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 Aug 19 awarded Popular Question Aug 9 comment How to test whether a set of four points can form a parallelogram We can save the calculation just by calculating the midpoint times 2 to avoid dividing by 2. Aug 9 comment How to test whether a set of four points can form a parallelogram How about the case there are 3 points on a line? Aug 9 accepted How to test whether a set of four points can form a parallelogram Aug 9 comment How to test whether a set of four points can form a parallelogram But all of your three tests may be false even though the given 4 points can be vertices of a parallelogram. Aug 9 comment How to test whether a set of four points can form a parallelogram If $P_1$ is the opposite of $P_3$ then the last two tests are false. So the first test might be either false or true. Aug 9 comment How to test whether a set of four points can form a parallelogram I think we need 4 tests. Your answer needs one more test which is $\vec{P_1P_2}=\vec{P_3P_4}$. Aug 9 comment How to test whether a set of four points can form a parallelogram Please explain why you compared just those vectors. Aug 9 comment How to test whether a set of four points can form a parallelogram @augurar: The given points are randomly chosen from a set of some points. The order is not known. Aug 9 asked How to test whether a set of four points can form a parallelogram Jul 28 revised How to find the intersection points of lines that are normal to two curves? added 182 characters in body Jul 28 asked How to find the intersection points of lines that are normal to two curves? Jul 4 comment Is my theorem correct? $f(x) \leq g(x)$ for $x\geq a$ iff $f'(x) \leq g'(x)$ for $x\geq a$ and $f(a)=g(a)$. what is the name of the well known corollary? Jul 4 comment Is my theorem correct? $f(x) \leq g(x)$ for $x\geq a$ iff $f'(x) \leq g'(x)$ for $x\geq a$ and $f(a)=g(a)$. By assuming the right side is satisfied first and prove that the left is either correct or incorrect. Jul 4 comment Is my theorem correct? $f(x) \leq g(x)$ for $x\geq a$ iff $f'(x) \leq g'(x)$ for $x\geq a$ and $f(a)=g(a)$. Could you prove in both directions? Jul 4 asked Is my theorem correct? $f(x) \leq g(x)$ for $x\geq a$ iff $f'(x) \leq g'(x)$ for $x\geq a$ and $f(a)=g(a)$. Jul 2 awarded Curious May 9 answered What is the non-piecewise curve that resembles the following roller coaster track? May 7 comment What is the non-piecewise curve that resembles the following roller coaster track? @Neil: Any parameter is accepted. May 7 comment What is the non-piecewise curve that resembles the following roller coaster track? @vonbrand: I don't want to use if-then-else construct in my code. :-)