<prompt> Nyuki anaanza kuruka kutoka pointi P_0. Anaruka inchi 1 kuelekea mashariki kuelekea P_1. Kwa j ge 1, nyuki anapofika hatua ya P_j, anabadilisha 30circ kinyume cha saa na kisha kuruka inchi j1 moja kwa moja kuelekeza P_j1. Nyuki anapofikia P_2015, yuko umbali gani kutoka P_0, kwa inchi?  <response>: Acha omega epi i6. Kisha tukichukulia kuwa nyuki anaanzia kwenye asili, P_2015 iko kwenye uhakika.z 1 2 omega 3 omega2 4 omega3 nukta 2015 omega2014.Kishaomega z omega 2 omega2 3 omega3 4 omega4 nukta 2015 omega2015.Tukiondoa milinganyo hii, tunapataanzaalignomega - 1 z 2015 omega2015 - omega2014 - omega2013 - vidoti - omega - 1 2015 omega2015 - fracomega2015 - 1omega - 1.mwishoalignKwa kuwa omega6 1, omega2015 omega6335 cdot omega5 omega5. Kwa hivyo,anzaalignomega - 1 z 2015 omega5 - fracomega5 - 1omega - 1 2015 omega5 - omega4 - omega3 - omega2 - omega - 1.endalignNa kwa kuwa omega3 -1, hii inapungua hadianzaalignomega - 1 z -2015 omega2 omega 1 - omega2 - omega - 1 -2015 omega2 - omega2 -2016 omega2,mwishoalignhivyoz -frac2016 omega2omega - 1.Kwa hiyo,z kushoto -frac2016 omega2omega - 1 kulia frac2016omega - 1.Tukipanga 0, 1, na omega katika ndege changamano, tunapata pembetatu ya isosceles.asyukubwa wa kitengo 4 cm;jozi M, O, P, Q;O 0,0;P 1,0;Q dir30;M P Q2;kuchoraO--P--Q--mzunguko;kuchoraO--M;lebo0, O, SW;lebo1, P, SE;leboomega, Q, NE;lebo1, O P2, S, nyekundu;lebo1, O Q2, NW, nyekundu;asyKwa hivyo, umbali kati ya 1 na omega ni omega - 1 2 sin fracpi12 fracsqrt6 - sqrt22, hivyoz frac2016fracsqrt6 - sqrt22 frac4032sqrt6 - sqrt2 frac4032 sqrt6 sqrt24 1008 sqrt6 1008 sqrt2. 