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Products of Sines in Two Simple Arrangements of Six Lines

Carroll, Jeremy

HPL-2006-36

Keyword(s): angles; lines; sines; Ringel

Abstract: We show that in two different arrangements of six lines in the Euclidean plane an inequality holds between the products of the sines of selected angles from the arrangement. Either of these then provides a short proof of the falsity of Ringel's conjecture, using no more than schoolbook geometry, as opposed to the oriented matroid techniques of Las Vergnas.

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