# 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...

- Curves of infinite length may enclose finite areas
- Much as with people, there are irrational, perfect, complex numbers
- To get cafe au lait one should carry coffee to milk and not milk to coffee
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- How to write an equation of the union of two sets
- You can add apples and oranges
- There exist triangular numbers that are also square
- One is morally obligated not to do anything impossible
- As in philosophy, there are transcendental numbers
- Altitudes have ears, foot, stem, and root
- There is order in chaos
- Every composite number is the product of some factors and also the sum of the same numbers
- There is a simple solution to the affirmative action problem
- Sets may be thick, thin and normal
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- You are wrong if you think Mathematics is not fun
- You can't compare two complex numbers
- Among all shapes with the same area circle has the shortest perimeter
- Sets may be thick, thin and normal

Last updated:
What has changed?
February 23, 2018 |

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