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[Community Question] Linear-algebra: Make shapes with inequality

One of our user asked:

The following set : $$\{(x,y) \in \mathbb{R}^2 \mid x+y \leq 1, x\geq 0, y \geq 0 \}$$ is a triangle. One way to see it is simply that we draw all points under the line of equation $y = 1-x$ with positive coordinates.

My question is :

  • Is it possible with inequalities (just as the one that describe a triangle) to draw some other nice shapes like parallelogram or more generally regular polygons ?

  • Moreover I suspect that there is some linear algebra behind these inequalities. So maybe for example linear algebra can help proving that the above inequality makes a triangle.

Thank you !


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