4: Space Curves

Question 1

K(s) measures the rate at which alpha(s) is bending away from its ___ straight line

Answer 1

tangent

Question 2

torsion measures the rate at which alpha(s) is twisting say from its ___

Answer 2

osculating plane

Question 3

if alpha is regular and K(u)=/=0 and ___ stays within an affine plane then torsion(u)=0

Answer 3

tracea

Question 4

Fundamental local theorem of space curves: K(s)>0, smooth unit speed space curve alpha. alpha is unique up to orientation preserving ___

Answer 4

isometries