Why there is no general equation to denote polygons?We have algebraic equations for conic sections, like circle, ellipses and parabolas, but why there is no such result for polygons like triangle or square or hexagon? Is it impossible to represent polygons as algebraic identities?

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Prezrenjes0n · Accepted Answer

Step 1For the square with corners (1,0), (0,1), (-1,0), and (0,-1), we have the equation       |    x      |    +      |    y      |    =  1. From this we can get the general equation of a square. If one does not want to use absolute values, we can replace |w| by             w      2      .Step 2One can with some effort get equations for regular n-gons. They are not particularly useful.

We have algebraic equations for conic sections, like circle, ellipses and parabolas, but why there is no such result for polygons like triangle or square or hexagon? Is it impossible to represent polygons as algebraic identities?

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