Let (A, B, C, D) be an ordered quadruple of distinct collinear points in II. Let G = S4((A,B,C, D)) = {(A, B, C, D), …, (D,C,B,A)} be the set of all possible ordered quadruples which can be formed from the set of points{A,B,C,D}. ... Prove that that there are six subsets of G which each contain four elements whose cross ratio is equal.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let (A, B, C, D) be an ordered quadruple of distinct collinear points in II. Let
G = S4((A, B, C, D)) = {(A, B, C , D), . , (D,C,B,A)} be the set of all possible
ordered quadruples which can be formed from the set of points{A, B,C,D}.
...
Prove that that there are six subsets of G which each contain four elements
whose cross ratio is equal.
Transcribed Image Text:Let (A, B, C, D) be an ordered quadruple of distinct collinear points in II. Let G = S4((A, B, C, D)) = {(A, B, C , D), . , (D,C,B,A)} be the set of all possible ordered quadruples which can be formed from the set of points{A, B,C,D}. ... Prove that that there are six subsets of G which each contain four elements whose cross ratio is equal.
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