Kimiyyar Sararin Samaniya a Sawwake (7)

BABI NA UKU

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Muhimmancin Ilmin Lissafi Ga Ilmin Sararin Samaniya

Na shiga makarantar sharar fagen shiga Jami’a (School of Preliminary Studies) da ke Jami’ar Bayero a Kano, da niyyar karanta fannin Ilmin Sararin Samaniya (Astronomy) ne. Lokacin da na hadu da jami’in da ke baiwa dalibai shawara kan fannin da suke son karantawa (Carrier Guidance Counsel), sai ya tambaye ni, “Wani fannin ilmi kake son karantawa?” Sai na amsa, “Fannin Ilmin Sararin Samaniya.”  Sai ya jujjuya takardun shedan karatu na, don ya tabbatar ko akwai wata shedar karatun a baya a jone, da ya ga babu sai yace, “Amma ga dukkan alamu kai malamin makaranta ne,” sai nan take na amsa masa cewa, “Ina kuma so ne in karantar da fannin.”  Daga nan sai ya miko mini takardun shedan gama karatu na, ya ce, “Ba mu karantar da wannan fannin ilmi a nan. Ka je ka karanta fannin Ilmin Kasa (Geography), da Fannin Lissafi (Mathematics), da fannin Malanta (Education) a hade.”  Wannan al’amari ya faru ne cikin shekarar 1984.

Duk da haka, burina na ganin na karanci fannin Sararin Samaniya bai yi tasgaro ba, domin Allah ya hada ni da Malam Suleiman Khan, wanda yake daukarmu darasin fannin Lissafi a halin karatuna, kuma shi ne ya yi ta karfafa ni ta hanyar shawarwarinsa.  Watarana yace mini, “Kada ka damu, ai dukkanmu (makaranta fannin lissafi) masana fannin Ilmin Sararin Samaniya ne. Domin fannin Kimiyyar Lissafi asalinsa ya kunshi fannin Sararin Samaniya ne.”  Wannan ke nuna cewa shi kanshi Fannin Lissafi, da fannin da a yanzu ake kira Fiziya (Physics), su ne kashin bayan fannin Ilmin Sararin Samaniya.  Sai ya ci gaba da cewa, “Kai, ba ma fannin Ilmin Sararin Samaniya kadai ba, fannin Lissafi uwa ce ga dukkan fannonin Ilmin Kimiyya baki dayansu.” Nan take na ji gamsuwa a tare da ni cewa, muddin na karanci fannin Lissafi (Mathematics) da Ilmin Kasa (Geography), to, hakika zan zama kwararre kan fannin Ilmin Sararin Samaniya. Wasu lokuta kuma sai in rika tambayar kaina, “To shi Fannin Fiziya kuma fa?”  Sai kawai in yi biris da shi, domin na san ina da sanayyar matakin farko iya gwargwado a fannin.

Ta hanyar darussan Malam Khan ne na fahimci cewa, fannin Lissafi na kunshe ne da ressa guda uku muhimmai: reshen Ma’aunin alwatika (Trigonometry), da reshen Aljabra (Algebra), da kuma reshen Ma’aunin kusurwowi da layuka – wato Jometary (Geometry). Malam Suleiman Khan, wanda shi ma dan kasar Pakistan ne, ya kara tuna mini da babban malami na da na baro a kwaleji, wato Malam Ali.  Mutum ne mai saukin kai shi ma, ya san fannin lissafi sosai, kuma cikin nishadi da kwarewa yake karantar da dalibansa.  Da zarar ya fara magana, bai da bambanci da Malam Ali.  Yana da natsuwa, da kankan da kai, da kuma kwazo tukuru. Yana fara darussansa ne mataki-mataki; inda ya fara mana da reshen Ma’aunin alwatika (Trigonometry).  Idan yana darasi, yakan zagaya cikin dalibai, yana lura da su, da kuma tabbatar da cewa kowane dalibi ya mallaki dukkan littattafan da aka bukaci ya mallaka don darasi. Wato littattafan da Blair, da Thomas Finney, da kuma Backhouse suka wallafa.

A darasinsa na farko, nan take ya sanar da mu abin da Ma’aunin alwatika yake nufi, inda yace, shi ne reshen fannin lissafi mai lura da yadda ake awon nisa a tsakanin kusurwowin alwatika.  Ya ce, da ilmin ma’aunin alwatika ne ake auna nisan da ke tsakanin abubuwa.  Ina jin ya ambaci kalmar “Nisa”, sai na yi farat na tambaya, “Shin, Malam kana nufin nisa a sararin duniya ko a sararin iskar samaniya?” Sai yace, “A duka muhallin biyu,” daga nan ya ci gaba da darasinsa.  Ta hanyar karantarwar Malam Khan ne na san cewa, fannin Ilmin Sararin Samaniya na dogaro ne kacokam kan sananniyar ka’aidar lissafin nan mai suna Pythagorean Theorem, wacce Pythogoras, wani masanin fannin lissafi da ya rayu tsakanin shekarun 582 – 507 BC, ya assasa ta.  Ina jin wannan suna, sai na ce duk yadda aka yi shi ma dan kasan Girka ne.

Malam ya ce, abin da ka’idar ke cewa shi ne, “Adadin kusurwowin alwatika mai lungu mikakke (right angle triangle), daidai yake da adadin nisan kusurwowin da ke lungu mai nisa (hypotenuse), idan aka hada da adadin nisan kusurwan da ke lungu makusanci (adjacent).”  Ko kuma a harshen turancin Ilmin Lissafi: “The sum of the squares of the sides of a right angle triangle is equal to the square of the hypotenuse plus the square of the adjacent.” Sai da ya tabbata kowannenmu ya haddace wannan ka’ida a kwakwalwarsa.  Nan take kuma ya zana mana misalin da ke nuna wannan ma’ana da ka’idar ke tabbatarwa (a² + b² = c²).

Haka kuma, Malam Khan ya karantar da mu yadda ake samo adadin nisan da ke tsakanin dukkan kusurwowin da ke jikin kowane da’ira da ya fara daga dama zuwa hagu (anticlockwise circle), ta amfani da ka’idojin lissafin kusurwa masu suna Sine, da Cosine, da kuma Tangent.  Cikin sauki ya kwatanta mana yadda ake wannan aiki, kamar yadda yake cikin littafin Backhouse, wanda a lokacin kowane dalibin kwaleji ya sani.  Sai dai kuma, abin da zan iya tunawa kadai daga cikin wancan darasi, su ne ka’idojin da ke cewa Sineᶿ = b/c (adadin kusurwan akasi a raba da adadin kusurwa mai nisa), da Cosᶿ = a/c (adadin kusurwa na kusa a raba da adadin kusurwa mai nisa), sai kuma tanᶿ = b/a (adadin kusurwan akasi a raba da adadin kusurwa na kusa).  Nakan kuma tuna wadannan ka’idoji ba tare da wani dogon lissafi ba.  Har wa yau kuma, an karantar da mu yadda ake lissafin bambancin adadin nisa da ke tsakanin dukkan kusurwowin da’ira, ta amfani da ka’idojin Cotangent, da Secant, da Cosecant, da Versine, da kuma Coversine.