# 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 three plane regions that share exactly the same boundary
- Curves of infinite length may enclose finite areas
- 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
- Every composite number is the product of some factors and also the sum of the same numbers
- A continuous linear function must have the form f(x)=ax. Discontinuous linear functions look dreadful
- 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
- In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
- The Length of the diagonal of the unit square equals the square root of 2
- Simple quadrilaterals tessellate the plane
- Irrational number to an irrational power may be rational
- No two integers are equidistant from the square root of 2
- There are just five regular polyhedra
- Demographic tests show that the person least likely to buy Wired magazine is an American schoolteacher
- Sphere has two sides. However, there are one-sided surfaces
- There are trisectable angles that are not constructible
- A straight line has dimension 1, a plane 2. Fractals have mostly fractional dimension
- There is a simple solution to the affirmative action problem
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- In the sequence of all integers, there are arbitrary long runs with no primes

Last updated:
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July 25, 2017 |

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