Pythagoras da Ka'idar sa [SAUKI]
Ka'idar Pythagorean yana daya daga cikin ka'idoji masu amfani. Tushe a cikin lissafi, lissafi, trigonometry, algebra kuma ana amfani dashi ko'ina cikin rayuwar yau da kullun kamar gini, kewayawa, yanayin kasa, da sauransu.
Ka'idar Pythagorean yana baka damar samun tsayin bangarorin triangle na dama, kuma kodayake alwatiran da yawa basu yi daidai ba, duk za'a iya raba su zuwa alwatika biyu dama, inda za'a iya amfani da ka'idar Pythagorean.
GASKIYAR GASKIYA "Don fahimtar ka'idar Pythagorean"
Alwatika:
Adadin lissafi, a cikin jirgin, wanda aka kafa ta bangarori uku da ke haduwa a tsaye. An rubuta wuraren yin baƙaƙen ne da manyan baƙaƙe da kuma gefen da ke gaban fatar tare da ƙaramin ƙaramin harafi. Duba hoto na 1. A cikin triangles:
- Jimlar bangarorinta biyu ya fi ɗayan girma.
- Adadin kusurwoyin alwati uku ya auna 180º.
Rarraba triangles
Dogaro da tsayin bangarorin, alwatika zai iya zama daidai idan yana da uku daidai, isosceles idan yana da gefe biyu daidai, ko kuma mizani idan babu ɗaya daga cikin bangarorin da suka yi daidai. Duba hoto na 2.
Kwancen dama shine wanda yakai 90 °. Idan kusurwar bata kai 90 ° ba ana kiranta "m angle". Idan kusurwar ta fi 90 ° to ana kiranta "obtuse angle". Dangane da kusurwoyin, an rarraba triangles zuwa:
- M kwana: idan suna da 3 m kwana.
- Rektangles: idan suna da kusurwar dama kuma sauran kusurwa biyu suna da hanzari.
- Kusassun kwana: idan suna da wani obtuse kwana da sauran m. Duba hoto na 3.
Dama alwatika:
Madaidaicin madaidaici yana ɗaya tare da kusurwar dama (90 °). Daga bangarori uku na alwatiran nan na dama, mafi tsayi ana kiransa "hypotenuse", sauran ana kiransu "kafafu" [1]:
- Tsarin jini: gefe daura da kusurwar dama a cikin triangle ɗin dama. Ana kiran gefe mai tsayi hypotenuse wanda yake gaban kusurwar dama.
- Kafafu: kowane ɗayan ƙananan gefuna ne na alwatiran triangle mai madaidaici wanda ya daidaita kusurwa ta dama. Duba hoto na 4.
Pythagoras ka'idar
Bayanin ka'idar Pythagorean:
Ka'idar Pythagorean ya faɗi cewa, don alwatiran dama, ma'aunin murabba'i ɗaya ya yi daidai da adadin murabba'in ƙafafu biyu. [biyu]. Duba hoto na 2.
Tsarin Pythagorean Hakanan za'a iya bayyana shi kamar haka: Filin da aka gina akan maƙasudin alwatika mai dama yana da yanki iri ɗaya da jimillar wuraren murabba'ai da aka gina akan ƙafafu. Duba hoto na 6.
Tare da Pythagoras ka'idar Kuna iya ƙayyade tsawon kowane ɓangaren triangle ɗin dama. A cikin adadi na 7 su ne dabarun gano mahimmancin tunani ko wasu ƙafafun triangle.
Amfani da ka'idar Pythagora
Gini:
Tsarin Pythagorean Yana da amfani a cikin ƙira da gina gangare, matakala, sifofi iri daban-daban, da sauransu, alal misali, don kirga tsawon rufin kwanciya. Hoto na 8 ya nuna cewa don ginin ginshiƙan ginin, ana amfani da igiya da igiyoyi waɗanda dole ne su bi ka'idar Pythagorean.
Yanayin ƙasa:
A cikin yanayin sararin samaniya, ana nuna yanayin farfaɗo ko sauƙin yanayin ƙasa a cikin jirgi. Misali, ana iya kirga karkatar filin ta amfani da sandar awo wanda sanannen tsayi ne da kuma hangen nesa. An kafa kusurwa ta dama tsakanin layin gani na telescope da sanda, kuma da zarar an san tsayin sanda, ana amfani da ka'idar Pythagorean don tantance gangaren filin. Duba hoto na 8.
Yanayi:
Hanya ce da ake amfani da ita don tantance wurin da abu yake, sanannun wuraren nuni biyu. Ana amfani da Triangulation a cikin bin wayar salula, a cikin tsarin kewayawa, a cikin gano jirgi a sararin samaniya, da sauransu. Duba hoto na 9.
Wanene Pythagoras?
An haifi Pythagoras a Girka 570 BC, ya mutu a 490 BC Ya kasance masanin falsafa da lissafi. Falsafar sa itace kowace lamba tana da ma'anar allahntaka, kuma hadewar lambobin ya bayyana wasu ma'anoni. Kodayake bai buga wani rubutu a tsawon rayuwarsa ba, amma sananne ne wajen gabatar da ka'idojin da ke dauke da sunansa, masu amfani ga nazarin bangarori uku. An dauke shi masanin lissafi na farko, wanda ya ci gaba ilimin lissafi a cikin ilimin lissafi da ilimin taurari. [biyu]. Duba hoto na 2.
Aiki
Don amfani da Ka'idar Pythagorean, abu na farko da za'a yi shine gano inda aka kafa alwatika mai kyau, wanne daga cikin ɓangarorin shine tunanin mutum da ƙafafu.
Darasi 1. Dayyade ƙimar abin da ake amfani da shi don alwatika mai kyau a cikin adadi
Magani:
Hoto na 12 yana nuna lissafin abubuwan almara na alwatiran.
Darasi 2. Ana buƙatar sanda don a goyan ta saitin igiyoyi guda uku, kamar yadda aka nuna a cikin hoto na 13. Mita nawa na kebul dole ne a saya?
Magani
Idan aka yi la'akari da kebul ɗin a matsayin tsinkayen alwatika mai dama wanda aka kafa tsakanin kebul, sandar da ƙasa, za a tsayar da tsawon ɗayan igiyoyin ta hanyar amfani da ka'idar Pythagorean. Tunda akwai igiyoyi uku, tsayin da aka samu ana ninka shi zuwa 3 don samun jimlar tsawon da ake buƙata. Duba hoto na 14.
Darasi 3. Don jigilar wasu akwatina, daga hawa na biyu zuwa bene, kuna so ku sayi bel mai ɗaukar hankali kamar wanda aka nuna a cikin hoto na 15. Yaya tsawon lokacin da mai ɗaukar motar zai yi?
Magani:
Idan aka yi la’akari da bel din mai daukar kaya kamar yadda ake nuna alwatiran nan na dama da aka kirkira tsakanin bel, kasa da bango, a cikin hoto na 16 an kirga tsawon bel din.
Darasi 4. Masassaƙi ya tsara zane ɗaya daga inda ya kamata littattafai su tafi, da talabijin 26 ”. Yaya fadi da girma ya kamata bangare ya kasance inda TV zata tafi? Duba hoto na 17.
Magani:
Mizanin da aka yi amfani da shi a cikin na'urorin lantarki irin su tarho, da alli, da talabijin, da sauransu, a cikin hoton allo. Don TV na 26 ”, allon fuska yana 66,04 cm. Idan aka yi la’akari da alwatiran da ya dace wanda aka zana shi ta fuskar allon, da kuma bangarorin talabijin, za a iya amfani da ka'idar Pythagorean don tantance faɗin talabijin. Duba hoto na 18.
ƘARUWA a kan Ka'idar Pythagorean
Ka'idar Pythagorean ba ka damar samun tsayin bangarorin triangle ɗin dama, har ma da kowane irin alwatilen, tunda ana iya raba waɗannan zuwa alwatiran dama.
Ka'idar Pythagorean yana nuna cewa muhallin maƙasudin alwatika mai daidai daidai yake da jimlar murabba'in ƙafafu, kasancewar yana da amfani ƙwarai a cikin nazarin ilimin lissafi, trigonometry, da lissafi gabaɗaya, tare da fa'idar amfani da gini, kewayawa, yanayin kasa, tsakanin wasu aikace-aikace da yawa.
Muna gayyatarku ku ga labarin Dokokin Newton suna da saukin fahimta
