# 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 exist triangular numbers that are also square
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- Every infinite set contains uncountably many nested subsets
- A clock never showing right time might be preferable to the one showing right time twice a day
- Falsity implies anything
- Almost every integer has the digit 3 in it
- Everything you can do with a ruler and a compass you can do with the compass alone
- Every infinite set contains uncountably many nested subsets
- Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex
- Altitudes have ears, foot, stem, and root
- There are just five regular polyhedra
- A clock never showing right time might be preferable to the one showing right time twice a day
- One can drill holes that are almost square
- Irrational number to an irrational power may be rational
- A continuous linear function must have the form f(x)=ax. Discontinuous linear functions look dreadful
- There are many things that can be added
- Everything you can do with a ruler and a compass you can do with the compass alone
- For every object there is a distance at which it looks its best
- There are three plane regions that share exactly the same boundary
- Every composite number is the product of some factors and also the sum of the same numbers

Last updated:
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July 6, 2018 |

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