Pappus's Theorem starts with any two lines. On each, three arbitrary points are chosen. Taking two points from the top line, and two from the bottom, the point of intersection of the diagonals is found. This is done three times, giving three points2 Here the diagonals are coloured blue, green and brown.

The three points are collinear!

Another formulation is in terms of a hexagon, where alternate vertices lie are collinear. The hexagon therefore needs to be folded over itself.

Play with this diagram by moving the lines and points. The red line shows the collinear intersections of diagonals. You can reorder the points on the lines.

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