000RM.dvi

Recreational Mathematics Paul Yiu Department of Mathematics Florida Atlantic University Summer 2003 Chapters 1– Version 031209 ...

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1 Lattice polygons 1.1 Pick’s Theorem: area of lattice polygon .... 1.2 Counting primitive triangles ........... 1.3 The Farey ...

Chapter 1 Lattice polygons 1 Pick’s Theorem: area of lattice polygon 2 Counting primitive triangles 3 The Farey sequences Append ...

102 Lattice polygons 1.1 Pick’s Theorem: area of lattice polygon .... A lattice point is a point with integer coordinates. A lat ...

1.2 Counting primitive triangles 103 1.2 Counting primitive triangles ........... We shall make use of the famous Euler polyhedr ...

104 Lattice polygons 1.3 The Farey sequence .................. Letnbe a positive integer. The Farey sequence of ordernis the seq ...

1.3 The Farey sequence 105 The Farey polygonsP 10 andP 20 ...

106 Lattice polygons Appendix: Regular solids A regular solid is one whose faces of regular polygons of the same type, say,n-gon ...

1.3 The Farey sequence 107 Exercise 1.Can a lattice triangle be equilateral? Why? 2.Can a lattice polygon be regular? Why? [You ...

108 Lattice polygons A cross number puzzle 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 123 4 567 8 9 10 11 12 13 14 15 16 17 18 19 2 ...

Chapter 2 Lattice points 1 Counting interior points of a lattice triangle 2 Lattice points on a circle Appendix: The floor and t ...

110 Lattice points 2.1 Counting interior points of a lattice triangle .... A lattice triangle has vertices at(0,0),(a,0), and(a, ...

2.2 Lattice points on a circle 111 2.2 Lattice points on a circle ........... How many lattice points are there on the circlex^2 ...

112 Lattice points Appendix: The floor and the ceiling Thefloorof a real numberxis the greatest integer not exceedingx:^1 x:= ...