# 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...

- Among all shapes with the same perimeter a circle has the largest area
- Almost every integer has the digit 3 in it
- There are three plane regions that share exactly the same boundary
- To get cafe au lait one should carry coffee to milk and not milk to coffee
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- 1/3 + 1/4 = 7/12
- There are curves that fill a plane without holes
- In the sequence of all integers, there are arbitrary long runs with no primes
- One can cut a pie into 8 pieces with three movements
- A continuous linear function must have the form f(x)=ax. Discontinuous linear functions look dreadful
- 1/3 + 1/4 = 7/12
- Everything you can do with a ruler and a compass you can do with the compass alone
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- Complex number to a complex power may be real
- Irrational number to an irrational power may be rational
- A continuous linear function must have the form f(x)=ax. Discontinuous linear functions look dreadful
- The only triangle with rational sides and angles is equilateral.
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- There are trisectable angles that are not constructible
- There exist triangular numbers that are also square

Last updated:
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July 6, 2018 |

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