## Using the Sawtooth Wave to Create Some Beautiful Images

When we want to create a beautiful image by drawing line segments or circles, we can use

**3,000 Line Segments (III)**

This image shows 3,000 line segments. For each k=1,2,3,…,3000 the endpoints of the k-th line segment are:

(S(20k/3000)cos(2πk/3000), S((18k/3000)+(1/2))(sin(2πk/3000))^3)

and

(S(16k/3000)(cos(2πk/3000))^3, S((14k/3000)+(1/2))sin(2πk/3000)).

**7,000 Circles (II)**

This image shows 7,000 circles. For each k=1,2,3,…,7000 the center of the k-th circle is:

(S((14k/7000)+(1/2))sin(10πk/7000), S(14k/7000)cos(10πk/7000))

and the radius of the k-th circle is:

(1/400)+(1/9)(S(14k/7000)cos(50πk/7000))^2.

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