetse uwu unenge usina gonyo kana munyonga.

Munyonga (Curve) - izwi iri rinotsanangudza mutsetse kana uso husina kuti twasa; panenge pane kutsveyama kana kutesva. Iri izwi richange rakakosha kana todzidza chidzidzo Kutara Mutaro (drawing graphs).

Hubumbe (convex) iri izwi rinotsanangudza chiumbwa chine uso hwakabumbira kunze. Mufananidzo ungapiwa kuumbwa kwakaitwa dumbu rakaguta kana kuti dutu revhu rinounganidzwa pakugadzira gandiwa rinoeredza mvura.

Hufombwe (Concave) - iri izwi rinotsanangudza chiumbwa chine uso hwakafovera mukati. Mufananidzo ungapiwa imbiya inopakurirwa usavi kana kuti mugero unocherwa pakugadzira gandiwa rinoeredza mvura.

Mutwi (Perpendicular, vertical) - iri izwi rapiwa kutsangudza uso kana mutsetse wakamira kuti tasa kubva panzvimbo kuenda mudenga kana pasi. Muenzaniso ungapiwa itambo yakasungirwa padavi remuti yakaremedzwa nedombo kuzasi kwainoperera. Tambo iyi inoita mutwi kudzika kubva padavi. Iri shoko rinotoredzera kubva pamutswi unoshandiswa kutswa muduri; pano ndasiyanisa zvishomane, asi pfungwa ichinge iripo yokuti mutswi kana uchitswa muduri unouya umire kuita "vertical" kana pedyo nokuva "vertical".

rurama (Right angled, normal) - mitsetse inosangana pamukwava ne90o ichange ichinzi yakarurama, uku kuri kutaura muchidumbu. Apa kufananidza kutaura kuri kuEnglish kunonzi "the wall is normal to the floor - which means wall forms angle of 90o with the wall.

Sandarara (Horizontal) - izwi rinoreva uso hwakatichechetere kunge pamusoro pemvura yakagadzikana isina masaisai. Mutsetse wakatichechtere semvura unonzi musandarara.

Mutsendo (Plane, flat area) - izwi iri rapiwa richireva uso hwakatichechetere kunge pamusoro pemvura. Mutsendo unogonga kunge wakamiswa wakaita mutwi kana kurara kuti sandarara kana kurereka neipi zvayo gonyo. Izwi iri ririkutorwa kubva pamutsendo chinova chombo chinoshandiswa nevanoveza mapuranga. Mutsendo (plane KuChirungu) unoshandiswa kuveza mapuranga kuti puranga rive neuso hwakati chechetere husina makomba uye husina kumanzika. Mutsendo uso hune nzenda mbiri chete, hwasha nehurefu; mutsendo hauna hudzamu.

Nharaunda (Area) - izwi rinoreva kukura kwakaita nzvimbo kana hwasha huchitsinhaniswa nehurefu hwenzvimbo iyoyo.

Chiso(surface)- iyi inzvimbo ine miganhu unotarwa nehwasha uye hurefu asi pasina hudzamu. Muenzaniso ungapiwa ndeuyo watinoouna takatarisa pamusoro petafura.

Mumhu (Volume) - iri izwi rapiwa kuti rireve kukura kwakaita nzvimbo kana hwasha, hurefu, nehudzamu zvatsinhaniswa. Shoko iri rinoreva kukura kwakaita munhu, mhuka kana chinhu mukutaura kwemazuva ose. Ndiro shoko randaona riri pedyo kutsanangudza volume.

Poyindi (point) - iri rinotsangura kanzvimbo katokotoko, katopoka, kasina hwasha, hurefu, kana hudzamu. Takatsimbidzira penzura papepa tingaedzesera kucherechedza poyindi; asi kana nepo dowo rinoitwa nemurumo wepenzura rine nhambwe - poyindi hachina nhambwe.

Nzenda (dimensions) rinoreva nhamba shomane (minimum) yezviringani inokwana kudoma pane poyindi munzvimbo iri kutaurwa nezvayo. Iri shoko rinotsanangudza inonzi dimensions kuEnglish. Shoko iri rinotoredzera pane rokuti kuenda; saka 3-dimensiional shape unokwanisa kuenda uchitevedza mupimo wehwasha, hurefu, nehudzamu - nzenda nhatu.

  • Mutsetse une nzenda imwe (1), hurefu chete.
  • Chiumbwa chiri pauso hwakati sandarara (plane) chine nzenda mbiri (2), hwasha nehurefu. Somuenzaniso zviumbwa zvinoterevra zvine 2-nzenda: tsazano; gonyonhatu; kayiti zvichingodaro.
  • Chiumbwa chine mumhu chinonzi chine nzenda nhatu (3); hwasha, hurefu, nehudzamu. Somuenzaniso zviumbwa zvinoterevra zvine 3-nzenda: dumba; charaka; zhumwi; chiwarikwa kana kuti chiware.


Zviringani (Coordinates KuChirungu) - zviringani zvinoringanisa (align) nhambwe dzinoverengwa dzichitevedza maakiso anotarwa akarurama kuti tigone kudoma pane poyindi chiri kutsvakwa. Izvi zvinoreva kuti nhambwe mbiri idzi, dzinokwanisa kunongedza poyindi chimwechete, chiricho choga - ipapo toti zvaringana nokuti hapana kurasika. Tichinge tatara maakiso ane zviringani nenzira iyi tinenge tave neGumbapamwe reZviringani (Coordinates System). Ruzivo urwu rwakaunganidzwa naRené Descartes paakanyora Gumbapamwe reZviringani raDescartes (Cartesian Coordinates System).

Tsazaniso (Equation) - iri izwi rinoreva chinyorwa chinotaridza kuti mativi maviri ezvakanyorwa akaenzana kana kuti anotaura zvakaenzana. Pakati pemativi maviri panonyorwa vara rinoti (=) rinotiudza kuti mativi maviri akaenzana pane zvose. Shoko iri rinotodza kubva pashoko reChiManyika rinoti kutsazana rinoreva kuenzana. Nokuda kwekuti mamwe mashoko haasiri anoshandiswa mazuvaose ndiri kukwereta mashoko iwayo ndichiita kuti ashande muchidzidzo chepimanyika.

Tsaza- (Equi-) - ichi chivakamberi chichange chiri kushandiswa kuratidza kuti zvakadomwa kumashure kwaicho chivakamberi ichi zvakaenzana uye zvakafanana. Tsaza- achange achishandiswa nenzira imwe inoshandiswa prefix equi- inoshandiswa kuEnglish pamwazwi akaita sa: equidistant; equilateral; equiangular. Sarudzo iyi yaitwa pachicherechedzwa kuti kufanana hazvirevi kuenzana; sokuti baba nemwana wavo nyangwe vakafanana, havana kuenzana.

Mutsazanisi (equator) - iri zita rapiwa kutsanangura mutsetse unopangidza panosangana uso hweurungano nemutsendo une goko rehuremu uye wakarurama neakiso yeurungano yacho. Kureva kuti mutsendo uyu wakaita mutwi neaksio uye kuti wakatakuraGoko rehuremu (centre of mass) yeurungano yacho. Iri zita rinoshandiswazve pakutsangudza kuumbwa kweRinopasi, (Earth).

Chidzudzani (Congruency) zvinoreva kuti zvivakwa zviviri zvine chiumbwa (shape) chakafanana uye hukuru (size) hwakaenzana. Izvi zvoreva kuti chiumbwa chokutanga chinokwanisa kushandurwa mamiriro kusvikira chati gedye-gedye kupindirana nechiumbwa chepiri; zvimwechitezvo tichitanga kushanda nechiumbwa chepiri.

Kupimirana (Symmetry)- iri izwi rinotaura kuti chiumbwa chine zvikamu zvakafanana pazvinhu zvose: kukura kwakaita magonyo, uwandu hwemativi, nhambwe dziri pamativi, uye kuringana kwakaita mativi nemagonyo. Zvikamu izvi zvinofananidzwa maringe neAkiso dzichatsanangurwa mberi. Shoko rokuti kupimirana rinobva pakuti chikamu chimwe nechimwe chinoita kunge chidhindo chechimwe - takapima chikamu chokutanga zvakafanana nokunge tapima chikamu chepiri. Kumipirana kunotsangudza zvizere chinyorwa chine zita irori.


Mashoko Anomirira Zviumbwa[chinja | edit source]

Pachikamu chiri pamusoro pataurwa mazita anosanganisira gonyo (angle) nemukwava (intersection of lines and surfaces). Tichasimuka apa tichipa mazita tichiumba kubva pamashoko maviri aya.

Gonyozhinji (Polygon): KuChirungu izwi rokuti "polygon" rinoreva chiumbwa chine mativi mazhinji uye gonyo zhinji. Mitsetse inobatana pamukwava inenge iri yakati twasa. Shoko rinoti "poly" rinoreva "many" - kuwanda. Shoko rinoti "gon" rinobva pashoko rekuti "gonia" (Latin) rinoreva "bent" kana kuti "ankle". Isu kuChiShona tichapa zita rokuti gonyozhinji kududzira shoko rokuti "polygon". Zvichinge zvamira nenzira iyoyi hazvichanetsi kupa mazita eShona kuzviumbwa; tinenge toverenga kuti chiumbwa chine gonyo (mikwava) ngani kana kuti mativi mangani.

  • Triangle ine mativi matatu inenge yonzi gonyonhatu.
  • Quadrilateral ine mativi mana inenge yonzi gonyoina.
  • Pentagon ine mativi mashanu inenge yonzi gonyoshanu.

Tinoramba tichienda kusvika decagon ine mativi gumi ichinzi gonyogumi zvichingodaro.

Tichiri ipapo zvakafanira kuti tionesane kuti gonyozhinji rega-rega rakaumbwa riine mativi anoverengwa kuenzana nemikwava (gonyo) iri mukati mechiumbwa ichocho.

Gonyonhatu: Tichataura pamusoro pemarudzi egonyonhatu; aya anotumidzwa mazita zvichienderana nekupimwa kwemativi uye gonyo dziri paari. Kune gonyonhatu tsazakose (equilateral triangle) - iri rine mativi ose akaenza uye gonyo nhatu dzose dzakaenzana. Kune gonyonhatu mutseyekwa (scalene triangle) - iri rine mativi ose ane nhambwe dzakasiyana uye gonyo nhatu dzose dzakasiyana. Hazvinei gonyonhatu mutseyekwa agara nedivi ripi anotaridzika seanorerekera (kana kuwandira) kune rimwe divi nguva dzose. Kune gonyonhatu tsazamaviri (isosceles triangle) - iri rine mativi maviri akaenzana, negonyo mbiri dzakaenzana. Kunoitawo gonyonhatu yemutwi (right-angled triangle) - iyi ine mativi maviri anosvika pamukwava une gonyo re 90o.

Gonyonhatu yemutwi: Mativi matatu egonyonhatu iri anopiwa mazita akasiyana zvichibva pamamiriro akaita gonyonhatu. Kune mativi maviri anosvika pamukwava une gonyo ye 90o; pamativi aya rokutanga rikanzi hwaro(adjacent), repiri richabva ranzi darisanwa (opposite side). Divi guru rine nhambwe yakareba kupfura mamwe rinonzi muzendami (hypotenuse) nokuti rinoita sokunge rakazendamiswa rakatsigirwa kuhwaro nemutwi.

Sarudzo yokuti darisanwa idivi ripi uye hwaro divi ripi inodudzirwa nokuti timire mugonyo ripi. Muzendami ndiye murefu anoramba aine zita rimwechete - uyu haachinje. Divi rakabatana negonyo ratiri kushanda naro ndiro rinova hwaro, repiri rakaita mutwi nehwaro ndiro rinova darisanwa. Zvizhinji zvichatsanangurwa muchikamu chePimagonyonhatu, (trigonometry) chichatevera mberi.

Tsananguro: Iro shoko reChirungu rinoti hypotenuse rinomborevei? Shoko rokuti hypo rinobva pashoko reLatin rinoreva kuti under. Shoko rokuti tenuse rinobva zvakare kuLatin richireva kuti stretched. Vakare vakatanga chidzidzo Kupimanyika vakacherechedza vakaona divi refu regonyonhatu richitaridzika seratatamurwa kana kuti paChirungu riri under tension or stretched. Vakare ava vakaenda mberi kwedu vaipawo mazita maererano nemaonero avaiita panguva yavo - ini ndinoonawo zvakafanira kuti kuChiShona tipe mazita maererano nemaonero edu sekuitawo kwakaita vakare vakaumba chidzidzo ichi kuChirungu. Nekukurawo kweruzivo tinoramba tichivandudza chidzidzo ichi kuti chitsangure zvine hudzamu hunokurawo.

Denderedzwa (circle kuEnglish)

Nhara (Radius)- iri izita remutsetse unobatanidza goko redenderedzwa nemuganhu wedenderedzwa; nhara ndiyo inotara panogumira denderedzwa. Izwi iri rinoshaniswazve kutsanangudza mutsetse unobatanidza goko reurungano, neuso hweurungano - uso hweurungano hune nhambwe dzakaenzana panzvimbo dzose kubva pagoko.

Gurapakati (Diameter) - uyu mutsetse unopfuura nepakati (centre) redenderedzwa uchinobata muganhu panzvimbo mbiri. Mutsetse uyu unotema denderedzwa kuita zvikamu zviviri zvakaenzana.

Guramakonyo (Diagonal muChiRungu) - iri izwi rinoreva mutsetse wakati twasa unobva pagonyo uchidanha nemukati megonyozhinji kuenda pane rimwe gonyo. Guramakonyo rinobatanidza makonyo asina kutevedzana chete. Kana chiumbwa chiri skweya, guramakonyo rinobatanidza goko (centre) negonyo mbiri dzakatarisana. Zviumbwa zvine mativi anodarika mana zvinoita zviguramakonyo zvinodarika maviri.

Pimamuganhu (Perimeter) - iri izita rinopiwa nhambwe yemitsetse inovaka chiumbwa chine nzenda mbiri. KuChiShona tichashandisa zita rimwechete kududza pimamuganhu yezviumbwa zvose kusanganisira denderedzwa.


Zhumwi (Prism) - chiumbwa chine nzenda nhatu (3-dimensional) chinotaridzika kunge chiumbwa chine nzenda mbiri chakatatamurwa zvichitevedza kunoenda mutwi unobva pahwaro. (Appears like a 2-dimensional shape that has been translated along a line perpendicular to the base, so that all parallel cross-sections have the same shape) Somuenzaniso, zhumwi regonyonhatu (triangular prism) rine uso huviri hwakati sambamba; mucheko yose yakati sambamba nemiviri yarehwa pamusoro inenge ine chiumbwa chegonyonhatu zvakare.

Chikunguru (cylinder kuEnglish) zvinoreva chiumbwa chine uso hutatu; huviri hwakati sambamba, hwechitatu hune mucheko wedenderedzwa. Huso hwechitatu hunobatanidza huviri hwakati sambamba. Chikunguru ndiwo muenzaniso wezhumwi redenderedzwa.

Mucheko (Cross-section) - iri shoko rinoreva uso hunoonekwa kana chiumbwa chine mumhu chachekwa. Chiumbwa chinogona chiri kuchekwa zvichitevedza: mutsetse wakati sambamba nehwaro hwachakagara nacho, mutsetse wakarurama pahwaro, kana mutsetse unoita gonyo ripi zvaro pahwaro.

Nharaunda yeMucheko (Cross-sectional area) - izwi iri rinotaura kukura kweuso hunoonekwa kana zhumwi yachekwa. Muzvinyorwa zviri kutevera tichange tichidzidza pamusoro petsazaniso dzekutsvaka kukura kwakaita nharaunda yeMucheko

Gonyoina sambamba (Parallelogram) - ichi chiumbwa chine mativi mana - mativi maviri akati sambamba anenge akaenzana - uye gonyo mbiri dzinobatanidzwa nedanhamakonyo dzinenge dzakaenzana.

Skweya (Square) iri shoko rinoreva chiumbwa chine mativi mana ose akaenzana negonyo ina dzose dzakaenzana. Skweya iri mubandiko wegonyoina.

Gonyoina tsazamativi (Rhombus) - iri izwi rinoreva gonyoina rine mativi akaenzana nhambwe. gonyo dzemukati dzakatarisana dzinenge dzakaenzana zvakare. Chiumbwa ichi chine madanhamakonyo maviri anochekana negonyo re 90o. Skweya iri pamupanda wegonyoina tsazamativi zvakare.

Gonyoina tsazamakonyo (Rectangle) - iri izwi rapiwa kureva chiumbwa chine makonyo mana ose akaenzana; gonyo rimwe nerimwe riine 90o. Mativi maviri akatarisana anenge akaenzana uye akati sambamba. Skweya rinogona kupinda pamupanda wechiumbwa ichi asi kazhinji tinosarudza kuti skweya rimire roga.


Gonyoina sambambiri (Trapezium, trapezoid) - sokutaura kwezita racho, chiumbwa ichi chine mativi mana; zvakare chine mativi maviri akati sambamba.

Urungano (Sphere) - izwi iri rinoreva chiumbwa chakaurungana kuita bhora. Nokumwe kutaura tinogona kupa zita rokuti chimburungwa.

Charaka (Cone) - iri izwi rinoreva chiumbwa chine uso huviri, humwe huri hwaro hwedenderedzwa hwakati sandarara hwepiri huri uso hunopfirira hwaro kusvika pachisuvi (apex). Nguva zhinji chisuvi chinenge chakaita kururama nepakati pedenderedzwa riri pauso hunova hwaro. Shoko reShona iri rinotodzana necharaka chinowanikwa paduwo rinoteyeswa hove rine kuumbwa kwe cone - hove inopinda nekwakapamhama, yave mukati charaka chakamanika zvokuti hove itadze kubuda.

Denderende (Ellipse) - iri zita rinoreva munyonga uri pamutsendo, unoonekwa panochekwa charaka zvichitevedza mutsendo nenzira inopa munyonga wakavharwa kwese (closed curve). Izvi zvinoreva kuti mutsendo wacho unocheka nenzira yokuti chiumbwa chinosara pachekwa chine munyonga chete pasina mutsetse wakati twasa; mutsendo haucheke hwaro kana chisuvi chiri pacharaka. Muenzaniso wedenderende ndiro boterekwa rinowanikwa Earth iri kupotereta zuva, kamwe pagore.

Dumba (Pyramid)- iri shoko rinotoredzera kubva pachiumbwa chinoonekwa kana tichitema mashanga echigabe nokuamisa kuita matumba. Tiri muchidzidzo Pimanyika kune marudzi ematumba anodanwa zvakasiyana zvichienderana nechiumbwa chiri pahwaro hwedumba racho. Sokuti kune: dumba regonyonhanhatu (hexagonal pyramid); kwoita dumba reSkweya (square based pyramid); dumba regonyonhatu (triangular pyramid); dumba regonyoina tsazamakonyo (rectangular pyramid), zvichingodaro.

Akiso (Axis)- uyu mutsetse uri pakati pechiumbwa kana zviumbwa unoshandiswa kufananidza kupimirana kwechiumbwa. Kana chiumbwa chine kupimirana, zvinoreva kuti zviri kumativi maviri emutsetse iwoyu zvinenge zvakaenzanza huremu nekuumbwa.


Masvomhu T
Pimanzvimbo Chiyero chekupimisa | Mutsetse | Chiumbwa | Hurefu | Hwasha | Hudzamu | Hukwidza | Gonya | Sambamba | Twasuka | Munyonga | Hubumbe | Hufombwe | Mutwi | rurama | Sandarara | Mutsendo | Nharaunda | Uso | Mumhu | Chimiso | Nzenda | Zviringani | Tsazaniso | Mutsazanisi | Chidzudzani | Kupimirana | Gonyazhinji: Gonyanhatu (Gonyanhatu tsazakose | Gonyanhatu tsazakose | Gonyanhatu yemutwi) | Gonyaina (Gonyaina tsazamativi | Gonyaina sambamba | Gonyaina tsazamakonya | Gonyaina sambambiri | Skweya) | Denderedzwa (Nhara | Pimadanho | Danhamakonya | Pimamuganhu) | Zhumwi (Chikunguru | Urungano | Charaka | Dumba | Akiso)
Huwandu Kubwerengedza/kuwedzera | Kubvisa | Kutsinhanisa | Kukamura kana kuti kugovanisa
Zviperengo zvehuwandu chipasina | motsi | piri | tatu | china | shanu | tanhatu | nomwe | sere | pfumbamwe | gumi | zana | chiuru