# 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...

- There are three plane regions that share exactly the same boundary
- There are things distant yet near. There are others that are near yet distant
- There is something the dead eat but if the living eat it, they die
- Complex number to a complex power may be real
- Among all shapes with the same area circle has the shortest perimeter
- You can't add apples and oranges but you can add their shapes
- 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
- No two integers are equidistant from the square root of 2
- A continuous function may grow considerably virtually without changing
- Simple Quadrilaterals Tessellate the Plane
- Irrational number to an irrational power may be rational
- 0!=1
- In some circumstances index equals the content
- Sets may be thick, thin and normal
- How to write an equation of the union of two sets
- Irrational number to an irrational power may be rational
- Simple quadrilaterals tessellate the plane
- There are really impossible things

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September 22, 2017 |

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