# 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 really impossible things
- How to write an equation of the union of two sets
- There is order in chaos
- There are really impossible things
- Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex
- Falsity implies anything
- A clock never showing right time might be preferable to the one showing right time twice a day
- Bisector of an imaginary angle may be real
- Altitudes have ears, foot, stem, and root
- 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
- A straight line has dimension 1, a plane 2. Fractals have mostly fractional dimension
- 0!=1
- Complex number to a complex power may be real
- Sometimes in order to add one has to take the difference
- For every object there is a distance at which it looks its best
- There are really impossible things
- Sets may be thick, thin and normal
- Sets may be thick, thin and normal
- In some circumstances, an index may have a content of its own
- At any given time in New York there live at least two people with the same number of hairs

Last updated:
What has changed?
July 6, 2018 |

|Contact| |Front page| |Index|

Copyright © 1996-2017 Alexander Bogomolny