Farey Fraction Visual Patterns

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The Farey Sequence, $$F_{n}$$ is the list of all simplified fractions between $$\dfrac{0}{1}$$ and $$\dfrac{1}{1}$$ with denominator less than or equal to $$n$$. For example,   $$\large F_{5}=\dfrac{0}{1},\dfrac{1}{5},\dfrac{1}{4},\dfrac{1}{3},\dfrac{2}{5},\dfrac{1}{2},\dfrac{3}{5},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5},\dfrac{1}{1}$$

The Handshake Problem

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The handshake problem is an old chestnut — if everyone in the room shook hands with everyone else, how many handshakes would there be? Then generalize. What I have to add to teaching the problem is a handout (doc version, … Read More