# 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...

- Simple Quadrilaterals Tessellate the Plane
- No two integers are equidistant from the square root of 2
- To get cafe au lait one should carry coffee to milk and not milk to coffee
- In some circumstances, an index may have a content of its own
- How to write an equation of the union of two sets
- 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
- The Length of the diagonal of the unit square equals the square root of 2
- One can drill holes that are almost square
- Complex number to a complex power may be real
- Curves of infinite length may enclose finite areas
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- Every infinite set contains uncountably many nested subsets
- The only triangle with rational sides and angles is equilateral.
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- A continuous function may grow considerably virtually without changing
- Bisector of an imaginary angle may be real
- There is something the dead eat but if the living eat it, they die
- There is something the dead eat but if the living eat it, they die
- 0!=1
- There are really impossible things

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

|Contact| |Front page| |Index|

Copyright © 1996-2017 Alexander Bogomolny