所屬科目：研究所、轉學考(插大)-幾何
(a) ([10%]) Find the curvature of where x is the curvature and n is the unit normal vector on y and
(b) ([10%])be a family of plane curves defined by where.Show that Ir intersects at exactly one point for each and the angle between the tangent vectors of andΓT at the intersection point is independent of T.
(3) ([30%]) Consider a regular surface S where and the inversion Φ :R3＼ given by Compare the mean curvature and the Gauss urvatures of S and of the image surface S' = Φ(S). More precisely, show that and where N(p) is the unit normal of S at p, H'(Φ(p) is the mean curvature of s' at Φ(p), K'(Φ(p) is the Gauss curvature of S' at Φ(p).
阿摩線上測驗
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阿摩線上測驗
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where x is the curvature and n is the unit normal vector on y and
be a family of plane curves defined by
.Show that Ir intersects 
at exactly one point for each 
and the inversion Φ :R3＼ 
given by 
and
where N(p) is the unit normal of S at p, H'(Φ(p) is the mean curvature of s' at Φ(p), K'(Φ(p) is the Gauss curvature of S' at Φ(p).