Coordinate Geometry Question

T

TUC

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If you have the number of sides of a shape, it's inner degrees, coordinates of two of its corners and the shape is two dimensional; is there a formula for calculating the coordinates of the other vertices?


'Note that the vertices don't need to be next to each other and the shape can be rotated.'
 
Seems like a good exploration. Let's see your first attempts. I think we're talking about a REGULAR polygon; if you know one angle or side, you know them all.
 
I would start with the case where you know two adjacent vertices; in some, but not all, cases that will extend to the general problem.

How to do it depends on your knowledge. I'd probably want to use vectors and rotation matrices, if you have that background; such a method could be turned into a formula of sorts with work. (Actually, it would be a set of formulas.)

Note that the angles can be easily determined from the number of sides, so that doesn't have to be a separate input. Are you familiar with how to do that part?
 
I know in the case of a regular polygon and for ANY two starting sides and it is easy to determine the inner angles of a regular polygon. The formula is easily described in one fashion as 180*(n-2)/n. As I already have a formula for regular polygons, I am wondering for any type of polygon regular or irregular.
If there isn't yet, that would be great as a formula of that magnitude could describe every straight shape " as curves, positions and their areas is in basic calculus."
 
Ever been to Manhatten? Remember how easy it was to follow directions there? How about Boston? Quite the opposite. Manhatten is regular, Boston is not.
 
The more irregular something is, the more information is needed to describe it. If you want a formula for an irregular polygon, you'll have to figure out what inputs you need. There can't possibly be a mere formula (with potentially hundreds of variables?), but there might be an algorithm. But, again, you have to specify the inputs and assumptions.
 
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