3320hw2 - Math 3320 Problem Set 2 1 1. This problem...

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Unformatted text preview: Math 3320 Problem Set 2 1 1. This problem involves another version of the Farey diagram, or at least the positive part of the diagram, the part consisting of the triangles whose vertices are labeled by fractions p/q with p 0 and q 0. In this variant of the diagram the vertex labeled p/q is placed at the point (q, p) in the plane. (Thus p/q is the slope of the line through the origin and (q, p) .) The edges of the new Farey diagram are straight line segments connecting the pairs of vertices that are connected in the original Farey diagram. Thus for example there is a triangle with vertices ( 1 , ) , ( , 1 ) , and ( 1 , 1 ) corresponding to the big triangle in the upper half of the circular Farey diagram. What you are asked to do in this problem is just to draw the portion of the new Farey diagram consisting of all the triangles whose vertices (q, p) satisfy 0 q 5 and p 5. Note that since fractions p/q labeling vertices are always in lowest terms, the points (q, p)...
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3320hw2 - Math 3320 Problem Set 2 1 1. This problem...

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