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Can 180 Straight Lines Hide One Curve?
曲線と幾何学

Can 180 Straight Lines Hide One Curve?

翻訳の準備中は英語の原文を表示しています。

作品について

Can 180 straight lines create a curve that none of them actually draws?

For each angle, one endpoint moves along the x-axis and another moves along the y-axis. A straight segment joins them. As 180 segments accumulate, neighboring lines become tangent to the same four-cusped astroid. The curved star appears only as the envelope of the empty gaps.

Artismathic turns equations into visual art—one function at a time.

Music: 'Taking Chances' by The Soundings

#MathArt #Astroid #Geometry

作品を生み出す数式

tk=2πk/180tₖ=2πk/180Ak=(acostk,0),Bk=(0,asintk)Aₖ=(a cos tₖ,0), Bₖ=(0,a sin tₖ)Lk(u)=(1−u)Ak+uBkLₖ(u)=(1-u)Aₖ+uBₖx=acos3t,y=asin3tx=a cos³t, y=a sin³t
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