作者TampaBayRays (坦帕灣光芒)
看板Math
標題[幾何] Regular Surface
時間Sat Jan 12 23:27:22 2013
Let x =f(v),z=g(v) a<v<b f(v)>0 be a parametrization for a
rugular plane curve C. Let S belong to R^3 be the set obtained by rotating
C about z axis. Show the parametrization of S and prove that S is a regular
surface.
請問他的參數化是x(u,v)=(f(v)cos u,f(v)sin u,g(v))嗎?
我知道要證regular surface 要證他可微,一對一,跟homeomorphism
可是課本上說可微跟1-1很簡單 可是我不會
所以想請問各位大大如何證明他是regular surface
謝謝!!!
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◆ From: 220.136.71.234
推 turboho :要用到(f,g)是regular plan curve吧 01/13 16:06
→ turboho :然後參數化第二項應該是sin u不是sin v？ 01/13 16:07
推 herstein :homeomorphism 01/13 16:35
→ herstein :你得一個變數應該寫錯了, f(v)sin u才對 01/13 16:38
※ 編輯: TampaBayRays 來自: 220.136.52.23 (01/14 16:14)