# 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...

- Almost every integer has the digit 3 in it
- Sometimes in order to add one has to take the difference
- There exist triangular numbers that are also square
- There are trisectable angles that are not constructible
- cos(36) = (1 + sqrt(5))/4
- Sets may be thick, thin and normal
- For every object there is a distance at which it looks its best
- Much as with people, there are irrational, perfect, complex numbers
- You can't add apples and oranges but you can add their shapes
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- Simple Quadrilaterals Tessellate the Plane
- The only triangle with rational sides and angles is equilateral.
- There are trisectable angles that are not constructible
- C - C = [-1, 1]
- The Length of the diagonal of the unit square equals the square root of 2
- Almost every integer has the digit 3 in it
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- Some numbers are square, yet others are triangular
- Falsity implies anything
- 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

Last updated:
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January 22, 2018 |

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