Maqaal ku saabsan Isle'egta muraayadaha kala duwan (concave)
Kahor inta aan la soo saarin isla'egta muraayadda qaloocan, marka hore waxaan fahmay xeerarka calaamadaha muraayadda qaloocan.
Xeerarka calaamadee muraayadda qaloocan
Kuwa soo socda waa xeerarka calaamadaha ee muraayadda qaloocan.
– Masaafada shayga (samayn)
Haddii shaygu uu ku yaal dhinaca muraayadda oo la mid ah jihada iftiinka iftiinka, markaa masaafada shaygu waa togan tahay.
– Masaafada sawirka (di)
Haddii iftiin iftiin ah uu dhaafo sawirka, markaas masaafada sawirku waa togan tahay (sawir dhab ah). Haddii sawirku uusan dhex marin iftiinka, masaafada sawirku waa taban tahay (sawir dalwad ah).
– Dhererka diiradda (f)
Haddii barta diiradda ee muraayadda laga dhex mariyo iftiinka, dhererka diiradda ee muraayadda waa togan. Taas beddelkeeda, haddii barta diiradda ee muraayadda aan la marin iftiin, dhererka diiradda ee muraayadda waa taban. Barta diiradda ee muraayadda qaloocan iftiin ma dhaafo, sidaa darteed dhererka diiradda ee muraayadda qaloocan waa taban.
– Dhererka shayga (ho)
Haddii shaygu ka sarreeyo dhidibka ugu muhiimsan, dhererka shaygu wuxuu calaamad u yahay togan (shaygu waa toosan yahay). Taas beddelkeeda, haddii shaygu ka hooseeyo dhidibka ugu muhiimsan, dhererka shaygu waa taban (shaygu waa la rogay).
– Dhererka sawirka (hi)
Haddii sawirku ka sarreeyo dhidibka ugu weyn, dhererka sawirku waa togan yahay (sawirku waa toosan yahay). Haddii sawirku ka hooseeyo dhidibka ugu weyn, dhererka sawirku waa taban yahay (sawirku waa rogrogmay).
– Weyneynta sawirka (m)
Haddii weynaynta sawirka > 1, markaas cabbirka sawirku wuu ka weyn yahay cabbirka shayga. Haddii weynaynta sawirka = 1, markaa cabbirka sawirku wuxuu la mid yahay cabbirka shayga. Haddii weynaynta sawirka < 1, cabbirka sawirku wuu ka yar yahay cabbirka shayga.
Isle'egta muraayadda qaloocan
Iyada oo ku saleysan sawirka hoose, laba iftiin ayaa loo jiidayaa dhinaca muraayadda qaloocan, muraayadda qaloocanna waxay dib u celinaysaa iftiinka.

s = do = masaafada shayga, s' = di = masaafada sawirka, h = P P' = dhererka shayga, h' = Q Q' = dhererka sawirka, F 1 iyo F 2 = barta diiradda ee muraayadda qaloocan.
Saddexagalka P'AP wuxuu la mid yahay saddexagalka Q'AQ. Sidaa darteed:
![]()
Saddexagal BF 2 A wuxuu la mid yahay saddexagal Q'F 2 Q, halkaasoo masaafada AB = dhererka shayga (h) iyo masaafada F 2 A = dhererka diiradda (f) ee muraayadda qaloocan. Sidaa darteed:


Iyada oo ku saleysan xeerarka calaamadaha muraayadda qaloocan, isla'egtan waxaa loo beddeli karaa sida isla'egta muraayadda qaloocan,
haddii masaafada sawirka (di) la siiyo calaamad taban sababtoo ah iftiinka iftiinku ma dhaafo sawirka
dhererka diiradda (f) sidoo kale waxaa la siiyaa calaamad taban sababtoo ah barta diiradda ee muraayadda qallafsan iftiin ma dhaafto (isbarbar dhig sawirka sameynta sawirka kore). Sida ku cad hadalkan, isle'egta muraayadda qallafsan waxay isu beddeshaa:
![]()
do = masaafada shayga, di = masaafada sawirka, f = dhererka diiradda
Weyneynta sawirka (m)
Fiiri sawirka qaab-dhismeedka sawirka kore. Saddexagalada P'AP iyo Q'AQ way isku mid yihiin si aan u soo saarno xiriirka ka dhexeeya masaafada shayga iyo masaafada sawirka iyadoo la adeegsanayo dhererka shayga iyo dhererka sawirka:
![]()
Isle'egtan waxaa mar kale loo qoray sida hoos ku xusan iyadoo lagu darayo m:
![]()
m = weyneynta sawirka
ho = dhererka shayga (togan haddii uu ka sarreeyo dhidibka ugu weyn ama shaygu uu toosan yahay)
hi = dhererka sawirka (togan haddii uu ka sarreeyo dhidibka ugu weyn ama sawirku uu toosan yahay)
do = masaafada shayga (togan haddii iftiinka iftiinku uu dhex maro shayga)
di = masaafada sawirka (togan haddii iftiinka iftiinku uu dhex maro sawirka ama sawirku uu dhab yahay)