Summary
Zindler’s theorem of 1920 says that each planar convex set admits two perpendicular lines that divide it into four parts of equal area. Call the intersection of the two lines a Zindler point. We show that each triangle admits either one, two or three Zindler points, and we classify all triangles according to these three numbers.
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Acknowledgments
We thank the referee for his/her careful reading and suggestions.
Additional information
Notes on contributors
Allan Berele
ALLAN BERELE (MR Author ID: 35020) received his Ph.D. from the University of Chicago and is a professor at DePaul University in Chicago. His main research interest is in algebras with polynomial identities, although he fell in love with Euclidean geometry many years before he ever heard of p. i. algebras.
Stefan Catoiu
STEFAN CATOIU (MR Author ID: 632038) received his Ph.D. from the University of Wisconsin-Madison and is an associate professor at DePaul University in Chicago. His research interest includes noncommutative algebra, real analysis, geometry, number theory and elementary mathematics.