List of Figures

1.1 Canadian flag

1.2 Penrose triangle

2.1 Pythagorean gnomon

2.2 Home plate

4.1 Zeno’s sphere: stage one

4.2 Zeno’s sphere: stage two

4.3 Zeno’s sphere: stage three

4.4 The stadium

5.1 Shadow block

8.1 Impossible crate

9.1 Lord Dunsany’s chess problem

10.1 Jigsaw people

16.1 Three gears

16.2 Four gears

17.1 Bertrand’s 1/3 solution

17.2 Bertrand’s 1/4 solution

17.3 Bertrand’s 1/2 solution

20.1 Subjective contour

22.1 Listing all the fractions

22.2 Self-mapping of the reals

22.3 The infinite square

22.4 The diagonal diagram