Planar graphs

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Grade Vs Difficulty:
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This hour and a half lesson introduces planar graphs, i.e., through the Handshake Lemma and Euler's formula. The "Planar Graph Basics" attachment provides some discussion and examples, which can be used to segway to constructing the dodecahedron out of cardboard (held together with a rubber band, without any adhesives; see the "Dedecahedron" attachment for printouts). We also used Zometools dipped in soap solution to describe the Platonic solids and mention minimal surfaces during a recreational math day. (Our Math Circle occasionally introduces higher math so that we might pique the students' interests.)