# 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 really impossible things
- One is morally obligated not to do anything impossible
- In the sequence of all integers, there are arbitrary long runs with no primes
- Every infinite set contains uncountably many nested subsets
- cos(36) = (1 + sqrt(5))/4
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- How to write an equation of the union of two sets
- Much as with people, there are irrational, perfect, complex numbers
- Simple Quadrilaterals Tessellate the Plane
- There is a simple solution to the affirmative action problem
- One can drill holes that are almost square
- Almost every integer has the digit 3 in it
- C - C = [-1, 1]
- Much as with people, there are irrational, perfect, complex numbers
- There is something the dead eat but if the living eat it, they die
- Complex number to a complex power may be real
- There is order in chaos
- How to write an equation of the union of two sets
- 0!=1
- Everything you can do with a ruler and a compass you can do with the compass alone

Last updated:
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April 19, 2018 |

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