# 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
- As in the art, there are imaginary and surreal numbers
- Irrational number to an irrational power may be rational
- One is morally obligated not to do anything impossible
- Every composite number is the product of some factors and also the sum of the same numbers
- How to write an equation of the union of two sets
- A continuous function may grow considerably virtually without changing
- One is morally obligated to do everything impossible
- There are curves that fill a plane without holes
- A clock never showing right time might be preferable to the one showing right time twice a day
- In some circumstances, an index may have a content of its own
- cos(36) = (1 + sqrt(5))/4
- Among all shapes with the same area circle has the shortest perimeter
- Almost every integer has the digit 3 in it
- Complex number to a complex power may be real
- Simple quadrilaterals tessellate the plane
- There are three plane regions that share exactly the same boundary
- Irrational number to an irrational power may be rational
- 12+3-4+5+67+8+9=100 and there exists at least one other representation of 100 with 9 digits in the right order and math operations in between
- As in philosophy, there are transcendental numbers

Last updated:
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January 20, 2018 |

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