Re: Cross-ratio induced from another pencil of rays
From: Hans-Peter Schroecker (hps_at_despammed.com)
Date: 09/19/04
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Date: 19 Sep 2004 06:20:18 -0400
mathma18@hotmail.com (Narasimham G.L.) writes:
> In projective geometry, a pencil P1 of four 2D straight lines through
> a vertex point are cut by another four lines of pencil P2 (line
> slopes m1 to m4) of arbitrary vertex location,inducing a cross-ratio
> XR in P1. How does XR depend on (m1 to m4)?
I don't understand your question. Four straight lines through a
common vertex always determine a cross-ratio by themselves, without
referring to the lines of a second pencil. The cross-ratio of the
four straight lines is the cross-ratio of their four intersection
points with an arbitrary straight line (not through the vertex).
Sincerely,
Hans-Peter
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