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visits member for 2 years, 5 months
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when someone smiles at me, all I see is an ape bearing its teethe


Jul
12
comment Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$
Does anyone have any ideas? I can't believe this thing is so difficult.
Jul
12
revised Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$
deleted 57 characters in body
Jul
12
revised Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$
added 4 characters in body
Jul
12
revised Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$
added 128 characters in body
Jul
12
asked Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$
Jul
11
comment Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
Ya you're right, I completely @#$%ed this whole problem up
Jul
11
comment Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
Shoot well you're right I don't know what is going on then, this integral is the arc length for $(t,t\sin(\frac{\pi}{t}))$ and according to the book (Do Carmo's Differential Geometry), the inequality should hold. so yah I don't know then
Jul
11
comment Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
I'm just getting a series expansion, how do you get wolfram definite integrator to approximate it?
Jul
11
comment Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
Ok actually it is for $n\geq 1$ so I'm not sure what to think then, what did you use to check the integral?
Jul
11
revised Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
added 45 characters in body
Jul
11
revised Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
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Jul
11
awarded  Teacher
Jul
11
revised Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
added 210 characters in body
Jul
11
revised Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
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Jul
11
asked Help proving that $\frac{2}{n+\frac{1}{2}} \leq \int_{\frac{1}{n+1}}^{\frac{1}{n}}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{1}{t}\cos(\frac{\pi}{t}))^2}dt$
Jul
7
comment If $E$ and $F$ are subfields of a finite field $K$ and $E\cong F$, prove that $E = F$
Oh that's right, a splitting field is the smallest field possible, ok cool thanks. Your conciseness is legendary André, unfortunately us mere mortals sometimes require a bit of redundancy in the answers we receive. (said in jest =])
Jul
7
accepted If $E$ and $F$ are subfields of a finite field $K$ and $E\cong F$, prove that $E = F$
Jul
7
comment If $E$ and $F$ are subfields of a finite field $K$ and $E\cong F$, prove that $E = F$
That result is one of my theorems yes, and Zev's comment answers my question (thank you Zev). But is knowing both contain all the roots of that poly enough without knowing it's separable? Not that it's particularly important, anyways thanks for the help.
Jul
7
comment If $E$ and $F$ are subfields of a finite field $K$ and $E\cong F$, prove that $E = F$
It seems intuitively obvious, but how do we know all the roots of $x^q - x$ are distinct?
Jul
7
revised If $E$ and $F$ are subfields of a finite field $K$ and $E\cong F$, prove that $E = F$
added 42 characters in body