# 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...

- Some numbers are square, yet others are triangular
- Every infinite set contains uncountably many nested subsets
- You can't add apples and oranges but you can add their shapes
- The word 'fraction' derives from the Latin fractio - to break. However, there are continuous fractions
- Bisector of an imaginary angle may be real
- Sometimes in order to add one has to take the difference
- There is something the dead eat but if the living eat it, they die
- There are three plane regions that share exactly the same boundary
- Simple Quadrilaterals Tessellate the Plane
- A straight line has dimension 1, a plane 2. Fractals have mostly fractional dimension
- Simple Quadrilaterals Tessellate the Plane
- There is order in chaos
- In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
- Everything you can do with a ruler and a compass you can do with the compass alone
- Altitudes have ears, foot, stem, and root
- There exist triangular numbers that are also square
- There is a simple solution to the affirmative action problem
- Simple quadrilaterals tessellate the plane
- A clock never showing right time might be preferable to the one showing right time twice a day
- There are three plane regions that share exactly the same boundary

Last updated:
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July 6, 2018 |

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