Saturday, April 24, 2010

Short And Bitter

Blog post # 65:

Yikes. I'm posting a new blog post just a day after the last time I posted one. (I'm going to freak out now.)

Two pictures, both made today.

Rotation Formed From Stillness

Dodecagonal Arrangement

Note: These pictures are both VERY MUCH plagiarized. The first I like, but only because it looks like someone else's art I saw years ago.

The second picture isn't even art, officially. It was made so as to illustrate a point.


The point: In my last blog post, I wrote that the two pairs of regular polygons (square/pentagon) and (triangle/octagon) were the only pairs of regular polygons of number of sides m and n, where they could be arranged in alternating fashion so as to form a big regular polygon in the center with exactly {m times n} sides.

What I should have said is that these are the only pairs of types of polygons if the smaller polygons are arranged along the OUTSIDE of the perimeter of the one large polygon in the center. If you arrange the smaller polygons along the INSIDE of the perimeter, then we could have polygons of m = 3 sides (triangles) alternating with polygons of n = 4 sides (squares), forming a polygon of {m times n} = 12 sides (dodecagon), as seen in the second picture above.

I hope this news isn't too upsetting to any of you.


One last thing. Remember that the full potential definitions for my latest poll can be found in the last blog post ("Polygonal", Blog post # 64).

No one has voted yet. Please get on it, people!



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