# 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...

- Bisector of an imaginary angle may be real
- You are wrong if you think Mathematics is not fun
- How to write an equation of the union of two sets
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- Some numbers are lucky. 13 is one
- There are things distant yet near. There are others that are near yet distant
- Almost every integer has the digit 3 in it
- 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
- The only triangle with rational sides and angles is equilateral.
- In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
- Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex
- Among all shapes with the same area circle has the shortest perimeter
- Some numbers are square, yet others are triangular
- 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
- Sphere has two sides. However, there are one-sided surfaces
- No two integers are equidistant from the square root of 2
- Every infinite set contains uncountably many nested subsets
- cos(36) = (1 + sqrt(5))/4
- You can add apples and oranges
- There is a simple solution to the affirmative action problem

Last updated:
What has changed?
July 6, 2018 |

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