Φ

z ) ∂ ( r , θ , φ ) = | sin ⁡ θ cos ⁡ φ r cos ⁡ θ cos ⁡ φ − r sin ⁡ θ sin ⁡ φ sin ⁡ θ sin ⁡ φ r cos ⁡ θ sin ⁡ φ r sin ⁡ θ cos ⁡ φ cos ⁡ θ − r sin ⁡

sin ⁡ φ d φ [ 1 − cos ⁡ ( φ + ψ ) 1 − cos ⁡ ( φ − ψ ) 1 + ε 2 − 1 ε 2 + 1 cos ⁡ ( φ − ψ ) 1 + ε 2 − 1 ε 2 + 1 cos ⁡ ( φ + ψ ) ] = a ρ ∫ π + φ π − φ sin

{\displaystyle q=C\varphi ,dq=C*d\varphi } Toʻla bajarilgan ish A = ∫ 0 φ C ∗ φ d φ = ∫ 0 φ φ d φ = C φ 2 2 {\displaystyle A=\int _{0}^{\varphi }C*\varphi d\varphi

zichligi φ N {\displaystyle \varphi _{N}} - zarralar flyuensi d F {\displaystyle dF} ning d t {\displaystyle dt} birlik vaqt ichida oʻzgarishi φ N = d F

logarifmik spiral boʻlib, uning oʻsish omili φ, oltin nisbati.hisoblanadi. Yaʼni, oltin spiral har chorak burilish uchun φ koeffitsientiga kengaytiriladi (yoki