# 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...

- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- There are really impossible things
- Some numbers are lucky. 13 is one
- There exist triangular numbers that are also square
- No two integers are equidistant from the square root of 2
- There are trisectable angles that are not constructible
- There are things distant yet near. There are others that are near yet distant
- There are three plane regions that share exactly the same boundary
- A clock never showing right time might be preferable to the one showing right time twice a day
- Complex number to a complex power may be real
- Much as with people, there are irrational, perfect, complex numbers
- Among all shapes with the same perimeter a circle has the largest area
- Curves of infinite length may enclose finite areas
- Curves of infinite length may enclose finite areas
- Sometimes in order to add one has to take the difference
- Every infinite set contains uncountably many nested subsets
- Bisector of an imaginary angle may be real
- Sometimes in order to add one has to take the difference
- As in the art, there are imaginary and surreal numbers
- Complex number to a complex power may be real

Last updated:
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July 6, 2018 |

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