According to similar triangles's theorem? It is easy to prove that the line segment is still a line segment after each zoom. The included angle with the coordinate axis is constant. That is, the slope is constant. But the starting point coordinates and length of the line segment will change.

Scaling of line segments centered on the origin. All scaling results fall on the vertex of the origin. In the light area surrounded by straight lines from the origin to both ends of the line segment.

And constantly change the center to scale the results. Is it possible for the starting point of a line segment to fall at any point in the coordinate system? The length of the line segment is not necessarily the same as the result of scaling the origin. The only thing in common is that the slope of the line segment remains the same.

So? This question should be reduced to:

The coordinate relationship between a point scaled n times by different centers and a point scaled n times by the origin.

Let the coordinates of the starting point of this line segment be (X0, Y0). The coordinates of the end point are (X0',? y0’)，？ Is (Y0'-Y0)/(X0'-X0) a constant k? (slope)?

The center of n scaling is:? (e0，f0)，？ (e 1，？ f 1)，？ ...？ ,? (well,? fn)

N The scaling factor is:? d0，？ d 1，？ d2，？ ...？ ,? dn d=0. 1？ Or? -0. 1

A brief proof of the equation.