Recent content by binglee

Fix a number L > 2. Consider all smooth plane curves r of length L that connect (−1, 0) and (1, 0) and are contained in the upper half-plane. Note that and the segment [−1, 1] of the X-axis together bound a plane domain D. Find r such that D has the maximal possible area.

bump can anybody help me?!~~~~ I thought about it for a while. what does it mean by the knowledge of n? if we know t n b, we can determine the curvature and the torsion, but here we only know n?? please!~ help me!~~

ya, we defined curvature = ||r''||=||t'||. It is a function of t, while we defined torsion = -n.b' it is not a function of t. I don't know if my understanding about torsion is right. Since we defined n as a function of t and b as a function of t so is t. Then in this question i just need to go...

Show that the knowledge of the vector function n = n(s) (normal vector) of a unit-speed curve , with non-zero torsion everywhere, determines the curvature and the torsion don't have any clues about what i am supposed to prove!~

Hi, I know this one is stupid, but i am still confused. why e^(iy) = cosy + i siny? thank you.