# 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...

- You can position 10 defenders of a square castle so that on every side there will be 5 men
- One can drill holes that are almost square
- Everything you can do with a ruler and a compass you can do with the compass alone
- Simple quadrilaterals tessellate the plane
- For every object there is a distance at which it looks its best
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- In some circumstances, an index may have a content of its own
- C - C = [-1, 1]
- Sets may be thick, thin and normal
- One can drill holes that are almost square
- In some circumstances, an index may have a content of its own
- There are three plane regions that share exactly the same boundary
- Altitudes have ears, foot, stem, and root
- A clock never showing right time might be preferable to the one showing right time twice a day
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- One can cut a pie into 8 pieces with three movements
- In some circumstances, an index may have a content of its own
- No two integers are equidistant from the square root of 2
- Some numbers are lucky. 13 is one
- Among all shapes with the same perimeter a circle has the largest area

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

|Contact| |Front page| |Index|

Copyright © 1996-2017 Alexander Bogomolny