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Dec
14
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 $x^y$.
Dec
14
accepted Is $(0,0)$ a solution to $x^y-y^x=0$?
Dec
14
revised Is $(0,0)$ a solution to $x^y-y^x=0$?
edited tags
Dec
14
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.
Dec
14
awarded  Editor
Dec
14
revised Is $(0,0)$ a solution to $x^y-y^x=0$?
deleted 13 characters in body; edited title
Dec
14
asked Is $(0,0)$ a solution to $x^y-y^x=0$?
Oct
19
comment Centroids of triangle
Better yet, do you see that $G_1G_2G_3$ and $G_4G_5G_6$ are equilateral?
Oct
19
comment Centroids of triangle
Can you solve the case when ABC is equilateral?
Oct
19
answered Centroids of triangle
Oct
8
awarded  Supporter
Sep
30
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.
Sep
28
awarded  Teacher
Sep
28
answered Permutations of n beads on a string.
Sep
14
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.
Sep
14
awarded  Scholar
Sep
14
accepted Area of twisted torus
Sep
14
awarded  Student
Sep
14
asked Area of twisted torus