[alogo] Nested Polygons

The following set of nested polygons is constructed using the tool [User-Defined\N-fold Scheme-Socket _ _ ].
1) Start with the scheme included in frame b.
2) Make a copy of the scheme b -- > b'.
3) Write a positive integer somewhere (15)
4) Select the tool [User-Defined\N-fold Scheme-Socket _ _ ]
5) 5 clicks are needed. First click on the number (15)
6) holding the CTRL down click on the number object of b', then on the number object of b
7) click on polygon p', then click on polygon p
That's all. To animate the image, select the number-object a, and while holding down the F2 key
press the up- or/and down- arrows on the (right) keyboard. F2-pressing causes a slowere variation of the number object.

[0_0] [0_1] [0_2] [0_3]


Details on the construction of scheme b.

1) Draw lines extending the sides of p (all in the same orientation clockwise)
2) Select the [Points2\Number on Line _ _ ] tool
3) Click alternatively, on the extension lines and on the number object
4) This creates the points on the (extensions of the) sides of p
5) Fit a polygon on the preceding points. This defines q
6) Hide the extension-lines (Look in the [Hidden Objects] menu (lots of hidden lines))

By the way, there is here an interesting fact. The nested polygons converge to a polygon that has equal sides and is central symmetric (if it has even number of sides), whatever the original polygon is.

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