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...
- Curves of infinite length may enclose finite areas
- There are things distant yet near. There are others that are near yet distant
- Much as with people, there are irrational, perfect, complex numbers
- You can't add apples and oranges but you can add their shapes
- Sets may be thick, thin and normal
- In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
- 12+3-4+5+67+8+9=100 and there exists at least one other representation of 100 with 9 digits in the right order and math operations in between
- One can cut a pie into 8 pieces with three movements
- Everything you can do with a ruler and a compass you can do with the compass alone
- No two integers are equidistant from the square root of 2
- Every infinite set contains uncountably many nested subsets
- Among all shapes with the same area circle has the shortest perimeter
- There are trisectable angles that are not constructible
- Among all shapes with the same area circle has the shortest perimeter
- In some circumstances index equals the content
- Sets may be thick, thin and normal
- There are just five regular polyhedra
- 1/3 + 1/4 = 7/12
- You can position 10 defenders of a square castle so that on every side there will be 5 men
- A continuous function may grow considerably virtually without changing
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Last updated: July 6, 2018 What has changed? |
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