## Weird Geometric Construction

For the discussion of math. Duh.

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Loganfs
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### Weird Geometric Construction

I was messing around in Geometer's Sketchpad and found a construction, but I can't figure out what it is. Any ideas?

That is connecting the midpoints of the outer polygon, then connecting the midpoints of the midpoints, etc. It seems to "regularize," but I can't see exactly what's happening or where it will stop.

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Every two iterations, you're essentially moving each vertex to the average point between the midpoints on either side of it (think vectors). If you instead move each vertex to the average of the point on either side (or all adjacent points, in a 3d polyhedron), you get an operation I've seen in Maya called, drumroll please, Average Vertices. It has the tendency to smooth a figure and decrease the volume, although for some convex shapes, the volume can increase. If you keep iterating that, they will converge to a point.
3.14159265... wrote:What about quantization? we DO live in a integer world?

crp wrote:oh, i thought you meant the entire funtion was f(n) = (-1)^n
i's like girls u crazy

The LuigiManiac
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Trippy. What version of Geometer's Sketchpad did you use? Or is there only the one really old version?
Spoiler:
THE CAKE IS A 3.141592653589...!