Star Polygons Essay

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They sparkle in the night sky, we see them on our clothing, in drawings and scattered some where in our surroundings. These beautiful shapes are stars, but their beauty isn’t all that’s behind them. These shapes all started with math. They are star polygons, which are evenly spaced vertices that are connected to every xth vertices, and I will explain that further later on. In the following I will present you with the knowledge I have gained about star polygons and the math behind them. Regular star polygons are the most commonly seen star polygons. They are star polygons which progressed from a regular polygon. To create a regular star polygon from a regular polygon you must connect one vertex of a regular n-sided polygon to a non-adjacent vertex, this process must be repeated until the starting vertex is reached once again. For instance to create a pentagram from a pentagon you would connect vertex one to vertex three, vertex three to vertex five, vertex five to vertex two, vertex two to vertex four, and finally vertex four to vertex one, the original starting vertex. Each regular star polygon has its own notation, {n/x}. N (n) represents the number of sides of the original regular polygon, and the number x to be continuously added is larger than one and less than n-1 (1<x<n-1), in more simpler words, number x represents how many vertices you are skipping to create the regular star polygon. This would then make the notation for the example presented above, {5/2}, (pentagon= 5 sides, 2= every 2nd vertex). Here are a few different examples of regular star polygons and their very own notations! {5/2} {7/2} {7/3} {8/3} {9/2} {9/4} (The figures in the first row are all regular star polygons, and the figures in the second column are their related polygons) A pentagram has three interpretations: Regular

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