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Balanced areas in quadrilaterals - Anne's Theorem and its unknown origin

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2019-07-04
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Copyright (c) 2022 Hans Humenberger, Berthold Schuppar

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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Humenberger, H., & Schuppar, B. (2019). Balanced areas in quadrilaterals - Anne’s Theorem and its unknown origin. Teaching Mathematics and Computer Science, 17(1), 93-103. https://doi.org/10.5485/TMCS.2019.0462
Abstract

There are elegant and short ways to prove Anne's Theorem using analytical geometry. We found also geometrical proofs for one direction of the theorem. We do not know, how Anne came to his theorem and how he proved it (probably not analytically), it would be interesting to know. We give a geometric proof (both directions), mention some possibilities – in more details described in another paper – for using this topic in teaching situations, and mention some phenomena and theorems closely related to Anne's Theorem.

Subject Classification: G10, G30