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September 4th, 2013, 05:37 AM   #1
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Circle at infinity

Hi all, I need a help in defining the circle at infinity.
The equation is x1^2+x2^2+x3^2 = x4 = 0. There are two points on the circle, and those are the circular points at infinity. For x_3 = 0, the two circular points are (1, i, 0, 0) and (1, -i, 0, 0). My question is..what is the other point that satisfies the equation of circle at infinity (other than the circular points and (0, 0, 0, 0))? I need one more.

The other question: the line at infinity and circle at infinity, are both defining the same object?
PS: The line at infinity can be visualized as a circle which surrounds the affine plane.
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September 4th, 2013, 07:09 AM   #2
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Re: Circle at infinity

Hi all, I've decided I will just use the other complex numbers for the next (2, 2i, 0, 0) and (2, -2i, 0)..and so on. And, i think the circle at infinity is not the line at infinity..since both equations are different. Points (except the circular points at infinity) which fulfill the eq of the line at infinity do not fulfill the eq of the circle at infinity.
I hope this conclusion will solve my problem. If any of you have another opinion..pls inform me. Any opinion would be greatly appreciated. Thx in advance
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