Izilinganiso ze-Trigonometric kumaPiramidi: Ukubuyekezwa Kwezibalo Zasendulo kanye Nezakhiwo
Amaphiramidi aseGibhithe, ikakhulukazi iPhiramidi Elikhulu laseGiza, sekuyisikhathi eside ewuphawu lobuchule bokwakha bomuntu kanye nemfihlakalo engakaxazululwa. Lezi zakhiwo azigcini nje ngokuhlaba umxhwele ngobukhulu bazo nangokunemba kwazo, kodwa futhi zinikeza ulwazi oluningi lwezibalo, ikakhulukazi ekusetshenzisweni kwe-trigonometry. Lesi sihloko sihlola indlela amasu nemibono ye-trigonometric asetshenziswa ngayo ekwakhiweni kwamaphiramidi aseGibhithe nokuthi kungani izilinganiso ze-trigonometric zibalulekile ekuqondeni lobu buchwepheshe bezakhiwo basendulo.
1. Umlando Omfushane Wemibhoshongo YaseGibhithe
Amaphiramidi aseGibhithe ayizakhiwo ezinkulu ezakhiwe njengamathuna oFaro nezindlovukazi enkolelweni yasendulo yaseGibhithe yokuphila ngemva kokufa. Iphiramidi endala kunazo zonke eyaziwayo yiPhiramidi laseDjoser eSaqqara, eyakhiwa ngesikhathi soBukhosi Besithathu ngu-Imhotep, umakhi wezakhiwo odumile kakhulu emlandweni waseGibhithe lasendulo. Isiqongo sokwakhiwa kwamaphiramidi senzeka ngesikhathi soBukhosi Besine, ngePhiramidi Elikhulu laseGiza, elakhelwe uFaro Khufu cishe ngo-2580–2560 BC.
2. I-Trigonometry: Imiqondo Eyisisekelo kanye Nezicelo
I-Trigonometry iyigatsha lezibalo elifunda ubudlelwano phakathi kwama-engeli nobude obuseceleni konxantathu. Imiqondo eyisisekelo ye-trigonometry ihilela imisebenzi ye-sine (sin), i-cosine (cos), kanye ne-tangent (tan) yama-engeli kanxantathu. Le misebenzi emithathu ihlobene nobude bezinhlangothi zonxantathu ongakwesokudla futhi isiza ekubaleni ama-engeli nezinhlangothi ezingaziwa.
Emongweni wokwakhiwa kwephiramidi, i-trigonometry isetshenziselwa ukunquma imithambeka yezinhlangothi kanye nesihloko sephiramidi. Imiqondo emibili ebalulekile ye-trigonometric evame ukusetshenziswa “ukuthambekela,” okuvame ukulinganiswa ngamadigri noma ama-radiant, kanye “nokuthambeka,” okuhlobene nesilinganiso phakathi kohlangothi oluphambene nomlenze wonxantathu kumongo wokuthambeka kwephiramidi.
3. Ukusetshenziswa kwe-Trigonometry kuMklamo wePhiramidi
Uma sibuyela enkathini yangaphambi kokubala namakhompyutha, i-trigonometry yasendulo ingase ibonakale imangalisa. Kodwa-ke, abaklami bezakhiwo baseGibhithe lasendulo bafaka ngobuhlakani imiqondo eyisisekelo ye-trigonometric ekwakhiweni kwamaphiramidi, njengePhiramidi Elikhulu.
a. I-engela Yokuthambekela Kwephiramidi
I-Great Pyramid yaseGiza inomthambeka oqondile kakhulu ongaba ama-degree angu-51,5. Bakwenze kanjani lokhu? Ake sikuhlaziye sisebenzisa i-trigonometry. Uma sicabangela unxantathu ongakwesokudla owakhiwe yingxenye yesisekelo sephiramidi, ukuphakama kwephiramidi, kanye ne-hypotenuse kusukela esisekelweni kuya esiqongweni, singasebenzisa umsebenzi we-tangent.
I-tangent ye-angle of inclination (θ) yisilinganiso sokuphakama kwephiramidi (h) kuya kuhhafu yobude besisekelo sephiramidi (b/2).
Uma u-d ubude besisekelo sephiramidi, khona-ke:
i-tan(θ) = h / (d / 2)
Njengoba i-engeli yokuthambekela ibalwe njengama-degree angu-51,5, sithola:
ukunsundu (51.5°) ≈ 1.273
Lokhu kusho ukuthi isilinganiso sokuphakama kwephiramidi nengxenye yobude besisekelo sayo kumele sibe cishe ngu-1.273. Lokhu kusenza sikwazi ukulinganisa ukuphakama kwephiramidi uma ubude besisekelo sayo buyaziwa.
b. Ukusebenzisa i-Pythagorean Theorem
Ngale komsebenzi we-tangent, i-Pythagorean theorem nayo isetshenziswa ukuqinisekisa ukunemba kwezilinganiso ekwakhiweni kwephiramidi. Kunxantathu ongakwesokudla okukhulunywe ngaye ekuqaleni, singasebenzisa i-Pythagorean theorem:
a² + b² = c²
Lapho u-a ewukuphakama kwephiramidi, u-b uyingxenye yobude besisekelo, kanti u-c ungokuphakama okuthambekele kwephiramidi.
4. Ubufakazi Bokusetshenziswa Kwe-Trigonometry Ngabakhi Bezakhiwo Basendulo
Nakuba abaningi bephikisana ngokuthi abaseGibhithe lasendulo kungenzeka babengazi ngemiqondo ehlelekile ye-trigonometry, ngokuqinisekile babenolwazi olwanele lokusebenza ukuze basebenzise amasu afanayo. Ubufakazi bokunemba okuphezulu busikisela ukuthi babenezindlela eziyinkimbinkimbi zokulinganisa nokuhlela.
Abaklami bezakhiwo bangaleso sikhathi baziwa ukuthi babesebenzisa uhlelo 'olusekelwe' lokulinganisa ama-engeli besebenzisa izingalo neminwe. Kulesi simiso, 'ingalo' eyodwa yayilingana nobude obuthile, kanti 'umunwe' owodwa wawuyi-ordal encane kakhulu - efana kakhulu nomqondo wanamuhla we-trigonometry, ohlukanisa ama-engeli abe izingxenye.
5. Ukuqhathaniswa kwe-Trigonometric Phakathi kwamaPhiramidi
Ngaphandle kwePiramidi Enkulu, akuzona zonke izipiramidi zaseGibhithe ezilandela i-engeli efanayo yokuthambeka. Isibonelo:
– Iphiramidi Ebomvu eDahshur ine-engeli yokuthambekela eqondile engama-degrees angu-43, ngokungafani ne-engeli yokuthambekela yePhiramidi Enkulu yaseGiza.
– Iphiramidi Egobile, eyaziwa ngokushintsha kwayo i-angle yokuthambekela kusukela kuma-degree angu-54 kuya kuma-degree angu-43 phakathi nendawo.
Lokhu kuhlukahluka kubonisa ukuthi abaklami basendulo bazama nama-engeli namasu ahlukene, bakhiqiza amaphiramidi anezilinganiso ezihlukile kanye nokubonakala okuhlukile.
6. Isiphetho
Ngokuhlanganisa ulwazi lwemivubukulo kanye nezibalo, ukuhlaziywa kwe-trigonometric kwamaphiramidi kwembula ubuhlakani bamasu okwakha asendulo. Abazange nje babale ama-engeli kanye nezilinganiso ngobuhlakani obungase bubonakale buyinto yakudala kodwa futhi babusebenza kahle kakhulu. Ukusetshenziswa kwe-trigonometry kwenza kwaba nokwenzeka ukudalwa kwezakhiwo ezazingezona nje ezinkulu ngobukhulu kodwa futhi ezazihlala isikhathi eside ngokunemba nangokulingana.
Ngokuqonda ukusetshenziswa kwe-trigonometry kulezi zipiramidi, asigcini nje ngokwazisa ikhono lobunjiniyela laseGibhithe lasendulo kodwa futhi sifunda kabanzi ngomlando wentuthuko yezibalo ekwakhiweni kwezakhiwo zasendulo. Lezi zipiramidi ziwubufakazi obukhulu bokuhlanganiswa kobuciko nesayensi okwafinyelela ukuphakama okungavamile eminyakeni eyizinkulungwane ngaphambi kokuba ubuchwepheshe bethu besimanje bube khona.
