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An Introduction to Pappus' TheoremPappus' Theorem was discovered by Pappus of Alexandria in the 4th century AD, and has extraordinarily beautiful properties that make it one of the nicest constructions to study in projective geometry. Begin with two lines, l and m, in
the projective plane. Then choose three points on each line, label the three
points on l X1, X2, and X
3 and the three points on m Y1, Y2
, and Y3. Then construct the point Z1
by intersecting the line Above is an interactive applet that demonstrates Pappus' Theorem. The blue dots represent the six points X1 , X2, X3, Y1, Y 2, and Y3 and the red dots represent the points Z1, Z2, and Z3.You can drag the blue dots around and the red dots are forced to change whenever the blue dots move. Notice that the red dots remain collinear. Next Step: Permutations and Pappus' Theorem
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