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y^x = x^y


fafalone

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I tried to graph the function implicitly in Maple, which is a very good maths software and weird things begun to happen.

 

heres the commands.

 

>with(plots);

>implicitplot(x^y=y^x,x=0..10,y=0..10);

 

g1.jpg

 

This is the result. Note the graph looks similar to the one above but its all wavy.

 

Now the strange things happens

 

i try

 

>implicitplot(x^y=y^x,x=0..100,y=0..100);

 

and this is what i get

 

g2.jpg

 

its all gone wrong.

 

IF anyone has maple , can you repeat what i have done and see if u get the same result. cheers

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  • 1 year later...

Oh geez. I only skimmed through the replies looking at a plot but only seen Q1 plot in post ~ #76 ? I see DQW posted it, its cool. I'm particularly interested in similarities between this particular function and the gamma function - since it does have some similar regions as well as curves which could be a little 'massaged' to make alike. What would be the purpose of that? Well maybe no really good purpose but just for a visual satisfaction, but then again so are most interesting functions in math :D

 

 

Sees an angry mob emerging on the horizon.. Booyakasha!

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Defining f as a function of two variables is fine, as you can see from the 3D plot. It's just when you attempt to solve for either of the variables that you have problems. It should be fairly obvious by looking at the plot that you can't re-arrange for x or y, though.

 

But yes, there looks to be a similarity (of sorts) between the gamma function over negative reals and the singularities you can see in the lower right and upper left quadrants. However, the gamma function has singularities at negative integers, and this doesn't seem to follow the same trend.

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Defining f as a function of two variables is fine' date=' as you can see from the 3D plot. It's just when you attempt to solve for either of the variables that you have problems. It should be fairly obvious by looking at the plot that you can't re-arrange for x or y, though.

 

But yes, there looks to be a similarity (of sorts) between the gamma function over negative reals and the singularities you can see in the lower right and upper left quadrants. However, the gamma function has singularities at negative integers, and this doesn't seem to follow the same trend.[/quote']

 

 

My brain Hurts NOW

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