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 Dec14 comment Is $(0,0)$ a solution to $x^y-y^x=0$? This answer and comment by Ross most closely represent my expected answer. Namely, it is a matter of how we are interpreting $x^y$. Dec14 accepted Is $(0,0)$ a solution to $x^y-y^x=0$? Dec14 revised Is $(0,0)$ a solution to $x^y-y^x=0$? edited tags Dec14 comment Is $(0,0)$ a solution to $x^y-y^x=0$? @StefanSmith The question stemmed from a discussion of whether the graph of $x^y=y^x$ contains the origin. Knowing the process of showing $0^0$ is an indeterminate form, I hoped to follow a similar procedure using paths/limits. Dec14 awarded Editor Dec14 revised Is $(0,0)$ a solution to $x^y-y^x=0$? deleted 13 characters in body; edited title Dec14 asked Is $(0,0)$ a solution to $x^y-y^x=0$? Oct19 comment Centroids of triangle Better yet, do you see that $G_1G_2G_3$ and $G_4G_5G_6$ are equilateral? Oct19 comment Centroids of triangle Can you solve the case when ABC is equilateral? Oct19 answered Centroids of triangle Oct8 awarded Supporter Sep30 comment Permutations of n beads on a string. Oops. Just logged back in and noted that I answered the wrong question. Rotations aside, the reflective symmetries part still applies and hence provides the desired solution $n!/2$ for the $n$-bead case. Sep28 awarded Teacher Sep28 answered Permutations of n beads on a string. Sep14 comment Area of twisted torus That is the exact explanation I was hoping for. It is counterintuitive to me that twisting the torus can increase the length of a fixed band, but twisting a region does not change its area. I guess this is similar to the idea that a shear transformation on a rectangle preserves the area. Thank-you for an excellent explanation. Sep14 awarded Scholar Sep14 accepted Area of twisted torus Sep14 awarded Student Sep14 asked Area of twisted torus