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CME12, 2012.07.02. – Rzeszów, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center.

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Presentation on theme: "CME12, 2012.07.02. – Rzeszów, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center."— Presentation transcript:

1 CME12, – Rzeszów, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center Faculty of Science Eötvös Loránd University, Budapest

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

3 Gergely WintschePart I / 3 – Coloring and folding regular solids, Introduction – Around the word The question

4 Gergely WintschePart I / 4 – Coloring and folding regular solids, Introduction – Around the word The answers –first student

5 Gergely WintschePart I / 5 – Coloring and folding regular solids, Introduction – Around the word The answers –second student

6 Gergely WintschePart I / 6 – Coloring and folding regular solids, Introduction – Around the word The answers –third student

7 Gergely WintschePart I / 7 – Coloring and folding regular solids, Introduction – Around the word The answers –wiki

8 Gergely WintschePart I / 8 – Coloring and folding regular solids, Introduction – Around the word The answers – wiki

9 Gergely WintschePart I / 9 – Coloring and folding regular solids, Introduction – Around the word The answers – Marriam-Webster dictionary

10 Gergely WintschePart I / 10 – Coloring and folding regular solids, Coloring the cube The frame of the cube

11 Gergely WintschePart I / 11 – Coloring and folding regular solids, Coloring the cube The possible frames of the cube

12 Gergely WintschePart I / 12 – Coloring and folding regular solids, Coloring the cube Coloring the opposite faces

13 Gergely WintschePart I / 13 – Coloring and folding regular solids, Coloring the cube Coloring the opposite faces

14 Gergely WintschePart I / 14 – Coloring and folding regular solids, Coloring the cube Coloring the matching vertices

15 Gergely WintschePart I / 15 – Coloring and folding regular solids, Coloring the cube Coloring the matching vertices

16 Gergely WintschePart I / 16 – Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) two colors

17 Gergely WintschePart I / 17 – Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) two colors

18 Gergely WintschePart I / 18 – Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) six colors

19 Gergely WintschePart I / 19 – Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) six colors

20 Gergely WintschePart I / 20 – Coloring and folding regular solids, Coloring the cube Coloring the faces of the cube with (exactly) six colors

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 3·2·1=6 different ways. The total number of different colorings are 5·6=30.

22 Gergely WintschePart I / 22 – Coloring and folding regular solids, Coloring the tetrahedron Coloring the faces of the tetrahedron with (exactly) four colors

23 Gergely WintschePart I / 23 – Coloring and folding regular solids, Coloring the tetrahedron Coloring the faces of the tetrahedron with (exactly) four colors

24 Gergely WintschePart I / 24 – Coloring and folding regular solids, Coloring the octahedron Coloring the faces of the octahedron (exactly) eight colors

25 Gergely WintschePart I / 25 – Coloring and folding regular solids, Coloring the octahedron Coloring the faces of the octahedron with (exactly) four colors

26 Gergely WintschePart I / 26 – Coloring and folding regular solids, Coloring the octahedron Coloring the faces of the octahedron with (exactly) four colors

27 Gergely WintschePart I / 27 – Coloring and folding regular solids, Coloring the octahedron Coloring the faces of the octahedron with (exactly) four colors

28 Gergely WintschePart I / 28 – Coloring and folding regular solids, Coloring the football Coloring the faces of the truncated icosahedron

29 Gergely WintschePart I / 29 – Coloring and folding regular solids, Symmetry

30 Gergely WintschePart I / 30 – Coloring and folding regular solids, Symmetry

31 Gergely WintschePart I / 31 – Coloring and folding regular solids, Symmetry

32 Gergely WintschePart I / 32 – Coloring and folding regular solids, Symmetry

33 Gergely WintschePart I / 33 – Coloring and folding regular solids, Symmetry

34 Gergely WintschePart I / 34 – Coloring and folding regular solids, Symmetry

35 Gergely WintschePart I / 35 – Coloring and folding regular solids, Symmetry

36 Gergely WintschePart I / 36 – Coloring and folding regular solids, Symmetry

37 Gergely WintschePart I / 37 – Coloring and folding regular solids, Summa Summarize

38 Gergely WintschePart I / 38 – Coloring and folding regular solids, Outlook

39 Gergely WintschePart I / 39 – Coloring and folding regular solids, Outlook

40 Gergely WintschePart I / 40 – Coloring and folding regular solids, Outlook The case of cube

41 Gergely WintschePart I / 41 – Coloring and folding regular solids, Outlook The case of cube


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