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...
- Sets may be thick, thin and normal
- No two integers are equidistant from the square root of 2
- There are trisectable angles that are not constructible
- You can't add apples and oranges but you can add their shapes
- Sometimes in order to add one has to take the difference
- In the sequence of all integers, there are arbitrary long runs with no primes
- For every object there is a distance at which it looks its best
- As in the art, there are imaginary and surreal numbers
- As in the art, there are imaginary and surreal numbers
- Much as with people, there are irrational, perfect, complex numbers
- As in philosophy, there are transcendental numbers
- One is morally obligated not to do anything impossible
- There are really impossible things
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- Falsity implies anything
- The word 'fraction' derives from the Latin fractio - to break. However, there are continuous fractions
- A clock never showing right time might be preferable to the one showing right time twice a day
- There are many things that can be added
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- At any given time in New York there live at least two people with the same number of hairs
Last updated: July 6, 2018 What has changed? |
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