# 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 are curves that fill a plane without holes
- There is a simple solution to the affirmative action problem
- How to write an equation of the union of two sets
- There exist triangular numbers that are also square
- You can't add apples and oranges but you can add their shapes
- Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex
- There are really impossible things
- There are many things that can be multiplied
- For every object there is a distance at which it looks its best
- Every composite number is the product of some factors and also the sum of the same numbers
- Irrational number to an irrational power may be rational
- 1/3 + 1/4 = 7/12
- 0!=1
- Among all shapes with the same area circle has the shortest perimeter
- Every composite number is the product of some factors and also the sum of the same numbers
- Every infinite set contains uncountably many nested subsets
- Curves of infinite length may enclose finite areas
- Complex number to a complex power may be real
- 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

Last updated:
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July 6, 2018 |

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