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...
- There are many things that can be multiplied
- Some numbers are square, yet others are triangular
- There is order in chaos
- The only triangle with rational sides and angles is equilateral.
- Much as with people, there are irrational, perfect, complex numbers
- The word 'fraction' derives from the Latin fractio - to break. However, there are continuous fractions
- C - C = [-1, 1]
- There is a simple solution to the affirmative action problem
- The only triangle with rational sides and angles is equilateral.
- Every infinite set contains uncountably many nested subsets
- A continuous function may grow considerably virtually without changing
- You can add apples and oranges
- Two simple polygons of equal area can be dissected into a finite number of congruent polygons
- In some circumstances index equals the content
- There are many things that can be added
- A continuous linear function must have the form f(x)=ax. Discontinuous linear functions look dreadful
- In some circumstances index equals the content
- Irrational number to an irrational power may be rational
- There are really impossible things
- 1/3 + 1/4 = 7/12
Last updated: July 6, 2018 What has changed? |
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