UPythagoras neTheorem yakhe [KULULA]
Umbono kaPythagoras kungenye yemibono ewusizo kakhulu. I-base kwizibalo, i-geometry, i-trigonometry, i-algebra futhi isetshenziswa kakhulu empilweni yansuku zonke efana nokwakhiwa, ukuzulazula, ukuma kwendawo, phakathi kwabanye.
Umbono kaPythagoras ikuvumela ukuthi uthole ubude bezinhlangothi zonxantathu ofanele, futhi yize onxantathu abaningi bengalungile, bonke bangahlukaniswa babe onxantathu ababili abangakwesokudla, lapho i-Pythagorean Theorem ingasetshenziswa khona.
Imiqondo eyisisekelo "Ukuqonda umbono kaPythagoras"
Unxantathu:
Isibalo seJiyomethri, endizeni, sakhiwe izinhlangothi ezintathu ezihlangana kuma-vertices. Ama-verices abhalwa ngofeleba nohlangothi olubhekene no-vertex ngohlamvu olufanayo. Bona umfanekiso 1. Konxantathu:
- Isamba sezinhlangothi zayo ezimbili sikhulu kunezinye izinhlangothi.
- Isamba sama-engeli kanxantathu silinganisa u-180º.
Ukwahlukaniswa konxantathu
Ngokuya ngobude bezinhlangothi, unxantathu angalingana uma unezinhlangothi ezintathu ezilinganayo, i-isosceles uma inezinhlangothi ezimbili ezilinganayo, noma i-scalene uma engekho ezinhlangothini zayo ezilinganayo. Bheka umfanekiso 2.
I-engeli engakwesokudla ilinganisa ama-90 °. Uma i-engeli ingaphansi kuka-90 ° ibizwa nge- “acute angle”. Uma i-engela ingaphezu kuka-90 ° ibizwa ngokuthi “i-engeuse yokufiphala”. Ngokwama-engeli, onxantathu bahlukaniswa baba:
- Ama-engeli acute: uma benama-engeli abukhali ama-3.
- Onxande: uma bane-engeli elungile kanti amanye ama-engeli amabili abukhali.
- Ama-Obtusangles: uma bane-engeli yokuqunjelwa kanti enye i-acute. Bheka umfanekiso 3.
Unxantathu ongakwesokudla:
Unxantathu ongakwesokudla munye one-engeli elungile (90 °). Ezinhlangothini ezintathu zonxantathu ongakwesokudla, ende kunazo zonke ibizwa nge- "hypotenuse", ezinye zibizwa ngokuthi "imilenze" [1]:
- I-Hypotenuse: uhlangothi olubheke engela elifanele kunxantathu ongakwesokudla. Uhlangothi olude lubizwa ngokuthi yi-hypotenuse ephambene ne-engeli engakwesokudla.
- Imilenze: kungenye yezinhlangothi ezimbili ezincane zonxantathu ongakwesokudla ezakha i-engeli elungile. Bheka umfanekiso 4.
Umbono kaPythagoras
Isitatimende sePythagorean Theorem:
Umbono kaPythagoras ithi, kukanxantathu ofanele, isikwele se-hypotenuse silingana nesamba sezikwele zemilenze emibili. [amabili]. Bheka umfanekiso 2.
Umbono kaPythagoras Kungashiwo futhi ngale ndlela elandelayo: Isikwele esakhiwe phezu kwe-hypotenuse kanxantathu ongakwesokudla sinendawo efanayo nenani lezindawo zezikwele ezakhiwe emilenzeni. Bheka umfanekiso 6.
Nge Umbono kaPythagoras Unganquma ubude bezinhlangothi zombili zonxantathu ongakwesokudla. Ku-figure 7 amafomula wokuthola i-hypotenuse noma eminye yemilenze yonxantathu.
Ukusetshenziswa kwethiyori kaPythagora
Ukwakha:
Umbono kaPythagoras Kuyasiza ekwakhiweni nasekwakhiweni kwezitebhisi, izitebhisi, izakhiwo ezi-diagonal, phakathi kwabanye, isibonelo, ukubala ubude bophahla oluthambile. Umdwebo 8 ukhombisa ukuthi ekwakhiweni kwamakholomu wokwakha, kusetshenziswa izintambo nezintambo okumele zihambisane nePythagorean Theorem.
Isimo sendawo:
Ebuningini bendawo, indawo noma ukukhululeka kwendawo kuboniswa imidwebo endizeni. Isibonelo, ungabala ithambeka lendawo usebenzisa induku yokulinganisa yobude obaziwayo nesibonakude. I-engeli engakwesokudla yakhiwa phakathi komugqa wokubona kwesibonakude nenduku, kuthi lapho ukwaziwa ukuphakama kwenduku, kusetshenziswe umbono kaPythagoras ukucacisa ithambeka lendawo. Bheka umfanekiso 8.
Unxantathu:
Kuyindlela esetshenziselwa ukucacisa indawo yento, amaphuzu amabili wenkomba aziwayo. Unxantathu usetshenziswa ekulandeleni umakhalekhukhwini, ezinhlelweni zokuzulazula, ekutholeni umkhumbi osemkhathini, phakathi kwabanye. Bheka umfanekiso 9.
Wayengubani uPythagoras?
UPythagoras wazalelwa eGrisi Ngo-570 BC, washona ngo-490 BC Wayengusosayensi wezibalo. Ifilosofi yakhe yayiwukuthi inombolo ngayinye yayinencazelo yaphezulu, futhi ukuhlanganiswa kwezinombolo kuveza ezinye izincazelo. Yize engazange ashicilele noma yikuphi ukubhala empilweni yakhe yonke, uyaziwa ngokwethula i-theorem enegama lakhe, ewusizo ekutadisheni onxantathu. Ubhekwa njengesazi sokuqala sezibalo esimsulwa, owathuthukisa izifundo zezibalo kuJiyomethri nakwisayensi yezinkanyezi. [amabili]. Bheka umfanekiso 2.
Ukuzivocavoca
Ukuze usebenzise i-Pythagorean Theorem, into yokuqala okufanele uyenze ukukhomba ukuthi kwakhiwa kuphi unxantathu ofanele, yikuphi kwamacala yi-hypotenuse nemilenze.
Ukuzivocavoca umzimba 1. Thola inani le-hypotenuse kanxantathu ongakwesokudla kulo mfanekiso
Isixazululo:
Umdwebo we-12 ukhombisa ukubalwa kwe-hypotenuse kanxantathu.
Ukuzivocavoca umzimba 2. Kudingeka isigxobo sosekelwa ngezintambo ezintathu, njengoba kukhonjisiwe kumfanekiso 13. Mangaki amamitha wekhebula okufanele athengwe?
Isixazululo
Uma ikhebula lithathwa njenge-hypotenuse kanxantathu ongakwesokudla owakhiwe phakathi kwekhebuli, isigxobo nomhlabathi, ubude benye yezintambo bunqunywa kusetshenziswa umbono kaPythagorean. Njengoba kunezintambo ezintathu, ubude obutholakele buphindaphindwa ngo-3 ukuthola ingqikithi yobude obudingekayo. Bheka umfanekiso 14.
Ukuzivocavoca umzimba 3. Ukuhambisa amanye amabhokisi, usuka esitezi sesibili uye esitezi esiphansi, ufuna ukuthenga ibhande lokuhambisa elithambekele njengaleli eliboniswe kumfanekiso we-15.
Isixazululo:
Uma kubhekwa ibhande lokuhambisa njenge-hypotenuse kanxantathu ongakwesokudla owakhiwe phakathi kwebhande, umhlabathi nodonga, kuMfanekiso 16 ubude bebhande elihambayo liyabalwa.
Ukuzivocavoca umzimba 4. Umbazi wakha ifenisha lapho kufanele izincwadi ziye khona, nethelevishini engu-26 ”. Kufanele ngabe ukwahlukana kube kubanzi futhi kuphakame kangakanani lapho i-TV izohamba khona? Bheka umfanekiso 17.
Isixazululo:
Isilinganiso esisetshenziswe kumadivayisi we-elekthronikhi anjengezingcingo, amathebulethi, amathelevishini, phakathi kokunye, ku-diagonal yesikrini. Ku-TV engu-26 ”, idiagonal yesikrini ingama-66,04 cm. Uma kubhekwa unxantathu ongakwesokudla owakhiwe ngokulingana kwesikrini, nezinhlangothi zethelevishini, umbono kaPythagoras ungasetshenziswa ukuthola ububanzi bethelevishini. Bheka umfanekiso 18.
Iziphetho ku-Theorem kaPythagoras
Umbono kaPythagoras ikuvumela ukuthi uthole ubude bezinhlangothi zonxantathu ongakwesokudla, futhi noma yimuphi omunye unxantathu, ngoba la angahlukaniswa abe onxantathu abalungile.
Umbono kaPythagoras kukhombisa ukuthi isikwele se-hypotenuse sikanxantathu ongakwesokudla silingana nesamba sesikwele semilenze, sisebenziseka kakhulu esifundweni se-geometry, i-trigonometry, kanye ne-mathematics jikelele, kusetshenziswa kakhulu ekwakhiweni, ekuzulazuleni, ezokuma komhlaba, phakathi ezinye izinhlelo zokusebenza eziningi.
Sikumema ukuba ubone le ndatshana Imithetho kaNewton "kulula ukuyiqonda"
