# 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...

- The Length of the diagonal of the unit square equals the square root of 2
- There are curves that fill a plane without holes
- There are really impossible things
- Simple Quadrilaterals Tessellate the Plane
- One is morally obligated to do everything impossible
- Sometimes in order to add one has to take the difference
- There are three plane regions that share exactly the same boundary
- Sometimes in order to add one has to take the difference
- For every object there is a distance at which it looks its best
- As in philosophy, there are transcendental numbers
- Sphere has two sides. However, there are one-sided surfaces
- You can't add apples and oranges but you can add their shapes
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- 1/3 + 1/4 = 7/12
- In some circumstances, an index may have a content of its own
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- There are things distant yet near. There are others that are near yet distant
- In some circumstances index equals the content
- Bisector of an imaginary angle may be real
- There are many things that can be multiplied

Last updated:
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July 6, 2018 |

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