This preview shows pages 1–2. Sign up to view the full content.
Math 4250/6250 Homework #1
This homework assignment covers DoCarmo 1.1  1.5. It accompanies Lectures 1 and 2 in the
course notes. Please pick 5 of the following 9 problems. Remember that undergraduate students
should average
one
challenge problem per assignment, while graduate students should average
two
challenge problems per assignment.
1. R
EGULAR
P
ROBLEMS
1. (Do Carmo, 13, #2) A circular disk of radius 1 in the
xy
plane rolls along the
x
axis without
slipping. The curve described by a point on the rim of the disk is called a
cycloid
.
(1) Find a parametrization
α
(
t
)
of the cycloid.
(2) Compute the arclength of the portion of the cycloid corresponding to one complete rotation
of the disk.
2. (Do Carmo, 13, #4) The curve
α
(
t
) =
±
sin
t,
cos
t
+ log tan
t
2
²
.
is called the tractrix. Show that
(1)
α
is a differentiable parametrized curve, regular except at
t
=
π/
2
.
(2) The length of the portion of the tangent line to the tractrix between
α
(
t
)
and the
y
axis is
always equal to
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Staff
 Math

Click to edit the document details