Four draggable points are given, producing a quadrangle ABCD.
These generate lines which intersect generating new points etc.
Generations of lines and intersections can be
shown and hidden using the buttons on the left side of the picture.
Reset by pushing the 'R' button.
Recall that the numbers
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1. How many sides do the quadrangle have?
2. Why is this number equal to
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3. The sides of the quadrangle intersect in the four initial points and 3 new points E, F and G. Why do we get only 7 points instead of
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4. How many lines are joining two-by-two the 7 points A, ..., G ?
5. Intersecting these lines two-by-two, we get 6 new points H, I, J, K, L and M. Explain why this number is equal to
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6. We join the last six points two-by-two, obtaining lines HJ, HK, HL, HM, IJ, IK, IL, IM, JL, JM, KL, KM. How many different lines are they? Why?
7. What is the value of all cross-ratios of collinear points [red, red; black, black] ?
8. We join all the 13 points of our figure two-by-two by lines. We get so all the lines of the picture. How many are they?
9. Intersecting all the lines of the figure two-by-two, we get the 13 points labeled from A to M and how many extra points?
10. Is it possible to increase the number of intersecting points
by moving A, B, C and/or D?
Is it possible to decrease it ?