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 Nov 27 comment Is the empty set the only possible set for $A$ such that $A=\{x|x\not\in A\}$? The most understandable answer. :-) Thanks. 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 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. 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? 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. :-) May 7 comment What is the non-piecewise curve that resembles the following roller coaster track? I cannot show my effort to solve this problem. Is it necessary to show it? May 7 comment Functions Question Commutative by accident. Mar 11 comment How to prove that we cannot see more than 3 faces of an opaque solid cube simultaneously? +1. Makes sense! Mar 11 comment How to prove that we cannot see more than 3 faces of an opaque solid cube simultaneously? But you can see 3 faces by focusing on one corner. Feb 10 comment How to prove the number of images of two mirrors inclined at $A$ is $360/A -1$ +1 Short respons: I ask myself to prove it analytically. :-) I will give other comments later as I am teaching right now. :-) thanks. Jan 21 comment How to find the closed solution for the following recursive vector equations? OK. I am waiting for other solutions if any. Jan 21 comment How to find the closed solution for the following recursive vector equations? @heropup's solution in his comment seems to be much more better.