應用數學期中報告 The Spell of Logic,Recreation & Games 通訊 4 A B 986 C00 34 陳詩佳

1. 應用數學期中報告 The Spell of Logic,Recreation & Games 通訊4A B986C0034陳詩佳

2. content • flexagon • Geometric Dissections • Magic Squares • The Knight’s Tour • Summary • Reference

3. What is a Flexagon? •  If you open the flexagon like a book on the reverse side, then a new face appears, which was hidden before. Hexa-Tetraflexagon

4. Geomatric Dissections • It is a fascinating paradox which seems to prove that 64 is equal to 65 simply by cutting a chessboard into four pieces and by assembling these pieces into a rectangle whose sides are made up of 5 squares and 13 squares.

5. x0 + x1 = x2 • x1x1 - x2 x0 = µ

6. Magic Square a magic square  of order n is an arrangement of n2 number, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant

7. Franklin Magic Square • A Franklin magic square is a semi-magic square with each of the four main bent row sums equal to the magic constant.  M = (n3 + n)/2

8. Magic Circle

9. Benjamin Franklin’s Magic Circle

10. The Knight Tour

11. Summary Latin Squares Magic Cube

12. Reference http://en.wikipedia.org/wiki/Flexagon http://www.mathematische-basteleien.de/tetraflexagons.htm http://mathematische-basteleien.de/flexagons.htm http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/jigsaw-paradox.html http://www.chessbase.com/newsdetail.asp?newsid=5311 http://en.wikipedia.org/wiki/Magic_square http://mathworld.wolfram.com/MagicSquare.html http://www.taliscope.com/Franklin_en.html http://www.magic-squares.net/unususqr.htm#Magic Circles http://www.magic-squares.net/unususqr.htm#Magic Circles http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2030%20Knights%20tour.pdf