## These Beautiful Images Are Created By Drawing Line Segments

The goal is to create many beautiful symmetrical images by drawing line segments. It is amazing for me to see very beautiful geometric shapes that are defined by some simple mathematical formulas. In order to create a beautiful image by this method, I define a family of line segments by using trigonometric functions. Sine and cosine are very useful mathematical functions to introduce beautiful drawings. Also, one powerful way to increase the beauty of such images is to choose an appropriate color for each of their line segments. I have created the following images by some computer programs. In fact, these are some mathematical objects, but also they can be considered as artworks. At the end of this post you can see the mathematical description of “5,000 Line Segments.” Please note that when we say “this image shows 5,000 line segments,” the 5,000 line segments are not necessarily pairwise distinct.

7,000 Line Segments (I)

7,000 Line Segments (II)

7,000 Line Segments (III)

7,000 Line Segments (IV)

8,000 Line Segments (I)

8,000 Line Segments (II)

8,000 Line Segments (III)

8,000 Line Segments (IV)

8,000 Line Segments (V)

5,000 Line Segments

This image shows 5,000 line segments. For each k=1,2,3,…,5000 the endpoints of the k-th line segment are:

(sin(56πk/5000)cos(6πk/5000), cos(54πk/5000)sin(6πk/5000))

and

(sin(52πk/5000)cos(6πk/5000), cos(50πk/5000)sin(6πk/5000)).

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