# 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...

- cos(36) = (1 + sqrt(5))/4
- 1/3 + 1/4 = 7/12
- A continuous linear function must have the form f(x)=ax. Discontinuous linear functions look dreadful
- Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex
- Falsity implies anything
- At any given time in New York there live at least two people with the same number of hairs
- Much as with people, there are irrational, perfect, complex numbers
- Bisector of an imaginary angle may be real
- A straight line has dimension 1, a plane 2. Fractals have mostly fractional dimension
- Complex number to a complex power may be real
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- There are many things that can be added
- Complex number to a complex power may be real
- For every object there is a distance at which it looks its best
- Bisector of an imaginary angle may be real
- A continuous function may grow considerably virtually without changing
- Among all shapes with the same perimeter a circle has the largest area
- Curves of infinite length may enclose finite areas
- Sometimes in order to add one has to take the difference
- Almost every integer has the digit 3 in it

Last updated:
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July 6, 2018 |

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