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Math 348 (2006): Assignment #3
due Monday, July 24, 2006
For problems 1, 2, and 3, let
γ
be a circle with centre
O
and radius
k
.
1. Show directly, using the deﬁnition of inversion, that if
δ
is a circle passing through
O
, then its
inverse
δ
0
(with respect to
γ
) is a line not passing through
O
. (Do not use the fact that the inverse
of a line not through
O
is a circle through
O
and that inversion is an involution. Show it directly,
similarly to the proof of the other direction, which we had done in class.)
2. We have shown that if
δ
is a circle not through
O
, then its inverse
δ
0
(with respect to
γ
) is again a
circle not through
O
. In this problem and the next, you will show that the inverse
C
0
of the centre
C
of the circle
δ
is
not
the centre of the inverted circle
δ
0
. That is, even though inversion takes
circles to circles, it does not take centres of circles to centres of circles!
Step One: Let
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This note was uploaded on 02/20/2011 for the course MATH 348 taught by Professor Karigiannis during the Summer '06 term at McGill.
 Summer '06
 Karigiannis
 Math, Geometry

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