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 δ0 (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 δ0 (with respect to γ ) is again a circle not through O . In this problem and the next, you will show that the inverse C0 of the centre C of the circle δ is not the centre of the inverted circle δ0 . 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.