# Fractions, Sam Loyd, and a MArTH Journal

This week we’re rewinding to July 2012 for some fun with the fabulous Farey Fractions—which have been on my mind recently—plus lots more! Bon appetit!

Welcome to this week’s Math Munch!

Check out this awesome graph:

What is it?  It’s a graph of the Farey Fractions, with the denominator of the (simplified) fraction on the vertical axis and the value of the fraction on the horizontal axis, made by mathematician and professor at Wheelock College Debra K. Borkovitz (previously).  Now, I’d never heard of Farey Fractions before I saw this image – but the graph was so cool that I wanted to learn all about them!

So, what are Farey Fractions, you ask?  Debra writes all about them and the cool visual patterns they make in this post.  To make a list of Farey Fractions you first pick a number – say, 5.  Then, you list all of the fractions between 0 and 1 whose denominators are less than or equal to the number you picked.  So, as Debra writes in…

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