engleski

On affine images of regular pentagons and pentagrams

we explore pentagons that are affine images of the regular pentagon and the regular pentagram. We obtain their characterizations in terms of two mild forms of regularity that deal with the notions of medians for a pentagon and the natural requirement that they are concurrent. Using these characterizations we show that there are various values involving the square root of 5 (thus related to the golden section) for which a careful selection of division points on appropriate segments determined by any pentagon will result in a pentagon that is the affine image of either a regular pentagon or a regular pentagram.

pentagon; regular pentagon; regular pentagram; affine image; ratio; golden section; ruler-and-compass construction; ellipse

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