# Interactive Mathematics Miscellany and Puzzles

Raymond Smullyan, a Mathematician, Philosopher and author of several outstanding books of logical puzzles, tells, in one of his books, a revealing story. A friend invited him for dinner. He told Smullyan that his teenage son was crazy about Smullyan's books and could not wait to meet him. The friend warned Smullyan not to mention that he is a Mathematician and that Logic is a part of Mathematics because the young fellow hated Mathematics.

#### Having told this story, would it be wise to announce up front what this site is about? Perhaps against a better judgement, I've put together a manifesto that aims to explain the purpose of this site.

## By the way, did you know that...

- Demographic tests show that the person least likely to buy Wired magazine is an American schoolteacher
- cos(36) = (1 + sqrt(5))/4
- Simple quadrilaterals tessellate the plane
- Sets may be thick, thin and normal
- C - C = [-1, 1]
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- Among all shapes with the same area circle has the shortest perimeter
- The Length of the diagonal of the unit square equals the square root of 2
- There are three plane regions that share exactly the same boundary
- Sets may be thick, thin and normal
- Sphere has two sides. However, there are one-sided surfaces
- To get cafe au lait one should carry coffee to milk and not milk to coffee
- There are things distant yet near. There are others that are near yet distant
- 12+3-4+5+67+8+9=100 and there exists at least one other representation of 100 with 9 digits in the right order and math operations in between
- Simple Quadrilaterals Tessellate the Plane
- As in the art, there are imaginary and surreal numbers
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- Irrational number to an irrational power may be rational
- One is morally obligated to do everything impossible

Last updated:
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July 6, 2018 |

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