Slide 1

CME12, 2012.07.02. Rzeszw, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center Faculty of Science Etvs Lornd University, Budapest Slide 2 Gergely Wintsche Outline 1. Introduction around the word 2. Coloring the cube The frames of the cube The case of two colors The case of six colors The case of the rest 3. Coloring the tetrahedron 4. Coloring the octahedron 5. The common points 6. The football Part I / 2 Coloring and folding regular solids Slide 3 Gergely WintschePart I / 3 Coloring and folding regular solids, Introduction Around the word The question Slide 4 Gergely WintschePart I / 4 Coloring and folding regular solids, Introduction Around the word The answers first student Slide 5 Gergely WintschePart I / 5 Coloring and folding regular solids, Introduction Around the word The answers second student Slide 6 Gergely WintschePart I / 6 Coloring and folding regular solids, Introduction Around the word The answers third student Slide 7 Gergely WintschePart I / 7 Coloring and folding regular solids, Introduction Around the word The answers wiki Slide 8 Gergely WintschePart I / 8 Coloring and folding regular solids, Introduction Around the word The answers wiki Slide 9 Gergely WintschePart I / 9 Coloring and folding regular solids, Introduction Around the word The answers Marriam-Webster dictionary Slide 10 Gergely WintschePart I / 10 Coloring and folding regular solids, Coloring the cube The frame of the cube Slide 11 Gergely WintschePart I / 11 Coloring and folding regular solids, Coloring the cube The possible frames of the cube Slide 12 Gergely WintschePart I / 12 Coloring and folding regular solids, Coloring the cube Coloring the opposite faces Slide 13 Gergely WintschePart I / 13 Coloring and folding regular solids, Coloring the cube Coloring the opposite faces Slide 14 Gergely WintschePart I / 14 Coloring and folding regular solids, Coloring the cube Coloring the matching vertices Slide 15 Gergely WintschePart I / 15 Coloring and folding regular solids, Coloring the cube Coloring the matching vertices Slide 16 Gergely WintschePart I / 16 Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) two colors Slide 17 Gergely WintschePart I / 17 Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) two colors Slide 18 Gergely WintschePart I / 18 Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) six colors Slide 19 Gergely WintschePart I / 19 Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) six colors Slide 20 Gergely WintschePart I / 20 Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) six colors Slide 21 Gergely WintschePart I / 21 Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) six colors These three faces fix the cube in the space so the remaining three faces are colorable 321=6 different ways. The total number of different colorings are 56=30. Slide 22 Gergely WintschePart I / 22 Coloring and folding regular solids, Coloring the tetrahedron Coloring the faces of the tetrahedron with (exactly) four colors Slide 23 Gergely WintschePart I / 23 Coloring and folding regular solids, Coloring the tetrahedron Coloring the faces of the tetrahedron with (exactly) four colors Slide 24 Gergely WintschePart I / 24 Coloring and folding regular solids, Coloring the octahedron Coloring the faces of the octahedron (exactly) eight colors Slide 25 Gergely WintschePart I / 25 Coloring and folding regular solids, Coloring the octahedron Coloring the faces of the octahedron with (exactly) four colors Slide 26 Gergely WintschePart I / 26 Coloring and folding regular solids, Coloring the octahedron Coloring the faces of the octahedron with (exactly) four colors Slide 27 Gergely WintschePart I / 27 Coloring and folding regular solids, Coloring the octahedron Coloring the faces of the octahedron with (exactly) four colors Slide 28 Gergely WintschePart I / 28 Coloring and folding regular solids, Coloring the football Coloring the faces of the truncated icosahedron Slide 29 Gergely WintschePart I / 29 Coloring and folding regular solids, Symmetry Slide 30 Gergely WintschePart I / 30 Coloring and folding regular solids, Symmetry Slide 31 Gergely WintschePart I / 31 Coloring and folding regular solids, Symmetry Slide 32 Gergely WintschePart I / 32 Coloring and folding regular solids, Symmetry Slide 33 Gergely WintschePart I / 33 Coloring and folding regular solids, Symmetry Slide 34 Gergely WintschePart I / 34 Coloring and folding regular solids, Symmetry Slide 35 Gergely WintschePart I / 35 Coloring and folding regular solids, Symmetry Slide 36 Gergely WintschePart I / 36 Coloring and folding regular solids, Symmetry Slide 37 Gergely WintschePart I / 37 Coloring and folding regular solids, Summa Summarize Slide 38 Gergely WintschePart I / 38 Coloring and folding regular solids, Outlook Slide 39 Gergely WintschePart I / 39 Coloring and folding regular solids, Outlook Slide 40 Gergely WintschePart I / 40 Coloring and folding regular solids, Outlook The case of cube Slide 41 Gergely WintschePart I / 41 Coloring and folding regular solids, Outlook The case of cube