"의구 (Pseudosphere)"의 두 판 사이의 차이

2013년 1월 12일 (토) 11:09 판

tractrix [1] 의 회전으로 얻어지는 곡면
매개화\[\mathbf{x}(u,v)=(\cos (u) \text{sech}(v),\sin (u) \text{sech}(v),v-\tanh (v))\]

[[파일:5797227-의구_(Pseudosphere)1.gif][/pages/5797227/attachments/5761026 의구_(Pseudosphere)2.gif]]

\(E=\text{sech}^2(v)\), \(F=0\),\(G=\tanh ^2(v)\)
크리스토펠 기호\[\begin{array}{ll} \Gamma _{11}^1 & 0 \\ \Gamma _{12}^1 & -\tanh (v) \\ \Gamma _{21}^1 & -\tanh (v) \\ \Gamma _{22}^1 & 0 \\ \Gamma _{11}^2 & \text{csch}(v) \text{sech}(v) \\ \Gamma _{12}^2 & 0 \\ \Gamma _{21}^2 & 0 \\ \Gamma _{22}^2 & \text{csch}(v) \text{sech}(v) \end{array}\]

@@ 23번째 줄: / 23번째 줄: @@
 * [[추적선 (tractrix)|tractrix]][https://lh6.googleusercontent.com/OriR23LjRnLDtmxu34JRepqxprNeVW-q_rsq7Prru1YML-PgPvjdr3Qsu_H6BWAhe5tVSpUEeTAgdJ9EsE6xUzJdlLLiLJXFD8M=w1600 ] 의 회전으로 얻어지는 곡면<br>
-*  매개화<br><math>\mathbf{x}(u,v)=(\cos (u) \text{sech}(v),\sin (u) \text{sech}(v),v-\tanh (v))</math><br>
+*  매개화:<math>\mathbf{x}(u,v)=(\cos (u) \text{sech}(v),\sin (u) \text{sech}(v),v-\tanh (v))</math><br>
@@ 38번째 줄: / 38번째 줄: @@
 * <math>E=\text{sech}^2(v)</math>, <math>F=0</math>,<math>G=\tanh ^2(v)</math><br>
-*  크리스토펠 기호<br><math>\begin{array}{ll}  \Gamma _{11}^1 & 0 \\  \Gamma _{12}^1 & -\tanh (v) \\  \Gamma _{21}^1 & -\tanh (v) \\  \Gamma _{22}^1 & 0 \\  \Gamma _{11}^2 & \text{csch}(v) \text{sech}(v) \\  \Gamma _{12}^2 & 0 \\  \Gamma _{21}^2 & 0 \\  \Gamma _{22}^2 & \text{csch}(v) \text{sech}(v) \end{array}</math><br>
+*  크리스토펠 기호:<math>\begin{array}{ll}  \Gamma _{11}^1 & 0 \\  \Gamma _{12}^1 & -\tanh (v) \\  \Gamma _{21}^1 & -\tanh (v) \\  \Gamma _{22}^1 & 0 \\  \Gamma _{11}^2 & \text{csch}(v) \text{sech}(v) \\  \Gamma _{12}^2 & 0 \\  \Gamma _{21}^2 & 0 \\  \Gamma _{22}^2 & \text{csch}(v) \text{sech}(v) \end{array}</math><br>