Concept explainers
Farey fractions. Let F be the collection of all rational numbers between 0 and 1 (we write 0 as 0n/1 and 1 as 1/1) whose numerators and denominators do not exceed n. So, for example,
Fn is called the nth Farey fraction. List F4, F5, F6, F7, and F8. Make a large number line segment between 0 and 1 and write in the Farey fractions. How can you generate F8 using F7? Generalize your observations and describe how to generate Fn. (Hint: Try adding fractions a wrong way.)
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The Heart of Mathematics: An Invitation to Effective Thinking
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