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Trifold Arrangements and Cevian Dissections

By Vincent J. Matsko, Douglas B. West and John E. Wetzel


Abstract We determine precisely how many triple points can be formed in the plane by an arrangement of n lines lying in three parallel families of p; q; r lines, respectively. Using this result we solve the Euclidean realization problem for such arrangements. We apply our results to solve an analogous problem in which a triangle is dissected by three families of cevians. We conclude by mentioning some related unsolved problems

Year: 2009
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