Principien Der Flächen Theorie

Reinhold Hoppe

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Bezeichnet femer r den Krümmungswinkel des Meridians, so dass dt dz du^ cost; g- = sinr wird, so hat man: dx ö- = COSTCOSt;; ^- =» cosTsmv ; dz dx g^=-«sint;; dy g^^tcost,; 1 = woraus : p = — sinrcosv: q = — sin T sin» • r = COST (72) (73) In einem Scheitel wird r = 0, also ^ = 0; (z = 0; r = l in einer Spitze r = const bleiben ^, q abhängig von v -, statt einer Normale hat hier die Fläche eine normale konische Fläche. Die Fundamentalgrössen 2. Ordnung werden: £=n ; F—Oi G = tsmr (74) Demnach s...ind die Parameterlinien (w), (t?), d. i. die Meridiane und Parallelkreise, auch Erümmungslinien. Infolge dessen hat man: Die Gleichungen der Mittelpunktsflächen werden: Digitized by CjOOQIC — 72 — «1 = x+ QiP = (* "' er ®^^ V cosr =^ 2^+Pl

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