Math 302, Assignment 2, Fall 2000
Due Fri September 8 (at the beginning of class)
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Consider the cylinder given by x^2 + y^2 = 1.
Find a parametric equation for a helix around this cylinder.
First, show that the speed of this path is constant;
if it is not, change your equation so that it is.
Next, compute its acceleration at a point.
Compute the normal vector to the cylinder at that point.
Finally, show that the acceleration is perpendicular to the tangent plane.
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A map f from X to Y is a bijection if it is one-to-one and onto.
A map g from Y to X is the inverse to f
if the composition of g with f is
the identity map, and also
the composition of f with g is the identity map.
Prove that f is is a bijection if and only if it has an inverse,
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Consider the map of the earth on the back of this sheet.
Draw onto this the "map" of lines which are straight
on the earth itself. Do at least four, and choose them to be
as many different types as possible.
Do any of these look straight on your map? Do all of them?
Explain.