# 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
- Sets may be thick, thin and normal
- Curves of infinite length may enclose finite areas
- Every composite number is the product of some factors and also the sum of the same numbers
- Bisector of an imaginary angle may be real
- Altitudes have ears, foot, stem, and root
- Complex number to a complex power may be real
- One can cut a pie into 8 pieces with three movements
- In some circumstances index equals the content
- A continuous linear function must have the form f(x)=ax. Discontinuous linear functions look dreadful
- Altitudes have ears, foot, stem, and root
- There are really impossible things
- Every infinite set contains uncountably many nested subsets
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- There are trisectable angles that are not constructible
- As in the art, there are imaginary and surreal numbers
- 1/3 + 1/4 = 7/12
- 0!=1
- 0!=1
- Everything you can do with a ruler and a compass you can do with the compass alone

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

|Contact| |Front page| |Index|

Copyright © 1996-2017 Alexander Bogomolny