\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2014f.00664}
\itemau{De Villiers, Michael}
\itemti{An investigation of some properties of the general Haag polygon.}
\itemso{Math. Sch. (Leicester) 43, No. 3, 15-18 (2014).}
\itemab
From the text: The famous Dutch artist, M. C. Escher (1898--1972) investigated in his notes a tiling of the plane first mentioned in a paper by Haag in 1923 with a specific type of congruent non-regular hexagon, called a Haag hexagon by John Rigby. For this investigation we'll be looking at applying the Haag `circle' construction mentioned here to a general triangle as well as to other polygons such as quadrilaterals, hexagons, etc. to create what I'm choosing to define as a `Haag polygon' and to explore some of its general and specific properties. The mathematical results discussed here are elementary and could be a suitable investigative activity for high school learners and teachers, giving them an opportunity to apply some basic geometric properties and theorems in a novel context. The reader is invited to dynamically explore some of the properties discussed below at \url{http://dynamicmathematicslearning.com/haag-hexagon-tiling.html}.
\itemrv{~}
\itemcc{G90}
\itemut{Haag polygon; tilings; tessellations; Haag hexagon; concurrency property; generalisation; polygons; hexagons; triangles; quadrilaterals; proofs; pentagons; Haag octagon; Haag dodecagon}
\itemli{}
\end