# 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 area circle has the shortest perimeter
- 1/3 + 1/4 = 7/12
- Complex number to a complex power may be real
- No two integers are equidistant from the square root of 2
- In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
- You can add apples and oranges
- Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex
- Everything you can do with a ruler and a compass you can do with the compass alone
- Altitudes have ears, foot, stem, and root
- You can't add apples and oranges but you can add their shapes
- There are many things that can be added
- Among all shapes with the same perimeter a circle has the largest area
- Simple quadrilaterals tessellate the plane
- There are really impossible things
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- Sets may be thick, thin and normal
- There are trisectable angles that are not constructible
- Simple quadrilaterals tessellate the plane
- There exist triangular numbers that are also square

Last updated:
What has changed?
July 6, 2018 |

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