# 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...

- 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
- Every composite number is the product of some factors and also the sum of the same numbers
- How to write an equation of the union of two sets
- A straight line has dimension 1, a plane 2. Fractals have mostly fractional dimension
- There are just five regular polyhedra
- Bisector of an imaginary angle may be real
- You can't compare two complex numbers
- No two integers are equidistant from the square root of 2
- Complex number to a complex power may be real
- There are just five regular polyhedra
- Sphere has two sides. However, there are one-sided surfaces
- Altitudes have ears, foot, stem, and root
- There is something the dead eat but if the living eat it, they die
- There is something the dead eat but if the living eat it, they die
- There are curves that fill a plane without holes
- cos(36) = (1 + sqrt(5))/4
- You can't add apples and oranges but you can add their shapes
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons

Last updated:
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July 6, 2018 |

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